LMFDB - Embedded newform 483.2.i.h.415.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(277,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("483.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.i (of order $3$, degree $2$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{19} + 22 x^{18} - 43 x^{17} + 245 x^{16} - 416 x^{15} + 1707 x^{14} - 2021 x^{13} + \cdots + 4 $ x^20 - 3x^19 + 22x^18 - 43x^17 + 245x^16 - 416x^15 + 1707x^14 - 2021x^13 + 7135x^12 - 6640x^11 + 20315x^10 - 10565x^9 + 29358x^8 - 9009x^7 + 30661x^6 - 4026x^5 + 15786x^4 - 84x^3 + 5800x^2 + 152*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			415.3
Root			$1.13751 + 1.97023i$ of defining polynomial
Character	$\chi$	$=$	483.415
Dual form			483.2.i.h.277.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.13751 + 1.97023i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.58786 - 2.75026i) q^{4} +(0.619347 - 1.07274i) q^{5} -2.27502 q^{6} +(1.84753 - 1.89384i) q^{7} +2.67481 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.13751 + 1.97023i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.58786 - 2.75026i) q^{4} +(0.619347 - 1.07274i) q^{5} -2.27502 q^{6} +(1.84753 - 1.89384i) q^{7} +2.67481 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.40903 + 2.44051i) q^{10} +(-3.06335 - 5.30587i) q^{11} +(1.58786 - 2.75026i) q^{12} +0.910400 q^{13} +(1.62971 + 5.79432i) q^{14} +1.23869 q^{15} +(0.133103 - 0.230540i) q^{16} +(-2.45436 - 4.25108i) q^{17} +(-1.13751 - 1.97023i) q^{18} +(3.45185 - 5.97878i) q^{19} -3.93376 q^{20} +(2.56388 + 0.653086i) q^{21} +13.9384 q^{22} +(-0.500000 + 0.866025i) q^{23} +(1.33740 + 2.31645i) q^{24} +(1.73282 + 3.00133i) q^{25} +(-1.03559 + 1.79370i) q^{26} -1.00000 q^{27} +(-8.14219 - 2.07403i) q^{28} +3.36004 q^{29} +(-1.40903 + 2.44051i) q^{30} +(-2.71868 - 4.70889i) q^{31} +(2.97762 + 5.15739i) q^{32} +(3.06335 - 5.30587i) q^{33} +11.1675 q^{34} +(-0.887339 - 3.15486i) q^{35} +3.17573 q^{36} +(-3.27333 + 5.66957i) q^{37} +(7.85304 + 13.6019i) q^{38} +(0.455200 + 0.788430i) q^{39} +(1.65663 - 2.86938i) q^{40} -2.52207 q^{41} +(-4.20317 + 4.30853i) q^{42} -0.231369 q^{43} +(-9.72835 + 16.8500i) q^{44} +(0.619347 + 1.07274i) q^{45} +(-1.13751 - 1.97023i) q^{46} +(-6.67889 + 11.5682i) q^{47} +0.266205 q^{48} +(-0.173272 - 6.99786i) q^{49} -7.88440 q^{50} +(2.45436 - 4.25108i) q^{51} +(-1.44559 - 2.50384i) q^{52} +(-2.11340 - 3.66052i) q^{53} +(1.13751 - 1.97023i) q^{54} -7.58909 q^{55} +(4.94179 - 5.06567i) q^{56} +6.90370 q^{57} +(-3.82209 + 6.62005i) q^{58} +(0.377100 + 0.653157i) q^{59} +(-1.96688 - 3.40673i) q^{60} +(-1.78832 + 3.09747i) q^{61} +12.3701 q^{62} +(0.716350 + 2.54693i) q^{63} -13.0159 q^{64} +(0.563853 - 0.976623i) q^{65} +(6.96918 + 12.0710i) q^{66} +(2.24703 + 3.89197i) q^{67} +(-7.79440 + 13.5003i) q^{68} -1.00000 q^{69} +(7.22516 + 1.84043i) q^{70} +15.8575 q^{71} +(-1.33740 + 2.31645i) q^{72} +(2.13888 + 3.70465i) q^{73} +(-7.44689 - 12.8984i) q^{74} +(-1.73282 + 3.00133i) q^{75} -21.9243 q^{76} +(-15.7081 - 4.00126i) q^{77} -2.07118 q^{78} +(0.111008 - 0.192271i) q^{79} +(-0.164873 - 0.285569i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.86889 - 4.96906i) q^{82} +15.5197 q^{83} +(-2.27493 - 8.08835i) q^{84} -6.08041 q^{85} +(0.263184 - 0.455849i) q^{86} +(1.68002 + 2.90988i) q^{87} +(-8.19386 - 14.1922i) q^{88} +(-0.279682 + 0.484423i) q^{89} -2.81806 q^{90} +(1.68199 - 1.72415i) q^{91} +3.17573 q^{92} +(2.71868 - 4.70889i) q^{93} +(-15.1946 - 26.3179i) q^{94} +(-4.27579 - 7.40588i) q^{95} +(-2.97762 + 5.15739i) q^{96} +17.6476 q^{97} +(13.9845 + 7.61875i) q^{98} +6.12669 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 3 q^{2} + 10 q^{3} - 15 q^{4} + 5 q^{5} - 6 q^{6} + 18 q^{8} - 10 q^{9}+O(q^{10}) $ 20 * q - 3 * q^2 + 10 * q^3 - 15 * q^4 + 5 * q^5 - 6 * q^6 + 18 * q^8 - 10 * q^9	\( 20 q - 3 q^{2} + 10 q^{3} - 15 q^{4} + 5 q^{5} - 6 q^{6} + 18 q^{8} - 10 q^{9} - 11 q^{10} - 8 q^{11} + 15 q^{12} + 11 q^{14} + 10 q^{15} - 37 q^{16} + 11 q^{17} - 3 q^{18} - q^{19} - 30 q^{20} + 12 q^{22} - 10 q^{23} + 9 q^{24} - 21 q^{25} - q^{26} - 20 q^{27} + 44 q^{28} + 44 q^{29} + 11 q^{30} + 3 q^{31} - 11 q^{32} + 8 q^{33} - 6 q^{34} - 9 q^{35} + 30 q^{36} + 3 q^{37} - 16 q^{38} - 39 q^{40} - 52 q^{41} + 7 q^{42} + 54 q^{43} - 16 q^{44} + 5 q^{45} - 3 q^{46} - 11 q^{47} - 74 q^{48} + 22 q^{49} + 4 q^{50} - 11 q^{51} - 29 q^{52} - 5 q^{53} + 3 q^{54} - 36 q^{55} + 43 q^{56} - 2 q^{57} - 16 q^{58} + 10 q^{59} - 15 q^{60} - 22 q^{61} - 64 q^{62} + 138 q^{64} + 11 q^{65} + 6 q^{66} + 2 q^{67} + 21 q^{68} - 20 q^{69} + 84 q^{70} + 54 q^{71} - 9 q^{72} + 8 q^{73} - 14 q^{74} + 21 q^{75} - 44 q^{76} + 8 q^{77} - 2 q^{78} - 21 q^{79} + 53 q^{80} - 10 q^{81} - 36 q^{82} - 24 q^{83} + 25 q^{84} + 46 q^{85} - 18 q^{86} + 22 q^{87} + 10 q^{88} - 6 q^{89} + 22 q^{90} - 62 q^{91} + 30 q^{92} - 3 q^{93} - 35 q^{94} - 44 q^{95} + 11 q^{96} + 12 q^{97} + 2 q^{98} + 16 q^{99}+O(q^{100}) \) 20 * q - 3 * q^2 + 10 * q^3 - 15 * q^4 + 5 * q^5 - 6 * q^6 + 18 * q^8 - 10 * q^9 - 11 * q^10 - 8 * q^11 + 15 * q^12 + 11 * q^14 + 10 * q^15 - 37 * q^16 + 11 * q^17 - 3 * q^18 - q^19 - 30 * q^20 + 12 * q^22 - 10 * q^23 + 9 * q^24 - 21 * q^25 - q^26 - 20 * q^27 + 44 * q^28 + 44 * q^29 + 11 * q^30 + 3 * q^31 - 11 * q^32 + 8 * q^33 - 6 * q^34 - 9 * q^35 + 30 * q^36 + 3 * q^37 - 16 * q^38 - 39 * q^40 - 52 * q^41 + 7 * q^42 + 54 * q^43 - 16 * q^44 + 5 * q^45 - 3 * q^46 - 11 * q^47 - 74 * q^48 + 22 * q^49 + 4 * q^50 - 11 * q^51 - 29 * q^52 - 5 * q^53 + 3 * q^54 - 36 * q^55 + 43 * q^56 - 2 * q^57 - 16 * q^58 + 10 * q^59 - 15 * q^60 - 22 * q^61 - 64 * q^62 + 138 * q^64 + 11 * q^65 + 6 * q^66 + 2 * q^67 + 21 * q^68 - 20 * q^69 + 84 * q^70 + 54 * q^71 - 9 * q^72 + 8 * q^73 - 14 * q^74 + 21 * q^75 - 44 * q^76 + 8 * q^77 - 2 * q^78 - 21 * q^79 + 53 * q^80 - 10 * q^81 - 36 * q^82 - 24 * q^83 + 25 * q^84 + 46 * q^85 - 18 * q^86 + 22 * q^87 + 10 * q^88 - 6 * q^89 + 22 * q^90 - 62 * q^91 + 30 * q^92 - 3 * q^93 - 35 * q^94 - 44 * q^95 + 11 * q^96 + 12 * q^97 + 2 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−1.13751	+	1.97023i	−0.804342	+	1.39316i	0.112392	+	0.993664i	$0.464149\pi$
$2$	−1.13751	+	1.97023i	−0.804342	+	1.39316i	−0.916734	+	0.399497i	$0.869185\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−1.58786	−	2.75026i	−0.793932	−	1.37513i
$5$	0.619347	−	1.07274i	0.276980	−	0.479744i	−0.693652	−	0.720310i	$-0.744000\pi$
$5$	0.619347	−	1.07274i	0.276980	−	0.479744i	0.970633	+	0.240566i	$0.0773330\pi$
$6$	−2.27502			−0.928774
$7$	1.84753	−	1.89384i	0.698300	−	0.715805i
$7$	1.84753	−	1.89384i	0.698300	−	0.715805i
$8$	2.67481			0.945688
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.40903	+	2.44051i	0.445574	+	0.771757i
$11$	−3.06335	−	5.30587i	−0.923633	−	1.59978i	−0.793745	−	0.608251i	$-0.791871\pi$
$11$	−3.06335	−	5.30587i	−0.923633	−	1.59978i	−0.129889	−	0.991529i	$-0.541462\pi$
$12$	1.58786	−	2.75026i	0.458377	−	0.793932i
$13$	0.910400			0.252500			0.126250	−	0.991998i	$-0.459706\pi$
$13$	0.910400			0.252500			0.126250	+	0.991998i	$0.459706\pi$
$14$	1.62971	+	5.79432i	0.435559	+	1.54860i
$15$	1.23869			0.319829
$16$	0.133103	−	0.230540i	0.0332756	−	0.0576351i
$17$	−2.45436	−	4.25108i	−0.595271	−	1.03104i	−0.993509	−	0.113757i	$-0.963711\pi$
$17$	−2.45436	−	4.25108i	−0.595271	−	1.03104i	0.398238	−	0.917282i	$-0.369622\pi$
$18$	−1.13751	−	1.97023i	−0.268114	−	0.464387i
$19$	3.45185	−	5.97878i	0.791909	−	1.37163i	−0.132875	−	0.991133i	$-0.542421\pi$
$19$	3.45185	−	5.97878i	0.791909	−	1.37163i	0.924784	−	0.380493i	$-0.124246\pi$
$20$	−3.93376			−0.879614
$21$	2.56388	+	0.653086i	0.559484	+	0.142515i
$22$	13.9384			2.97167
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i
$24$	1.33740	+	2.31645i	0.272997	+	0.472844i
$25$	1.73282	+	3.00133i	0.346564	+	0.600266i
$26$	−1.03559	+	1.79370i	−0.203096	+	0.351773i
$27$	−1.00000			−0.192450
$28$	−8.14219	−	2.07403i	−1.53873	−	0.391954i
$29$	3.36004			0.623944			0.311972	−	0.950091i	$-0.399010\pi$
$29$	3.36004			0.623944			0.311972	+	0.950091i	$0.399010\pi$
$30$	−1.40903	+	2.44051i	−0.257252	+	0.445574i
$31$	−2.71868	−	4.70889i	−0.488289	−	0.845741i	0.511621	−	0.859211i	$-0.329045\pi$
$31$	−2.71868	−	4.70889i	−0.488289	−	0.845741i	−0.999909	+	0.0134707i	$0.995712\pi$
$32$	2.97762	+	5.15739i	0.526374	+	0.911706i
$33$	3.06335	−	5.30587i	0.533260	−	0.923633i
$34$	11.1675			1.91521
$35$	−0.887339	−	3.15486i	−0.149988	−	0.533269i
$36$	3.17573			0.529288
$37$	−3.27333	+	5.66957i	−0.538132	+	0.932071i	0.460873	+	0.887466i	$0.347536\pi$
$37$	−3.27333	+	5.66957i	−0.538132	+	0.932071i	−0.999005	+	0.0446052i	$0.985797\pi$
$38$	7.85304	+	13.6019i	1.27393	+	2.20651i
$39$	0.455200	+	0.788430i	0.0728903	+	0.126250i
$40$	1.65663	−	2.86938i	0.261937	−	0.453688i
$41$	−2.52207			−0.393882			−0.196941	−	0.980415i	$-0.563101\pi$
$41$	−2.52207			−0.393882			−0.196941	+	0.980415i	$0.563101\pi$
$42$	−4.20317	+	4.30853i	−0.648563	+	0.664821i
$43$	−0.231369			−0.0352834			−0.0176417	−	0.999844i	$-0.505616\pi$
$43$	−0.231369			−0.0352834			−0.0176417	+	0.999844i	$0.505616\pi$
$44$	−9.72835	+	16.8500i	−1.46660	+	2.54023i
$45$	0.619347	+	1.07274i	0.0923268	+	0.159915i
$46$	−1.13751	−	1.97023i	−0.167717	−	0.290494i
$47$	−6.67889	+	11.5682i	−0.974217	+	1.68739i	−0.291721	+	0.956503i	$0.594228\pi$
$47$	−6.67889	+	11.5682i	−0.974217	+	1.68739i	−0.682496	+	0.730889i	$0.739105\pi$
$48$	0.266205			0.0384234
$49$	−0.173272	−	6.99786i	−0.0247532	−	0.999694i
$50$	−7.88440			−1.11502
$51$	2.45436	−	4.25108i	0.343680	−	0.595271i
$52$	−1.44559	−	2.50384i	−0.200468	−	0.347220i
$53$	−2.11340	−	3.66052i	−0.290298	−	0.502812i	0.683582	−	0.729874i	$-0.260421\pi$
$53$	−2.11340	−	3.66052i	−0.290298	−	0.502812i	−0.973880	+	0.227062i	$0.927088\pi$
$54$	1.13751	−	1.97023i	0.154796	−	0.268114i
$55$	−7.58909			−1.02331
$56$	4.94179	−	5.06567i	0.660374	−	0.676928i
$57$	6.90370			0.914418
$58$	−3.82209	+	6.62005i	−0.501864	+	0.869255i
$59$	0.377100	+	0.653157i	0.0490943	+	0.0850338i	0.889528	−	0.456880i	$-0.151033\pi$
$59$	0.377100	+	0.653157i	0.0490943	+	0.0850338i	−0.840434	+	0.541914i	$0.817700\pi$
$60$	−1.96688	−	3.40673i	−0.253923	−	0.439807i
$61$	−1.78832	+	3.09747i	−0.228971	+	0.396590i	−0.957503	−	0.288422i	$-0.906869\pi$
$61$	−1.78832	+	3.09747i	−0.228971	+	0.396590i	0.728532	+	0.685011i	$0.240203\pi$
$62$	12.3701			1.57100
$63$	0.716350	+	2.54693i	0.0902517	+	0.320883i
$64$	−13.0159			−1.62699
$65$	0.563853	−	0.976623i	0.0699374	−	0.121135i
$66$	6.96918	+	12.0710i	0.857847	+	1.48583i
$67$	2.24703	+	3.89197i	0.274518	+	0.475479i	0.970013	−	0.243051i	$-0.0781483\pi$
$67$	2.24703	+	3.89197i	0.274518	+	0.475479i	−0.695495	+	0.718531i	$0.744815\pi$
$68$	−7.79440	+	13.5003i	−0.945209	+	1.63715i
$69$	−1.00000			−0.120386
$70$	7.22516	+	1.84043i	0.863571	+	0.219974i
$71$	15.8575			1.88194			0.940968	−	0.338495i	$-0.109918\pi$
$71$	15.8575			1.88194			0.940968	+	0.338495i	$0.109918\pi$
$72$	−1.33740	+	2.31645i	−0.157615	+	0.272997i
$73$	2.13888	+	3.70465i	0.250337	+	0.433597i	0.963619	−	0.267281i	$-0.0861252\pi$
$73$	2.13888	+	3.70465i	0.250337	+	0.433597i	−0.713281	+	0.700878i	$0.752792\pi$
$74$	−7.44689	−	12.8984i	−0.865684	−	1.49941i
$75$	−1.73282	+	3.00133i	−0.200089	+	0.346564i
$76$	−21.9243			−2.51489
$77$	−15.7081	−	4.00126i	−1.79010	−	0.455986i
$78$	−2.07118			−0.234515
$79$	0.111008	−	0.192271i	0.0124893	−	0.0216322i	−0.859713	−	0.510777i	$-0.829358\pi$
$79$	0.111008	−	0.192271i	0.0124893	−	0.0216322i	0.872203	+	0.489145i	$0.162691\pi$
$80$	−0.164873	−	0.285569i	−0.0184334	−	0.0319276i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	2.86889	−	4.96906i	0.316816	−	0.548741i
$83$	15.5197			1.70351			0.851753	−	0.523944i	$-0.175540\pi$
$83$	15.5197			1.70351			0.851753	+	0.523944i	$0.175540\pi$
$84$	−2.27493	−	8.08835i	−0.248216	−	0.882512i
$85$	−6.08041			−0.659513
$86$	0.263184	−	0.455849i	0.0283799	−	0.0491554i
$87$	1.68002	+	2.90988i	0.180117	+	0.311972i
$88$	−8.19386	−	14.1922i	−0.873469	−	1.51289i
$89$	−0.279682	+	0.484423i	−0.0296462	+	0.0513487i	−0.880468	−	0.474106i	$-0.842771\pi$
$89$	−0.279682	+	0.484423i	−0.0296462	+	0.0513487i	0.850822	+	0.525455i	$0.176105\pi$
$90$	−2.81806			−0.297049
$91$	1.68199	−	1.72415i	0.176321	−	0.180740i
$92$	3.17573			0.331093
$93$	2.71868	−	4.70889i	0.281914	−	0.488289i
$94$	−15.1946	−	26.3179i	−1.56721	−	2.71448i
$95$	−4.27579	−	7.40588i	−0.438686	−	0.759827i
$96$	−2.97762	+	5.15739i	−0.303902	+	0.526374i
$97$	17.6476			1.79185			0.895923	−	0.444209i	$-0.146515\pi$
$97$	17.6476			1.79185			0.895923	+	0.444209i	$0.146515\pi$
$98$	13.9845	+	7.61875i	1.41264	+	0.769610i
$99$	6.12669			0.615756
$100$	5.50296	−	9.53141i	0.550296	−	0.953141i
$101$	4.06538	+	7.04144i	0.404520	+	0.700649i	0.994265	−	0.106940i	$-0.0341052\pi$
$101$	4.06538	+	7.04144i	0.404520	+	0.700649i	−0.589745	+	0.807589i	$0.700772\pi$
$102$	5.58374	+	9.67131i	0.552872	+	0.957603i
$103$	7.13975	−	12.3664i	0.703500	−	1.21850i	−0.263730	−	0.964597i	$-0.584953\pi$
$103$	7.13975	−	12.3664i	0.703500	−	1.21850i	0.967230	−	0.253902i	$-0.0817140\pi$
$104$	2.43515			0.238786
$105$	2.28852	−	2.34589i	0.223337	−	0.228935i
$106$	9.61609			0.933997
$107$	3.27882	−	5.67908i	0.316975	−	0.549017i	−0.662880	−	0.748726i	$-0.730666\pi$
$107$	3.27882	−	5.67908i	0.316975	−	0.549017i	0.979855	+	0.199708i	$0.0639994\pi$
$108$	1.58786	+	2.75026i	0.152792	+	0.264644i
$109$	−9.11792	−	15.7927i	−0.873338	−	1.51267i	−0.858522	−	0.512776i	$-0.828617\pi$
$109$	−9.11792	−	15.7927i	−0.873338	−	1.51267i	−0.0148158	−	0.999890i	$-0.504716\pi$
$110$	8.63268	−	14.9522i	0.823094	−	1.42564i
$111$	−6.54665			−0.621381
$112$	−0.190696	−	0.678005i	−0.0180191	−	0.0640655i
$113$	−18.5945			−1.74922			−0.874610	−	0.484828i	$-0.838882\pi$
$113$	−18.5945			−1.74922			−0.874610	+	0.484828i	$0.838882\pi$
$114$	−7.85304	+	13.6019i	−0.735504	+	1.27393i
$115$	0.619347	+	1.07274i	0.0577544	+	0.100034i
$116$	−5.33529	−	9.24099i	−0.495369	−	0.858005i
$117$	−0.455200	+	0.788430i	−0.0420833	+	0.0728903i
$118$	−1.71582			−0.157954
$119$	−12.5854	−	3.20582i	−1.15370	−	0.293877i
$120$	3.31327			0.302459
$121$	−13.2682	+	22.9811i	−1.20620	+	2.08919i
$122$	−4.06847	−	7.04680i	−0.368342	−	0.637988i
$123$	−1.26104	−	2.18418i	−0.113704	−	0.196941i
$124$	−8.63378	+	14.9541i	−0.775336	+	1.34292i
$125$	10.4863			0.937926
$126$	−5.83288	−	1.48579i	−0.519635	−	0.132364i
$127$	−4.19807			−0.372518			−0.186259	−	0.982501i	$-0.559636\pi$
$127$	−4.19807			−0.372518			−0.186259	+	0.982501i	$0.559636\pi$
$128$	8.85049	−	15.3295i	0.782280	−	1.35495i
$129$	−0.115684	−	0.200371i	−0.0101854	−	0.0176417i
$130$	1.28278	+	2.22184i	0.112507	+	0.194868i
$131$	−1.91771	+	3.32157i	−0.167551	+	0.290207i	−0.937558	−	0.347828i	$-0.886919\pi$
$131$	−1.91771	+	3.32157i	−0.167551	+	0.290207i	0.770007	+	0.638035i	$0.220253\pi$
$132$	−19.4567			−1.69349
$133$	−4.94547	−	17.5832i	−0.428827	−	1.52466i
$134$	−10.2241			−0.883226
$135$	−0.619347	+	1.07274i	−0.0533049	+	0.0923268i
$136$	−6.56496	−	11.3708i	−0.562940	−	0.975041i
$137$	−3.62823	−	6.28428i	−0.309981	−	0.536903i	0.668377	−	0.743823i	$-0.266989\pi$
$137$	−3.62823	−	6.28428i	−0.309981	−	0.536903i	−0.978358	+	0.206920i	$0.933656\pi$
$138$	1.13751	−	1.97023i	0.0968314	−	0.167717i
$139$	3.52170			0.298707			0.149353	−	0.988784i	$-0.452281\pi$
$139$	3.52170			0.298707			0.149353	+	0.988784i	$0.452281\pi$
$140$	−7.26773	+	7.44991i	−0.614235	+	0.629632i
$141$	−13.3578			−1.12493
$142$	−18.0381	+	31.2428i	−1.51372	+	2.62184i
$143$	−2.78887	−	4.83046i	−0.233217	−	0.403944i
$144$	0.133103	+	0.230540i	0.0110919	+	0.0192117i
$145$	2.08103	−	3.60445i	0.172820	−	0.299333i
$146$	−9.73201			−0.805427
$147$	5.97368	−	3.64899i	0.492701	−	0.300963i
$148$	20.7904			1.70896
$149$	5.46213	−	9.46069i	0.447475	−	0.775050i	−0.550746	−	0.834673i	$-0.685657\pi$
$149$	5.46213	−	9.46069i	0.447475	−	0.775050i	0.998221	+	0.0596230i	$0.0189899\pi$
$150$	−3.94220	−	6.82809i	−0.321879	−	0.557512i
$151$	7.92677	+	13.7296i	0.645071	+	1.11730i	0.984285	+	0.176587i	$0.0565057\pi$
$151$	7.92677	+	13.7296i	0.645071	+	1.11730i	−0.339214	+	0.940709i	$0.610161\pi$
$152$	9.23304	−	15.9921i	0.748899	−	1.29713i
$153$	4.90873			0.396847
$154$	25.7515	−	26.3970i	2.07512	−	2.12713i
$155$	−6.73521			−0.540985
$156$	1.44559	−	2.50384i	0.115740	−	0.200468i
$157$	4.59998	+	7.96740i	0.367118	+	0.635868i	0.989114	−	0.147153i	$-0.0470111\pi$
$157$	4.59998	+	7.96740i	0.367118	+	0.635868i	−0.621995	+	0.783021i	$0.713678\pi$
$158$	0.252545	+	0.437421i	0.0200914	+	0.0347993i
$159$	2.11340	−	3.66052i	0.167604	−	0.290298i
$160$	7.37672			0.583181
$161$	0.716350	+	2.54693i	0.0564563	+	0.200726i
$162$	2.27502			0.178743
$163$	0.824386	−	1.42788i	0.0645709	−	0.111840i	−0.831933	−	0.554877i	$-0.812765\pi$
$163$	0.824386	−	1.42788i	0.0645709	−	0.111840i	0.896504	+	0.443036i	$0.146099\pi$
$164$	4.00471	+	6.93636i	0.312715	+	0.541639i
$165$	−3.79455	−	6.57235i	−0.295405	−	0.511657i
$166$	−17.6538	+	30.5773i	−1.37020	+	2.37326i
$167$	5.46655			0.423015			0.211507	−	0.977376i	$-0.432163\pi$
$167$	5.46655			0.423015			0.211507	+	0.977376i	$0.432163\pi$
$168$	6.85789	+	1.74688i	0.529098	+	0.134775i
$169$	−12.1712			−0.936244
$170$	6.91654	−	11.9798i	0.530474	−	0.918808i
$171$	3.45185	+	5.97878i	0.263970	+	0.457209i
$172$	0.367382	+	0.636324i	0.0280126	+	0.0485193i
$173$	0.254586	−	0.440956i	0.0193558	−	0.0335253i	−0.856185	−	0.516669i	$-0.827172\pi$
$173$	0.254586	−	0.440956i	0.0193558	−	0.0335253i	0.875541	+	0.483144i	$0.160505\pi$
$174$	−7.64417			−0.579503
$175$	8.88548	+	2.26336i	0.671679	+	0.171094i
$176$	−1.63096			−0.122938
$177$	−0.377100	+	0.653157i	−0.0283446	+	0.0490943i
$178$	−0.636282	−	1.10207i	−0.0476914	−	0.0826039i
$179$	−4.17543	−	7.23207i	−0.312087	−	0.540550i	0.666727	−	0.745302i	$-0.267695\pi$
$179$	−4.17543	−	7.23207i	−0.312087	−	0.540550i	−0.978814	+	0.204752i	$0.934361\pi$
$180$	1.96688	−	3.40673i	0.146602	−	0.253923i
$181$	−2.42861			−0.180517			−0.0902584	−	0.995918i	$-0.528769\pi$
$181$	−2.42861			−0.180517			−0.0902584	+	0.995918i	$0.528769\pi$
$182$	1.48369	+	5.27515i	0.109979	+	0.391020i
$183$	−3.57664			−0.264393
$184$	−1.33740	+	2.31645i	−0.0985948	+	0.170771i
$185$	4.05465	+	7.02286i	0.298104	+	0.516331i
$186$	6.18505	+	10.7128i	0.453510	+	0.785502i
$187$	−15.0371	+	26.0451i	−1.09962	+	1.90460i
$188$	42.4207			3.09385
$189$	−1.84753	+	1.89384i	−0.134388	+	0.137757i
$190$	19.4550			1.41142
$191$	7.14656	−	12.3782i	0.517107	−	0.895656i	−0.482696	−	0.875788i	$-0.660342\pi$
$191$	7.14656	−	12.3782i	0.517107	−	0.895656i	0.999803	−	0.0198675i	$-0.00632445\pi$
$192$	−6.50795	−	11.2721i	−0.469671	−	0.813494i
$193$	−1.04502	−	1.81003i	−0.0752225	−	0.130289i	0.825961	−	0.563728i	$-0.190633\pi$
$193$	−1.04502	−	1.81003i	−0.0752225	−	0.130289i	−0.901183	+	0.433439i	$0.857300\pi$
$194$	−20.0744	+	34.7699i	−1.44126	+	2.49633i
$195$	1.12771			0.0807568
$196$	−18.9708	+	11.5882i	−1.35506	+	0.827728i
$197$	10.8863			0.775614			0.387807	−	0.921741i	$-0.373233\pi$
$197$	10.8863			0.775614			0.387807	+	0.921741i	$0.373233\pi$
$198$	−6.96918	+	12.0710i	−0.495278	+	0.857847i
$199$	−1.72027	−	2.97959i	−0.121946	−	0.211217i	0.798589	−	0.601877i	$-0.205580\pi$
$199$	−1.72027	−	2.97959i	−0.121946	−	0.211217i	−0.920535	+	0.390660i	$0.872247\pi$
$200$	4.63496	+	8.02799i	0.327741	+	0.567664i
$201$	−2.24703	+	3.89197i	−0.158493	+	0.274518i
$202$	−18.4976			−1.30149
$203$	6.20777	−	6.36339i	0.435700	−	0.446622i
$204$	−15.5888			−1.09143
$205$	−1.56204	+	2.70553i	−0.109097	+	0.188962i
$206$	16.2431	+	28.1339i	1.13171	+	1.96018i
$207$	−0.500000	−	0.866025i	−0.0347524	−	0.0601929i
$208$	0.121177	−	0.209884i	0.00840209	−	0.0145528i
$209$	−42.2968			−2.92573
$210$	2.01872	+	7.17739i	0.139305	+	0.495287i
$211$	11.6690			0.803324			0.401662	−	0.915788i	$-0.368433\pi$
$211$	11.6690			0.803324			0.401662	+	0.915788i	$0.368433\pi$
$212$	−6.71160	+	11.6248i	−0.460955	+	0.798397i
$213$	7.92874	+	13.7330i	0.543268	+	0.940968i
$214$	7.45939	+	12.9200i	0.509913	+	0.883196i
$215$	−0.143297	+	0.248198i	−0.00977280	+	0.0169270i
$216$	−2.67481			−0.181998
$217$	−13.9407	−	3.55106i	−0.946357	−	0.241062i
$218$	41.4869			2.80985
$219$	−2.13888	+	3.70465i	−0.144532	+	0.250337i
$220$	12.0504	+	20.8720i	0.812441	+	1.40719i
$221$	−2.23445	−	3.87019i	−0.150306	−	0.260337i
$222$	7.44689	−	12.8984i	0.499803	−	0.865684i
$223$	2.48168			0.166185			0.0830926	−	0.996542i	$-0.473520\pi$
$223$	2.48168			0.166185			0.0830926	+	0.996542i	$0.473520\pi$
$224$	15.2685	+	3.88929i	1.02017	+	0.259864i
$225$	−3.46564			−0.231043
$226$	21.1514	−	36.6353i	1.40697	−	2.43694i
$227$	11.0247	+	19.0954i	0.731738	+	1.26741i	0.956140	+	0.292910i	$0.0946237\pi$
$227$	11.0247	+	19.0954i	0.731738	+	1.26741i	−0.224402	+	0.974497i	$0.572043\pi$
$228$	−10.9621	−	18.9870i	−0.725985	−	1.25744i
$229$	−7.37334	+	12.7710i	−0.487244	+	0.843932i	−0.999892	−	0.0146672i	$-0.995331\pi$
$229$	−7.37334	+	12.7710i	−0.487244	+	0.843932i	0.512648	+	0.858599i	$0.328664\pi$
$230$	−2.81806			−0.185817
$231$	−4.38886	−	15.6042i	−0.288766	−	1.02668i
$232$	8.98747			0.590056
$233$	1.70807	−	2.95847i	0.111900	−	0.193816i	−0.804637	−	0.593768i	$-0.797640\pi$
$233$	1.70807	−	2.95847i	0.111900	−	0.193816i	0.916536	+	0.399952i	$0.130973\pi$
$234$	−1.03559	−	1.79370i	−0.0676987	−	0.117258i
$235$	8.27310	+	14.3294i	0.539678	+	0.934749i
$236$	1.19757	−	2.07425i	0.0779550	−	0.135022i
$237$	0.222015			0.0144215
$238$	20.6322	−	21.1494i	1.33739	−	1.37091i
$239$	−10.8751			−0.703453			−0.351727	−	0.936103i	$-0.614405\pi$
$239$	−10.8751			−0.703453			−0.351727	+	0.936103i	$0.614405\pi$
$240$	0.164873	−	0.285569i	0.0106425	−	0.0184334i
$241$	10.6982	+	18.5299i	0.689134	+	1.19361i	0.972119	+	0.234490i	$0.0753421\pi$
$241$	10.6982	+	18.5299i	0.689134	+	1.19361i	−0.282985	+	0.959124i	$0.591325\pi$
$242$	−30.1854	−	52.2826i	−1.94039	−	3.36085i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	11.3585			0.727150
$245$	−7.61420	−	4.14822i	−0.486453	−	0.265020i
$246$	5.73777			0.365827
$247$	3.14257	−	5.44308i	0.199957	−	0.346335i
$248$	−7.27194	−	12.5954i	−0.461769	−	0.799807i
$249$	7.75984	+	13.4404i	0.491760	+	0.851753i
$250$	−11.9283	+	20.6605i	−0.754413	+	1.30668i
$251$	4.68560			0.295752			0.147876	−	0.989006i	$-0.452756\pi$
$251$	4.68560			0.295752			0.147876	+	0.989006i	$0.452756\pi$
$252$	5.86725	−	6.01433i	0.369602	−	0.378867i
$253$	6.12669			0.385182
$254$	4.77535	−	8.27115i	0.299632	−	0.518978i
$255$	−3.04021	−	5.26579i	−0.190385	−	0.329757i
$256$	7.11917	+	12.3308i	0.444948	+	0.770673i
$257$	13.5087	−	23.3978i	0.842650	−	1.45951i	−0.0449969	−	0.998987i	$-0.514328\pi$
$257$	13.5087	−	23.3978i	0.842650	−	1.45951i	0.887647	−	0.460525i	$-0.152339\pi$
$258$	0.526369			0.0327703
$259$	4.68970	+	16.6739i	0.291404	+	1.03606i
$260$	−3.58129			−0.222102
$261$	−1.68002	+	2.90988i	−0.103991	+	0.180117i
$262$	−4.36283	−	7.55664i	−0.269536	−	0.466851i
$263$	10.0032	+	17.3260i	0.616822	+	1.06837i	0.990062	+	0.140632i	$0.0449134\pi$
$263$	10.0032	+	17.3260i	0.616822	+	1.06837i	−0.373240	+	0.927735i	$0.621753\pi$
$264$	8.19386	−	14.1922i	0.504297	−	0.873469i
$265$	−5.23572			−0.321628
$266$	40.2685	+	10.2574i	2.46902	+	0.628923i
$267$	−0.559363			−0.0342325
$268$	7.13595	−	12.3598i	0.435898	−	0.754997i
$269$	3.14036	+	5.43926i	0.191471	+	0.331638i	0.945738	−	0.324930i	$-0.105341\pi$
$269$	3.14036	+	5.43926i	0.191471	+	0.331638i	−0.754267	+	0.656568i	$0.772008\pi$
$270$	−1.40903	−	2.44051i	−0.0857507	−	0.148525i
$271$	−12.7101	+	22.0146i	−0.772085	+	1.33729i	0.164333	+	0.986405i	$0.447453\pi$
$271$	−12.7101	+	22.0146i	−0.772085	+	1.33729i	−0.936418	+	0.350886i	$0.885881\pi$
$272$	−1.30673			−0.0792321
$273$	2.33416	+	0.594570i	0.141270	+	0.0359850i
$274$	16.5086			0.997323
$275$	10.6164	−	18.3882i	0.640196	−	1.10885i
$276$	1.58786	+	2.75026i	0.0955782	+	0.165546i
$277$	7.57054	+	13.1126i	0.454869	+	0.787857i	0.998681	−	0.0513506i	$-0.0163526\pi$
$277$	7.57054	+	13.1126i	0.454869	+	0.787857i	−0.543811	+	0.839208i	$0.683019\pi$
$278$	−4.00597	+	6.93855i	−0.240262	+	0.416146i
$279$	5.43735			0.325526
$280$	−2.37346	−	8.43866i	−0.141841	−	0.504306i
$281$	−27.3149			−1.62947			−0.814736	−	0.579833i	$-0.803118\pi$
$281$	−27.3149			−1.62947			−0.814736	+	0.579833i	$0.803118\pi$
$282$	15.1946	−	26.3179i	0.904827	−	1.56721i
$283$	−4.27130	−	7.39812i	−0.253903	−	0.439772i	0.710694	−	0.703501i	$-0.248381\pi$
$283$	−4.27130	−	7.39812i	−0.253903	−	0.439772i	−0.964597	+	0.263729i	$0.915048\pi$
$284$	−25.1795	−	43.6122i	−1.49413	−	2.58791i
$285$	4.27579	−	7.40588i	0.253276	−	0.438686i
$286$	12.6895			0.750345
$287$	−4.65960	+	4.77641i	−0.275048	+	0.281942i
$288$	−5.95524			−0.350916
$289$	−3.54781	+	6.14499i	−0.208695	+	0.361470i
$290$	4.73439	+	8.20021i	0.278013	+	0.481533i
$291$	8.82382	+	15.2833i	0.517261	+	0.895923i
$292$	6.79251	−	11.7650i	0.397502	−	0.688493i
$293$	13.6153			0.795413			0.397707	−	0.917513i	$-0.369806\pi$
$293$	13.6153			0.795413			0.397707	+	0.917513i	$0.369806\pi$
$294$	0.394198	+	15.9203i	0.0229901	+	0.928490i
$295$	0.934224			0.0543926
$296$	−8.75552	+	15.1650i	−0.508905	+	0.881449i
$297$	3.06335	+	5.30587i	0.177753	+	0.307878i
$298$	12.4265	+	21.5233i	0.719847	+	1.24681i
$299$	−0.455200	+	0.788430i	−0.0263249	+	0.0455961i
$300$	11.0059			0.635427
$301$	−0.427460	+	0.438176i	−0.0246384	+	0.0252560i
$302$	−36.0672			−2.07543
$303$	−4.06538	+	7.04144i	−0.233550	+	0.404520i
$304$	−0.918900	−	1.59158i	−0.0527026	−	0.0912835i
$305$	2.21518	+	3.83681i	0.126841	+	0.219695i
$306$	−5.58374	+	9.67131i	−0.319201	+	0.552872i
$307$	−1.94494			−0.111003			−0.0555017	−	0.998459i	$-0.517676\pi$
$307$	−1.94494			−0.111003			−0.0555017	+	0.998459i	$0.517676\pi$
$308$	13.9378	+	49.5548i	0.794181	+	2.82365i
$309$	14.2795			0.812332
$310$	7.66138	−	13.2699i	0.435137	−	0.753680i
$311$	7.10098	+	12.2993i	0.402660	+	0.697427i	0.994046	−	0.108961i	$-0.0347525\pi$
$311$	7.10098	+	12.2993i	0.402660	+	0.697427i	−0.591386	+	0.806388i	$0.701419\pi$
$312$	1.21757	+	2.10890i	0.0689315	+	0.119393i
$313$	2.10228	−	3.64126i	0.118828	−	0.205816i	−0.800475	−	0.599366i	$-0.795420\pi$
$313$	2.10228	−	3.64126i	0.118828	−	0.205816i	0.919304	+	0.393549i	$0.128753\pi$
$314$	−20.9301			−1.18115
$315$	3.17586	+	0.808974i	0.178940	+	0.0455805i
$316$	−0.705061			−0.0396628
$317$	−0.369216	+	0.639501i	−0.0207373	+	0.0359180i	−0.876208	−	0.481933i	$-0.839935\pi$
$317$	−0.369216	+	0.639501i	−0.0207373	+	0.0359180i	0.855471	+	0.517851i	$0.173268\pi$
$318$	4.80804	+	8.32778i	0.269622	+	0.466998i
$319$	−10.2930	−	17.8279i	−0.576295	−	0.998173i
$320$	−8.06136	+	13.9627i	−0.450644	+	0.780537i
$321$	6.55764			0.366012
$322$	−5.83288	−	1.48579i	−0.325054	−	0.0827996i
$323$	−33.8884			−1.88560
$324$	−1.58786	+	2.75026i	−0.0882147	+	0.152792i
$325$	1.57756	+	2.73241i	0.0875072	+	0.151567i
$326$	1.87550	+	3.24846i	0.103874	+	0.179915i
$327$	9.11792	−	15.7927i	0.504222	−	0.873338i
$328$	−6.74607			−0.372489
$329$	9.56886	+	34.0213i	0.527548	+	1.87566i
$330$	17.2654			0.950427
$331$	10.2994	−	17.8392i	0.566108	−	0.980528i	−0.430837	−	0.902430i	$-0.641782\pi$
$331$	10.2994	−	17.8392i	0.566108	−	0.980528i	0.996946	−	0.0780988i	$-0.0248850\pi$
$332$	−24.6431	−	42.6832i	−1.35247	−	2.34254i
$333$	−3.27333	−	5.66957i	−0.179377	−	0.310690i
$334$	−6.21827	+	10.7704i	−0.340248	+	0.589327i
$335$	5.56676			0.304145
$336$	0.491822	−	0.504150i	0.0268311	−	0.0275037i
$337$	−27.9032			−1.51999			−0.759993	−	0.649932i	$-0.774797\pi$
$337$	−27.9032			−1.51999			−0.759993	+	0.649932i	$0.774797\pi$
$338$	13.8448	−	23.9800i	0.753060	−	1.30434i
$339$	−9.29723	−	16.1033i	−0.504956	−	0.874610i
$340$	9.65487	+	16.7227i	0.523609	+	0.906917i
$341$	−16.6565	+	28.8499i	−0.901999	+	1.56231i
$342$	−15.7061			−0.849287
$343$	−13.5730	−	12.6006i	−0.732871	−	0.680368i
$344$	−0.618867			−0.0333671
$345$	−0.619347	+	1.07274i	−0.0333445	+	0.0577544i
$346$	0.579189	+	1.00319i	0.0311374	+	0.0539316i
$347$	1.04267	+	1.80595i	0.0559732	+	0.0969485i	0.892654	−	0.450742i	$-0.148841\pi$
$347$	1.04267	+	1.80595i	0.0559732	+	0.0969485i	−0.836681	+	0.547690i	$0.815507\pi$
$348$	5.33529	−	9.24099i	0.286002	−	0.495369i
$349$	−4.04322			−0.216429			−0.108214	−	0.994128i	$-0.534513\pi$
$349$	−4.04322			−0.216429			−0.108214	+	0.994128i	$0.534513\pi$
$350$	−14.5667	+	14.9318i	−0.778621	+	0.798139i
$351$	−0.910400			−0.0485936
$352$	18.2430	−	31.5977i	0.972353	−	1.68416i
$353$	2.25397	+	3.90398i	0.119966	+	0.207788i	0.919754	−	0.392495i	$-0.128388\pi$
$353$	2.25397	+	3.90398i	0.119966	+	0.207788i	−0.799788	+	0.600283i	$0.795055\pi$
$354$	−0.857912	−	1.48595i	−0.0455975	−	0.0789772i
$355$	9.82128	−	17.0110i	0.521259	−	0.902848i
$356$	1.77639			0.0941483
$357$	−3.51637	−	12.5022i	−0.186106	−	0.661686i
$358$	18.9984			1.00410
$359$	10.4069	−	18.0252i	0.549254	−	0.951336i	−0.449072	−	0.893496i	$-0.648245\pi$
$359$	10.4069	−	18.0252i	0.549254	−	0.951336i	0.998326	−	0.0578401i	$-0.0184213\pi$
$360$	1.65663	+	2.86938i	0.0873123	+	0.151229i
$361$	−14.3305	−	24.8212i	−0.754239	−	1.30638i
$362$	2.76257	−	4.78490i	0.145197	−	0.251489i
$363$	−26.5363			−1.39280
$364$	−7.41265	−	1.88819i	−0.388528	−	0.0989682i
$365$	5.29884			0.277354
$366$	4.06847	−	7.04680i	0.212663	−	0.368342i
$367$	−4.28609	−	7.42373i	−0.223732	−	0.387515i	0.732206	−	0.681083i	$-0.238491\pi$
$367$	−4.28609	−	7.42373i	−0.223732	−	0.387515i	−0.955938	+	0.293568i	$0.905157\pi$
$368$	0.133103	+	0.230540i	0.00693845	+	0.0120178i
$369$	1.26104	−	2.18418i	0.0656470	−	0.113704i
$370$	−18.4488			−0.959109
$371$	−10.8370	−	2.76047i	−0.562631	−	0.143317i
$372$	−17.2676			−0.895281
$373$	0.727535	−	1.26013i	0.0376703	−	0.0652470i	−0.846576	−	0.532269i	$-0.821340\pi$
$373$	0.727535	−	1.26013i	0.0376703	−	0.0652470i	0.884246	+	0.467022i	$0.154673\pi$
$374$	−34.2098	−	59.2531i	−1.76895	−	3.06391i
$375$	5.24317	+	9.08143i	0.270756	+	0.468963i
$376$	−17.8648	+	30.9427i	−0.921305	+	1.59575i
$377$	3.05898			0.157546
$378$	−1.62971	−	5.79432i	−0.0838234	−	0.298028i
$379$	−2.61370			−0.134257			−0.0671283	−	0.997744i	$-0.521384\pi$
$379$	−2.61370			−0.134257			−0.0671283	+	0.997744i	$0.521384\pi$
$380$	−13.5787	+	23.5191i	−0.696574	+	1.20650i
$381$	−2.09903	−	3.63563i	−0.107537	−	0.186259i
$382$	16.2586	+	28.1607i	0.831862	+	1.44083i
$383$	5.66013	−	9.80363i	0.289219	−	0.500942i	−0.684404	−	0.729103i	$-0.739938\pi$
$383$	5.66013	−	9.80363i	0.289219	−	0.500942i	0.973624	+	0.228160i	$0.0732711\pi$
$384$	17.7010			0.903300
$385$	−14.0211	+	14.3725i	−0.714580	+	0.732492i
$386$	4.75491			0.242018
$387$	0.115684	−	0.200371i	0.00588056	−	0.0101854i
$388$	−28.0221	−	48.5356i	−1.42260	−	2.46402i
$389$	15.4855	+	26.8217i	0.785147	+	1.35991i	0.928911	+	0.370302i	$0.120746\pi$
$389$	15.4855	+	26.8217i	0.785147	+	1.35991i	−0.143765	+	0.989612i	$0.545921\pi$
$390$	−1.28278	+	2.22184i	−0.0649561	+	0.112507i
$391$	4.90873			0.248245
$392$	−0.463470	−	18.7179i	−0.0234088	−	0.945398i
$393$	−3.83542			−0.193471
$394$	−12.3833	+	21.4484i	−0.623859	+	1.08056i
$395$	−0.137505	−	0.238165i	−0.00691861	−	0.0119834i
$396$	−9.72835	−	16.8500i	−0.488868	−	0.846744i
$397$	−12.5198	+	21.6849i	−0.628350	+	1.08833i	0.359533	+	0.933132i	$0.382936\pi$
$397$	−12.5198	+	21.6849i	−0.628350	+	1.08833i	−0.987883	+	0.155201i	$0.950397\pi$
$398$	7.82728			0.392346
$399$	12.7548	−	13.0745i	0.638538	−	0.654545i
$400$	0.922571			0.0461285
$401$	−17.4873	+	30.2888i	−0.873272	+	1.51255i	−0.0146791	+	0.999892i	$0.504673\pi$
$401$	−17.4873	+	30.2888i	−0.873272	+	1.51255i	−0.858593	+	0.512659i	$0.828661\pi$
$402$	−5.11204	−	8.85431i	−0.254965	−	0.441613i
$403$	−2.47508	−	4.28697i	−0.123293	−	0.213549i
$404$	12.9105	−	22.3617i	0.642323	−	1.11254i
$405$	−1.23869			−0.0615512
$406$	5.47590	+	19.4692i	0.271765	+	0.966238i
$407$	40.1093			1.98815
$408$	6.56496	−	11.3708i	0.325014	−	0.562940i
$409$	12.0852	+	20.9322i	0.597576	+	1.03503i	0.993178	+	0.116610i	$0.0372026\pi$
$409$	12.0852	+	20.9322i	0.597576	+	1.03503i	−0.395602	+	0.918422i	$0.629464\pi$
$410$	−3.55367	−	6.15514i	−0.175503	−	0.303981i
$411$	3.62823	−	6.28428i	0.178968	−	0.309981i
$412$	−45.3478			−2.23413
$413$	1.93368	+	0.492558i	0.0951501	+	0.0242372i
$414$	2.27502			0.111811
$415$	9.61206	−	16.6486i	0.471838	−	0.817247i
$416$	2.71083	+	4.69529i	0.132909	+	0.230205i
$417$	1.76085	+	3.04988i	0.0862292	+	0.149353i
$418$	48.1131	−	83.3344i	2.35329	−	4.07602i
$419$	−19.9385			−0.974059			−0.487029	−	0.873386i	$-0.661920\pi$
$419$	−19.9385			−0.974059			−0.487029	+	0.873386i	$0.661920\pi$
$420$	−10.0857	−	2.56908i	−0.492131	−	0.125358i
$421$	−36.1003			−1.75942			−0.879711	−	0.475508i	$-0.842264\pi$
$421$	−36.1003			−1.75942			−0.879711	+	0.475508i	$0.842264\pi$
$422$	−13.2736	+	22.9905i	−0.646147	+	1.11916i
$423$	−6.67889	−	11.5682i	−0.324739	−	0.562464i
$424$	−5.65295	−	9.79120i	−0.274532	−	0.475503i
$425$	8.50594	−	14.7327i	0.412599	−	0.714642i
$426$	−36.0761			−1.74789
$427$	2.56213	+	9.10946i	0.123990	+	0.440837i
$428$	−20.8253			−1.00663
$429$	2.78887	−	4.83046i	0.134648	−	0.233217i
$430$	−0.326005	−	0.564657i	−0.0157214	−	0.0272302i
$431$	−5.43385	−	9.41171i	−0.261739	−	0.453346i	0.704965	−	0.709242i	$-0.250963\pi$
$431$	−5.43385	−	9.41171i	−0.261739	−	0.453346i	−0.966704	+	0.255896i	$0.917629\pi$
$432$	−0.133103	+	0.230540i	−0.00640390	+	0.0110919i
$433$	−26.1898			−1.25860			−0.629301	−	0.777161i	$-0.716659\pi$
$433$	−26.1898			−1.25860			−0.629301	+	0.777161i	$0.716659\pi$
$434$	22.8541	−	23.4270i	1.09703	−	1.12453i
$435$	4.16206			0.199556
$436$	−28.9560	+	50.1533i	−1.38674	+	2.40191i
$437$	3.45185	+	5.97878i	0.165124	+	0.286004i
$438$	−4.86601	−	8.42817i	−0.232507	−	0.402713i
$439$	15.7031	−	27.1986i	0.749468	−	1.29812i	−0.198611	−	0.980078i	$-0.563643\pi$
$439$	15.7031	−	27.1986i	0.749468	−	1.29812i	0.948078	−	0.318037i	$-0.103024\pi$
$440$	−20.2994			−0.967735
$441$	6.14696	+	3.34887i	0.292712	+	0.159470i
$442$	10.1669			0.483589
$443$	4.53943	−	7.86253i	0.215675	−	0.373560i	−0.737806	−	0.675013i	$-0.764138\pi$
$443$	4.53943	−	7.86253i	0.215675	−	0.373560i	0.953481	+	0.301453i	$0.0974715\pi$
$444$	10.3952	+	18.0050i	0.493334	+	0.854480i
$445$	0.346440	+	0.600052i	0.0164228	+	0.0284452i
$446$	−2.82293	+	4.88947i	−0.133670	+	0.231523i
$447$	10.9243			0.516700
$448$	−24.0473	+	24.6501i	−1.13613	+	1.16461i
$449$	23.9369			1.12965			0.564825	−	0.825211i	$-0.308944\pi$
$449$	23.9369			1.12965			0.564825	+	0.825211i	$0.308944\pi$
$450$	3.94220	−	6.82809i	0.185837	−	0.321879i
$451$	7.72598	+	13.3818i	0.363802	+	0.630124i
$452$	29.5255	+	51.1396i	1.38876	+	2.40541i
$453$	−7.92677	+	13.7296i	−0.372432	+	0.645071i
$454$	−50.1631			−2.35427
$455$	−0.807833	−	2.87219i	−0.0378718	−	0.134650i
$456$	18.4661			0.864754
$457$	2.40518	−	4.16589i	0.112509	−	0.194872i	−0.804272	−	0.594261i	$-0.797444\pi$
$457$	2.40518	−	4.16589i	0.112509	−	0.194872i	0.916781	+	0.399389i	$0.130778\pi$
$458$	−16.7745	−	29.0543i	−0.783822	−	1.35762i
$459$	2.45436	+	4.25108i	0.114560	+	0.198424i
$460$	1.96688	−	3.40673i	0.0917061	−	0.158840i
$461$	23.4694			1.09308			0.546540	−	0.837433i	$-0.315945\pi$
$461$	23.4694			1.09308			0.546540	+	0.837433i	$0.315945\pi$
$462$	35.7363	+	9.10295i	1.66260	+	0.423508i
$463$	23.4343			1.08908			0.544542	−	0.838733i	$-0.316703\pi$
$463$	23.4343			1.08908			0.544542	+	0.838733i	$0.316703\pi$
$464$	0.447230	−	0.774625i	0.0207621	−	0.0359611i
$465$	−3.36761	−	5.83287i	−0.156169	−	0.270493i
$466$	3.88591	+	6.73059i	0.180011	+	0.311789i
$467$	−6.72528	+	11.6485i	−0.311209	+	0.539029i	−0.978624	−	0.205656i	$-0.934067\pi$
$467$	−6.72528	+	11.6485i	−0.311209	+	0.539029i	0.667416	+	0.744685i	$0.267400\pi$
$468$	2.89118			0.133645
$469$	11.5222	+	2.93501i	0.532047	+	0.135526i
$470$	−37.6430			−1.73634
$471$	−4.59998	+	7.96740i	−0.211956	+	0.367118i
$472$	1.00867	+	1.74707i	0.0464279	+	0.0804154i
$473$	0.708762	+	1.22761i	0.0325889	+	0.0564456i
$474$	−0.252545	+	0.437421i	−0.0115998	+	0.0200914i
$475$	23.9257			1.09779
$476$	11.1670	+	39.7035i	0.511840	+	1.81981i
$477$	4.22681			0.193532
$478$	12.3706	−	21.4265i	0.565817	−	0.980023i
$479$	−3.38082	−	5.85575i	−0.154474	−	0.267556i	0.778394	−	0.627777i	$-0.216035\pi$
$479$	−3.38082	−	5.85575i	−0.154474	−	0.267556i	−0.932867	+	0.360220i	$0.882701\pi$
$480$	3.68836	+	6.38843i	0.168350	+	0.291590i
$481$	−2.98004	+	5.16158i	−0.135878	+	0.235348i
$482$	−48.6774			−2.21720
$483$	−1.84753	+	1.89384i	−0.0840655	+	0.0861728i
$484$	84.2722			3.83055
$485$	10.9300	−	18.9313i	0.496306	−	0.859627i
$486$	1.13751	+	1.97023i	0.0515986	+	0.0893713i
$487$	−9.93329	−	17.2050i	−0.450121	−	0.779632i	0.548273	−	0.836300i	$-0.315286\pi$
$487$	−9.93329	−	17.2050i	−0.450121	−	0.779632i	−0.998393	+	0.0566681i	$0.981952\pi$
$488$	−4.78342	+	8.28513i	−0.216535	+	0.375050i
$489$	1.64877			0.0745601
$490$	16.8342	−	10.2830i	0.760491	−	0.464541i
$491$	4.20340			0.189697			0.0948483	−	0.995492i	$-0.469763\pi$
$491$	4.20340			0.189697			0.0948483	+	0.995492i	$0.469763\pi$
$492$	−4.00471	+	6.93636i	−0.180546	+	0.312715i
$493$	−8.24677	−	14.2838i	−0.371416	−	0.643311i
$494$	7.14941	+	12.3831i	0.321667	+	0.557144i
$495$	3.79455	−	6.57235i	0.170552	−	0.295405i
$496$	−1.44745			−0.0649925
$497$	29.2972	−	30.0316i	1.31416	−	1.34710i
$498$	−35.3076			−1.58217
$499$	−3.47420	+	6.01749i	−0.155527	+	0.269380i	−0.933251	−	0.359226i	$-0.883041\pi$
$499$	−3.47420	+	6.01749i	−0.155527	+	0.269380i	0.777724	+	0.628606i	$0.216374\pi$
$500$	−16.6509	−	28.8402i	−0.744650	−	1.28977i
$501$	2.73328	+	4.73417i	0.122114	+	0.211507i
$502$	−5.32992	+	9.23169i	−0.237886	+	0.412030i
$503$	5.90346			0.263222			0.131611	−	0.991301i	$-0.457985\pi$
$503$	5.90346			0.263222			0.131611	+	0.991301i	$0.457985\pi$
$504$	1.91610	+	6.81255i	0.0853499	+	0.303455i
$505$	10.0715			0.448176
$506$	−6.96918	+	12.0710i	−0.309818	+	0.536620i
$507$	−6.08559	−	10.5405i	−0.270270	−	0.468122i
$508$	6.66596	+	11.5458i	0.295754	+	0.512261i
$509$	13.3324	−	23.0923i	0.590947	−	1.02355i	−0.403158	−	0.915130i	$-0.632088\pi$
$509$	13.3324	−	23.0923i	0.590947	−	1.02355i	0.994105	−	0.108420i	$-0.0345790\pi$
$510$	13.8331			0.612539
$511$	10.9677	+	2.79375i	0.485181	+	0.123588i
$512$	3.00941			0.132998
$513$	−3.45185	+	5.97878i	−0.152403	+	0.263970i
$514$	30.7326	+	53.2304i	1.35556	+	2.34789i
$515$	−8.84396	−	15.3182i	−0.389712	−	0.675000i
$516$	−0.367382	+	0.636324i	−0.0161731	+	0.0280126i
$517$	81.8390			3.59928
$518$	−38.1859	−	9.72693i	−1.67779	−	0.427377i
$519$	0.509172			0.0223502
$520$	1.50820	−	2.61228i	0.0661390	−	0.114556i
$521$	−2.65655	−	4.60129i	−0.116386	−	0.201586i	0.801947	−	0.597395i	$-0.203798\pi$
$521$	−2.65655	−	4.60129i	−0.116386	−	0.201586i	−0.918333	+	0.395809i	$0.870464\pi$
$522$	−3.82209	−	6.62005i	−0.167288	−	0.289752i
$523$	−8.51931	+	14.7559i	−0.372524	+	0.645230i	−0.989953	−	0.141397i	$-0.954841\pi$
$523$	−8.51931	+	14.7559i	−0.372524	+	0.645230i	0.617430	+	0.786626i	$0.288174\pi$
$524$	12.1802			0.532096
$525$	2.48261	+	8.82673i	0.108350	+	0.385230i
$526$	−45.5149			−1.98454
$527$	−13.3452	+	23.1146i	−0.581328	+	1.00689i
$528$	−0.815478	−	1.41245i	−0.0354891	−	0.0614690i
$529$	−0.500000	−	0.866025i	−0.0217391	−	0.0376533i
$530$	5.95569	−	10.3156i	0.258699	−	0.448079i
$531$	−0.754201			−0.0327295
$532$	−40.5057	+	41.5211i	−1.75615	+	1.80017i
$533$	−2.29610			−0.0994550
$534$	0.636282	−	1.10207i	0.0275346	−	0.0476914i
$535$	−4.06145	−	7.03464i	−0.175592	−	0.304134i
$536$	6.01037	+	10.4103i	0.259609	+	0.449655i
$537$	4.17543	−	7.23207i	0.180183	−	0.312087i
$538$	−14.2888			−0.616033
$539$	−36.5989	+	22.3562i	−1.57643	+	0.962950i
$540$	3.93376			0.169282
$541$	−19.3980	+	33.5984i	−0.833986	+	1.44451i	0.0608675	+	0.998146i	$0.480613\pi$
$541$	−19.3980	+	33.5984i	−0.833986	+	1.44451i	−0.894853	+	0.446360i	$0.852720\pi$
$542$	−28.9158	−	50.0837i	−1.24204	−	2.15128i
$543$	−1.21430	−	2.10323i	−0.0521107	−	0.0902584i
$544$	14.6163	−	25.3162i	0.626670	−	1.08542i
$545$	−22.5886			−0.967590
$546$	−3.82657	+	3.92249i	−0.163762	+	0.167867i
$547$	29.7356			1.27140			0.635701	−	0.771935i	$-0.280711\pi$
$547$	29.7356			1.27140			0.635701	+	0.771935i	$0.280711\pi$
$548$	−11.5223	+	19.9572i	−0.492208	+	0.852529i
$549$	−1.78832	−	3.09747i	−0.0763237	−	0.132197i
$550$	24.1527	+	41.8336i	1.02987	+	1.78379i
$551$	11.5984	−	20.0889i	0.494107	−	0.855818i
$552$	−2.67481			−0.113847
$553$	−0.159041	−	0.565457i	−0.00676311	−	0.0240457i
$554$	−34.4463			−1.46348
$555$	−4.05465	+	7.02286i	−0.172110	+	0.298104i
$556$	−5.59198	−	9.68559i	−0.237153	−	0.410761i
$557$	16.7822	+	29.0677i	0.711086	+	1.23164i	0.964450	+	0.264266i	$0.0851297\pi$
$557$	16.7822	+	29.0677i	0.711086	+	1.23164i	−0.253364	+	0.967371i	$0.581537\pi$
$558$	−6.18505	+	10.7128i	−0.261834	+	0.453510i
$559$	−0.210638			−0.00890904
$560$	−0.845431	−	0.215353i	−0.0357260	−	0.00910033i
$561$	−30.0743			−1.26974
$562$	31.0710	−	53.8166i	1.31065	−	2.27012i
$563$	15.2766	+	26.4598i	0.643831	+	1.11515i	0.984570	+	0.174991i	$0.0559895\pi$
$563$	15.2766	+	26.4598i	0.643831	+	1.11515i	−0.340739	+	0.940158i	$0.610677\pi$
$564$	21.2104	+	36.7374i	0.893117	+	1.54692i
$565$	−11.5164	+	19.9470i	−0.484499	+	0.839178i
$566$	19.4346			0.816898
$567$	−2.56388	−	0.653086i	−0.107673	−	0.0274270i
$568$	42.4157			1.77972
$569$	−21.0580	+	36.4735i	−0.882797	+	1.52905i	−0.0345799	+	0.999402i	$0.511009\pi$
$569$	−21.0580	+	36.4735i	−0.882797	+	1.52905i	−0.848218	+	0.529648i	$0.822324\pi$
$570$	9.72751	+	16.8485i	0.407441	+	0.705708i
$571$	−3.25852	−	5.64391i	−0.136365	−	0.236190i	0.789753	−	0.613425i	$-0.210209\pi$
$571$	−3.25852	−	5.64391i	−0.136365	−	0.236190i	−0.926118	+	0.377234i	$0.876875\pi$
$572$	−8.85669	+	15.3402i	−0.370317	+	0.641408i
$573$	14.2931			0.597104
$574$	−4.11026	−	14.6137i	−0.171559	−	0.609964i
$575$	−3.46564			−0.144527
$576$	6.50795	−	11.2721i	0.271165	−	0.469671i
$577$	−20.7678	−	35.9709i	−0.864575	−	1.49749i	−0.867468	−	0.497492i	$-0.834254\pi$
$577$	−20.7678	−	35.9709i	−0.864575	−	1.49749i	0.00289316	−	0.999996i	$-0.499079\pi$
$578$	−8.07135	−	13.9800i	−0.335724	−	0.581491i
$579$	1.04502	−	1.81003i	0.0434297	−	0.0752225i
$580$	−13.2176			−0.548830
$581$	28.6731	−	29.3918i	1.18956	−	1.21938i
$582$	−40.1488			−1.66422
$583$	−12.9482	+	22.4269i	−0.536259	+	0.928827i
$584$	5.72110	+	9.90924i	0.236741	+	0.410047i
$585$	0.563853	+	0.976623i	0.0233125	+	0.0403784i
$586$	−15.4875	+	26.8252i	−0.639784	+	1.10814i
$587$	12.6109			0.520506			0.260253	−	0.965540i	$-0.416194\pi$
$587$	12.6109			0.520506			0.260253	+	0.965540i	$0.416194\pi$
$588$	−19.5211	−	10.6351i	−0.805035	−	0.438584i
$589$	−37.5379			−1.54672
$590$	−1.06269	+	1.84063i	−0.0437503	+	0.0757777i
$591$	5.44313	+	9.42778i	0.223901	+	0.387807i
$592$	0.871376	+	1.50927i	0.0358134	+	0.0620305i
$593$	−5.19295	+	8.99445i	−0.213249	+	0.369358i	−0.952729	−	0.303820i	$-0.901738\pi$
$593$	−5.19295	+	8.99445i	−0.213249	+	0.369358i	0.739481	+	0.673178i	$0.235071\pi$
$594$	−13.9384			−0.571898
$595$	−11.2337	+	11.5153i	−0.460538	+	0.472083i
$596$	−34.6925			−1.42106
$597$	1.72027	−	2.97959i	0.0704058	−	0.121946i
$598$	−1.03559	−	1.79370i	−0.0423484	−	0.0733497i
$599$	−14.0179	−	24.2797i	−0.572757	−	0.992044i	−0.996281	−	0.0861591i	$-0.972541\pi$
$599$	−14.0179	−	24.2797i	−0.572757	−	0.992044i	0.423525	−	0.905885i	$-0.360793\pi$
$600$	−4.63496	+	8.02799i	−0.189221	+	0.327741i
$601$	3.81190			0.155491			0.0777454	−	0.996973i	$-0.475228\pi$
$601$	3.81190			0.155491			0.0777454	+	0.996973i	$0.475228\pi$
$602$	−0.377065	−	1.34062i	−0.0153680	−	0.0546397i
$603$	−4.49406			−0.183012
$604$	25.1733	−	43.6014i	1.02429	−	1.77411i
$605$	16.4352	+	28.4666i	0.668186	+	1.15733i
$606$	−9.24882	−	16.0194i	−0.375708	−	0.650745i
$607$	−0.0799650	+	0.138503i	−0.00324568	+	0.00562168i	−0.867644	−	0.497187i	$-0.834366\pi$
$607$	−0.0799650	+	0.138503i	−0.00324568	+	0.00562168i	0.864398	+	0.502808i	$0.167700\pi$
$608$	41.1132			1.66736
$609$	8.61474	+	2.19440i	0.349087	+	0.0889215i
$610$	−10.0792			−0.408094
$611$	−6.08047	+	10.5317i	−0.245989	+	0.426066i
$612$	−7.79440	−	13.5003i	−0.315070	−	0.545717i
$613$	8.26694	+	14.3188i	0.333899	+	0.578329i	0.983273	−	0.182140i	$-0.0583023\pi$
$613$	8.26694	+	14.3188i	0.333899	+	0.578329i	−0.649374	+	0.760469i	$0.724969\pi$
$614$	2.21239	−	3.83197i	0.0892846	−	0.154646i
$615$	−3.12408			−0.125975
$616$	−42.0162	−	10.7026i	−1.69288	−	0.431220i
$617$	35.8727			1.44418			0.722091	−	0.691798i	$-0.243181\pi$
$617$	35.8727			1.44418			0.722091	+	0.691798i	$0.243181\pi$
$618$	−16.2431	+	28.1339i	−0.653393	+	1.13171i
$619$	18.3475	+	31.7788i	0.737448	+	1.27730i	0.953641	+	0.300947i	$0.0973028\pi$
$619$	18.3475	+	31.7788i	0.737448	+	1.27730i	−0.216192	+	0.976351i	$0.569364\pi$
$620$	10.6946	+	18.5236i	0.429506	+	0.743926i
$621$	0.500000	−	0.866025i	0.0200643	−	0.0347524i
$622$	−32.3098			−1.29550
$623$	0.400700	+	1.42466i	0.0160537	+	0.0570777i
$624$	0.242353			0.00970189
$625$	−2.16942	+	3.75754i	−0.0867767	+	0.150302i
$626$	4.78274	+	8.28395i	0.191157	+	0.331093i
$627$	−21.1484	−	36.6301i	−0.844586	−	1.46287i
$628$	14.6083	−	25.3023i	0.582934	−	1.00967i
$629$	32.1358			1.28134
$630$	−5.20644	+	5.33695i	−0.207430	+	0.212629i
$631$	12.3865			0.493098			0.246549	−	0.969130i	$-0.420703\pi$
$631$	12.3865			0.493098			0.246549	+	0.969130i	$0.420703\pi$
$632$	0.296925	−	0.514288i	0.0118110	−	0.0204573i
$633$	5.83448	+	10.1056i	0.231900	+	0.401662i
$634$	−0.839976	−	1.45488i	−0.0333597	−	0.0577807i
$635$	−2.60006	+	4.50344i	−0.103180	+	0.178713i
$636$	−13.4232			−0.532264
$637$	−0.157747	−	6.37085i	−0.00625016	−	0.252422i
$638$	46.8335			1.85415
$639$	−7.92874	+	13.7330i	−0.313656	+	0.543268i
$640$	−10.9630	−	18.9886i	−0.433353	−	0.750589i
$641$	−13.5191	−	23.4158i	−0.533974	−	0.924870i	−0.999212	−	0.0396845i	$-0.987365\pi$
$641$	−13.5191	−	23.4158i	−0.533974	−	0.924870i	0.465238	−	0.885185i	$-0.345969\pi$
$642$	−7.45939	+	12.9200i	−0.294399	+	0.509913i
$643$	−27.4371			−1.08201			−0.541006	−	0.841019i	$-0.681956\pi$
$643$	−27.4371			−1.08201			−0.541006	+	0.841019i	$0.681956\pi$
$644$	5.86725	−	6.01433i	0.231202	−	0.236998i
$645$	−0.286595			−0.0112847
$646$	38.5484	−	66.7679i	1.51667	−	2.62695i
$647$	−0.437768	−	0.758237i	−0.0172104	−	0.0298094i	0.857292	−	0.514831i	$-0.172145\pi$
$647$	−0.437768	−	0.758237i	−0.0172104	−	0.0298094i	−0.874502	+	0.485021i	$0.838812\pi$
$648$	−1.33740	−	2.31645i	−0.0525382	−	0.0909989i
$649$	2.31038	−	4.00169i	0.0906902	−	0.157080i
$650$	−7.17796			−0.281543
$651$	−3.89505	−	13.8485i	−0.152659	−	0.542767i
$652$	−5.23606			−0.205060
$653$	7.77433	−	13.4655i	0.304233	−	0.526947i	−0.672857	−	0.739772i	$-0.734933\pi$
$653$	7.77433	−	13.4655i	0.304233	−	0.526947i	0.977090	+	0.212825i	$0.0682665\pi$
$654$	20.7435	+	35.9287i	0.811134	+	1.40493i
$655$	2.37545	+	4.11440i	0.0928166	+	0.160763i
$656$	−0.335694	+	0.581440i	−0.0131067	+	0.0227014i
$657$	−4.27776			−0.166891
$658$	−77.9144	−	19.8468i	−3.03742	−	0.773710i
$659$	21.1989			0.825794			0.412897	−	0.910778i	$-0.364517\pi$
$659$	21.1989			0.825794			0.412897	+	0.910778i	$0.364517\pi$
$660$	−12.0504	+	20.8720i	−0.469063	+	0.812441i
$661$	4.32546	+	7.49192i	0.168241	+	0.291402i	0.937801	−	0.347172i	$-0.112858\pi$
$661$	4.32546	+	7.49192i	0.168241	+	0.291402i	−0.769560	+	0.638574i	$0.779525\pi$
$662$	23.4315	+	40.5845i	0.910690	+	1.57736i
$663$	2.23445	−	3.87019i	0.0867790	−	0.150306i
$664$	41.5122			1.61099
$665$	−21.9252	−	5.58491i	−0.850223	−	0.216574i
$666$	14.8938			0.577122
$667$	−1.68002	+	2.90988i	−0.0650507	+	0.112671i
$668$	−8.68014	−	15.0345i	−0.335845	−	0.581700i
$669$	1.24084	+	2.14919i	0.0479736	+	0.0830926i
$670$	−6.33225	+	10.9678i	−0.244636	+	0.423722i
$671$	21.9130			0.845942
$672$	4.26604	+	15.1676i	0.164566	+	0.585102i
$673$	−9.05137			−0.348905			−0.174452	−	0.984666i	$-0.555816\pi$
$673$	−9.05137			−0.348905			−0.174452	+	0.984666i	$0.555816\pi$
$674$	31.7402	−	54.9757i	1.22259	−	2.11758i
$675$	−1.73282	−	3.00133i	−0.0666962	−	0.115521i
$676$	19.3262	+	33.4739i	0.743314	+	1.28746i
$677$	8.44978	−	14.6354i	0.324751	−	0.562486i	−0.656711	−	0.754143i	$-0.728053\pi$
$677$	8.44978	−	14.6354i	0.324751	−	0.562486i	0.981462	+	0.191657i	$0.0613860\pi$
$678$	42.3028			1.62463
$679$	32.6045	−	33.4218i	1.25125	−	1.28261i
$680$	−16.2639			−0.623694
$681$	−11.0247	+	19.0954i	−0.422469	+	0.731738i
$682$	−37.8939	−	65.6341i	−1.45103	−	2.51326i
$683$	−11.3709	−	19.6950i	−0.435097	−	0.753610i	0.562207	−	0.826997i	$-0.309953\pi$
$683$	−11.3709	−	19.6950i	−0.435097	−	0.753610i	−0.997304	+	0.0733869i	$0.976619\pi$
$684$	10.9621	−	18.9870i	0.419148	−	0.725985i
$685$	−8.98854			−0.343434
$686$	40.2654	−	12.4085i	1.53734	−	0.473758i
$687$	−14.7467			−0.562621
$688$	−0.0307958	+	0.0533398i	−0.00117408	+	0.00203356i
$689$	−1.92404	−	3.33254i	−0.0733002	−	0.126960i
$690$	−1.40903	−	2.44051i	−0.0536408	−	0.0929086i
$691$	−17.5809	+	30.4511i	−0.668810	+	1.15841i	0.309427	+	0.950923i	$0.399863\pi$
$691$	−17.5809	+	30.4511i	−0.668810	+	1.15841i	−0.978237	+	0.207490i	$0.933471\pi$
$692$	−1.61699			−0.0614689
$693$	11.3192	−	11.6030i	0.429982	−	0.440761i
$694$	−4.74418			−0.180086
$695$	2.18115	−	3.77787i	0.0827359	−	0.143303i
$696$	4.49373	+	7.78338i	0.170335	+	0.295028i
$697$	6.19009	+	10.7215i	0.234466	+	0.406108i
$698$	4.59921	−	7.96606i	0.174083	−	0.301520i
$699$	3.41615			0.129211
$700$	−7.88410	−	28.0313i	−0.297991	−	1.05948i
$701$	−35.0402			−1.32345			−0.661725	−	0.749746i	$-0.730175\pi$
$701$	−35.0402			−1.32345			−0.661725	+	0.749746i	$0.730175\pi$
$702$	1.03559	−	1.79370i	0.0390858	−	0.0676987i
$703$	22.5981	+	39.1410i	0.852302	+	1.47623i
$704$	39.8722	+	69.0607i	1.50274	+	2.60282i
$705$	−8.27310	+	14.3294i	−0.311583	+	0.539678i
$706$	−10.2556			−0.385976
$707$	20.8463	+	5.31008i	0.784005	+	0.199706i
$708$	2.39514			0.0900147
$709$	24.8322	−	43.0106i	0.932593	−	1.61530i	0.153721	−	0.988114i	$-0.450874\pi$
$709$	24.8322	−	43.0106i	0.932593	−	1.61530i	0.778871	−	0.627184i	$-0.215793\pi$
$710$	22.3436	+	38.7003i	0.838542	+	1.45240i
$711$	0.111008	+	0.192271i	0.00416312	+	0.00721073i
$712$	−0.748095	+	1.29574i	−0.0280361	+	0.0485599i
$713$	5.43735			0.203630
$714$	28.6321	+	7.29332i	1.07153	+	0.272946i
$715$	−6.90911			−0.258386
$716$	−13.2600	+	22.9671i	−0.495551	+	0.858320i
$717$	−5.43756	−	9.41813i	−0.203069	−	0.351727i
$718$	23.6759	+	41.0078i	0.883576	+	1.53040i
$719$	−1.77044	+	3.06648i	−0.0660261	+	0.114361i	−0.897149	−	0.441729i	$-0.854365\pi$
$719$	−1.77044	+	3.06648i	−0.0660261	+	0.114361i	0.831123	+	0.556089i	$0.187699\pi$
$720$	0.329747			0.0122889
$721$	−10.2291	−	36.3689i	−0.380952	−	1.35445i
$722$	65.2046			2.42667
$723$	−10.6982	+	18.5299i	−0.397872	+	0.689134i
$724$	3.85630	+	6.67930i	0.143318	+	0.248234i
$725$	5.82234	+	10.0846i	0.216236	+	0.374532i
$726$	30.1854	−	52.2826i	1.12028	−	1.94039i
$727$	7.64097			0.283388			0.141694	−	0.989911i	$-0.454745\pi$
$727$	7.64097			0.283388			0.141694	+	0.989911i	$0.454745\pi$
$728$	4.49900	−	4.61178i	0.166744	−	0.170924i
$729$	1.00000			0.0370370
$730$	−6.02749	+	10.4399i	−0.223087	+	0.386399i
$731$	0.567863	+	0.983568i	0.0210032	+	0.0363786i
$732$	5.67923	+	9.83671i	0.209910	+	0.363575i
$733$	−10.0728	+	17.4466i	−0.372047	+	0.644404i	−0.989880	−	0.141905i	$-0.954677\pi$
$733$	−10.0728	+	17.4466i	−0.372047	+	0.644404i	0.617833	+	0.786309i	$0.288011\pi$
$734$	19.5019			0.719829
$735$	−0.214631	−	8.66820i	−0.00791679	−	0.319731i
$736$	−5.95524			−0.219513
$737$	13.7668	−	23.8449i	0.507108	−	0.878337i
$738$	2.86889	+	4.96906i	0.105605	+	0.182914i
$739$	−19.4540	−	33.6953i	−0.715626	−	1.23950i	−0.962718	−	0.270508i	$-0.912808\pi$
$739$	−19.4540	−	33.6953i	−0.715626	−	1.23950i	0.247092	−	0.968992i	$-0.420525\pi$
$740$	12.8765	−	22.3027i	0.473348	−	0.819863i
$741$	6.28513			0.230890
$742$	17.7660	−	18.2113i	0.652210	−	0.668560i
$743$	−12.5828			−0.461617			−0.230809	−	0.972999i	$-0.574137\pi$
$743$	−12.5828			−0.461617			−0.230809	+	0.972999i	$0.574137\pi$
$744$	7.27194	−	12.5954i	0.266602	−	0.461769i
$745$	−6.76591	−	11.7189i	−0.247884	−	0.429347i
$746$	1.65516	+	2.86682i	0.0605997	+	0.104962i
$747$	−7.75984	+	13.4404i	−0.283918	+	0.491760i
$748$	95.5077			3.49211
$749$	−4.69757	−	16.7018i	−0.171645	−	0.610272i
$750$	−23.8566			−0.871122
$751$	11.6128	−	20.1139i	0.423756	−	0.733966i	−0.572548	−	0.819871i	$-0.694045\pi$
$751$	11.6128	−	20.1139i	0.423756	−	0.733966i	0.996303	+	0.0859051i	$0.0273782\pi$
$752$	1.77796	+	3.07951i	0.0648354	+	0.112298i
$753$	2.34280	+	4.05784i	0.0853763	+	0.147876i
$754$	−3.47963	+	6.02689i	−0.126721	+	0.219486i
$755$	19.6377			0.714688
$756$	8.14219	+	2.07403i	0.296128	+	0.0754316i
$757$	−31.3210			−1.13838			−0.569191	−	0.822205i	$-0.692744\pi$
$757$	−31.3210			−1.13838			−0.569191	+	0.822205i	$0.692744\pi$
$758$	2.97311	−	5.14958i	0.107988	−	0.187041i
$759$	3.06335	+	5.30587i	0.111192	+	0.192591i
$760$	−11.4369	−	19.8093i	−0.414860	−	0.718559i
$761$	12.9385	−	22.4101i	0.469020	−	0.812367i	−0.530353	−	0.847777i	$-0.677941\pi$
$761$	12.9385	−	22.4101i	0.469020	−	0.812367i	0.999373	+	0.0354105i	$0.0112739\pi$
$762$	9.55070			0.345985
$763$	−46.7545	−	11.9096i	−1.69263	−	0.431156i
$764$	−45.3911			−1.64219
$765$	3.04021	−	5.26579i	0.109919	−	0.190385i
$766$	12.8769	+	22.3035i	0.465262	+	0.805858i
$767$	0.343312	+	0.594634i	0.0123963	+	0.0214710i
$768$	−7.11917	+	12.3308i	−0.256891	+	0.444948i
$769$	2.66864			0.0962338			0.0481169	−	0.998842i	$-0.484678\pi$
$769$	2.66864			0.0962338			0.0481169	+	0.998842i	$0.484678\pi$
$770$	−12.3680	−	43.9736i	−0.445713	−	1.58470i
$771$	27.0174			0.973008
$772$	−3.31871	+	5.74818i	−0.119443	+	0.206881i
$773$	2.89143	+	5.00811i	0.103998	+	0.180129i	0.913328	−	0.407224i	$-0.133503\pi$
$773$	2.89143	+	5.00811i	0.103998	+	0.180129i	−0.809331	+	0.587353i	$0.800170\pi$
$774$	0.263184	+	0.455849i	0.00945997	+	0.0163851i
$775$	9.42195	−	16.3193i	0.338446	−	0.586206i
$776$	47.2041			1.69453
$777$	−12.0951	+	12.3983i	−0.433910	+	0.444787i
$778$	−70.4598			−2.52611
$779$	−8.70582	+	15.0789i	−0.311918	+	0.540259i
$780$	−1.79065	−	3.10149i	−0.0641154	−	0.111051i
$781$	−48.5769	−	84.1377i	−1.73822	−	3.01068i
$782$	−5.58374	+	9.67131i	−0.199674	+	0.345845i
$783$	−3.36004			−0.120078
$784$	−1.63635	−	0.891486i	−0.0584411	−	0.0318388i
$785$	11.3959			0.406738
$786$	4.36283	−	7.55664i	0.155617	−	0.269536i
$787$	3.77728	+	6.54244i	0.134645	+	0.233213i	0.925462	−	0.378841i	$-0.123677\pi$
$787$	3.77728	+	6.54244i	0.134645	+	0.233213i	−0.790817	+	0.612053i	$0.790344\pi$
$788$	−17.2859	−	29.9401i	−0.615785	−	1.06657i
$789$	−10.0032	+	17.3260i	−0.356122	+	0.616822i
$790$	0.625652			0.0222597
$791$	−34.3538	+	35.2150i	−1.22148	+	1.25210i
$792$	16.3877			0.582313
$793$	−1.62809	+	2.81993i	−0.0578151	+	0.100139i
$794$	−28.4828	−	49.3336i	−1.01082	−	1.75078i
$795$	−2.61786	−	4.53427i	−0.0928460	−	0.160814i
$796$	−5.46310	+	9.46236i	−0.193634	+	0.335384i
$797$	−17.6173			−0.624035			−0.312018	−	0.950076i	$-0.601005\pi$
$797$	−17.6173			−0.624035			−0.312018	+	0.950076i	$0.601005\pi$
$798$	11.2511	+	40.0022i	0.398283	+	1.41606i
$799$	65.5698			2.31969
$800$	−10.3194	+	17.8736i	−0.364844	+	0.631929i
$801$	−0.279682	−	0.484423i	−0.00988207	−	0.0171162i
$802$	−39.7839	−	68.9077i	−1.40482	−	2.43322i
$803$	13.1043	−	22.6973i	0.462440	−	0.800969i
$804$	14.2719			0.503331
$805$	3.17586	+	0.808974i	0.111934	+	0.0285126i
$806$	11.2617			0.396678
$807$	−3.14036	+	5.43926i	−0.110546	+	0.191471i
$808$	10.8741	+	18.8345i	0.382550	+	0.662596i
$809$	−11.6420	−	20.1646i	−0.409312	−	0.708950i	0.585501	−	0.810672i	$-0.300898\pi$
$809$	−11.6420	−	20.1646i	−0.409312	−	0.708950i	−0.994813	+	0.101722i	$0.967565\pi$
$810$	1.40903	−	2.44051i	0.0495082	−	0.0857507i
$811$	35.2946			1.23936			0.619680	−	0.784855i	$-0.287262\pi$
$811$	35.2946			1.23936			0.619680	+	0.784855i	$0.287262\pi$
$812$	−27.3581	−	6.96881i	−0.960080	−	0.244557i
$813$	−25.4203			−0.891527
$814$	−45.6248	+	79.0245i	−1.59915	+	2.76981i
$815$	−1.02116	−	1.76871i	−0.0357698	−	0.0619550i
$816$	−0.653365	−	1.13166i	−0.0228723	−	0.0396160i
$817$	−0.798650	+	1.38330i	−0.0279412	+	0.0483956i
$818$	−54.9883			−1.92262
$819$	0.652165	+	2.31872i	0.0227885	+	0.0810228i
$820$	9.92122			0.346464
$821$	−0.934194	+	1.61807i	−0.0326036	+	0.0564711i	−0.881867	−	0.471499i	$-0.843713\pi$
$821$	−0.934194	+	1.61807i	−0.0326036	+	0.0564711i	0.849263	+	0.527970i	$0.177047\pi$
$822$	8.25431	+	14.2969i	0.287902	+	0.498661i
$823$	9.72518	+	16.8445i	0.338999	+	0.587163i	0.984245	−	0.176812i	$-0.0565785\pi$
$823$	9.72518	+	16.8445i	0.338999	+	0.587163i	−0.645246	+	0.763975i	$0.723245\pi$
$824$	19.0975	−	33.0778i	0.665292	−	1.15232i
$825$	21.2329			0.739234
$826$	−3.17003	+	3.24950i	−0.110300	+	0.113064i
$827$	11.1883			0.389055			0.194527	−	0.980897i	$-0.437683\pi$
$827$	11.1883			0.389055			0.194527	+	0.980897i	$0.437683\pi$
$828$	−1.58786	+	2.75026i	−0.0551821	+	0.0955782i
$829$	−0.299484	−	0.518721i	−0.0104015	−	0.0180159i	0.860778	−	0.508981i	$-0.169978\pi$
$829$	−0.299484	−	0.518721i	−0.0104015	−	0.0180159i	−0.871179	+	0.490965i	$0.836644\pi$
$830$	21.8677	+	37.8759i	0.759038	+	1.31469i
$831$	−7.57054	+	13.1126i	−0.262619	+	0.454869i
$832$	−11.8497			−0.410814
$833$	−29.3232	+	17.9119i	−1.01599	+	0.620610i
$834$	−8.01195			−0.277431
$835$	3.38569	−	5.86419i	0.117167	−	0.202939i
$836$	67.1616	+	116.327i	2.32283	+	4.02327i
$837$	2.71868	+	4.70889i	0.0939712	+	0.162763i
$838$	22.6803	−	39.2834i	0.783477	−	1.35702i
$839$	−43.0684			−1.48689			−0.743443	−	0.668799i	$-0.766809\pi$
$839$	−43.0684			−1.48689			−0.743443	+	0.668799i	$0.766809\pi$
$840$	6.12136	−	6.27481i	0.211207	−	0.216501i
$841$	−17.7101			−0.610694
$842$	41.0645	−	71.1259i	1.41518	−	2.45116i
$843$	−13.6575	−	23.6554i	−0.470388	−	0.814736i
$844$	−18.5287	−	32.0927i	−0.637785	−	1.10468i
$845$	−7.53818	+	13.0565i	−0.259321	+	0.449157i
$846$	30.3893			1.04480
$847$	19.0093	+	67.5861i	0.653168	+	2.32229i
$848$	−1.12520			−0.0386395
$849$	4.27130	−	7.39812i	0.146591	−	0.253903i
$850$	19.3512	+	33.5173i	0.663741	+	1.14963i
$851$	−3.27333	−	5.66957i	−0.112208	−	0.194350i
$852$	25.1795	−	43.6122i	0.862636	−	1.49413i
$853$	32.0125			1.09609			0.548043	−	0.836450i	$-0.315373\pi$
$853$	32.0125			1.09609			0.548043	+	0.836450i	$0.315373\pi$
$854$	−20.8622	−	5.31413i	−0.713888	−	0.181846i
$855$	8.55157			0.292458
$856$	8.77022	−	15.1905i	0.299760	−	0.519199i
$857$	22.8842	+	39.6366i	0.781710	+	1.35396i	0.930945	+	0.365160i	$0.118986\pi$
$857$	22.8842	+	39.6366i	0.781710	+	1.35396i	−0.149235	+	0.988802i	$0.547681\pi$
$858$	6.34474	+	10.9894i	0.216606	+	0.375172i
$859$	21.6245	−	37.4548i	0.737820	−	1.27794i	−0.215656	−	0.976470i	$-0.569189\pi$
$859$	21.6245	−	37.4548i	0.737820	−	1.27794i	0.953475	−	0.301472i	$-0.0974778\pi$
$860$	0.910147			0.0310358
$861$	−6.46629	−	1.64713i	−0.220371	−	0.0561341i
$862$	24.7243			0.842112
$863$	18.0192	−	31.2101i	0.613380	−	1.06241i	−0.377286	−	0.926097i	$-0.623143\pi$
$863$	18.0192	−	31.2101i	0.613380	−	1.06241i	0.990666	−	0.136309i	$-0.0435239\pi$
$864$	−2.97762	−	5.15739i	−0.101301	−	0.175458i
$865$	−0.315354	−	0.546210i	−0.0107224	−	0.0185717i
$866$	29.7912	−	51.5999i	1.01235	−	1.75344i
$867$	−7.09562			−0.240980
$868$	12.3696	+	43.9792i	0.419852	+	1.49275i
$869$	−1.36022			−0.0461423
$870$	−4.73439	+	8.20021i	−0.160511	+	0.278013i
$871$	2.04569	+	3.54325i	0.0693157	+	0.120058i
$872$	−24.3887	−	42.2425i	−0.825905	−	1.43051i
$873$	−8.82382	+	15.2833i	−0.298641	+	0.517261i
$874$	−15.7061			−0.531266
$875$	19.3738	−	19.8595i	0.654954	−	0.671372i
$876$	13.5850			0.458995
$877$	−13.4716	+	23.3335i	−0.454903	+	0.787915i	−0.998683	−	0.0513130i	$-0.983659\pi$
$877$	−13.4716	+	23.3335i	−0.454903	+	0.787915i	0.543780	+	0.839228i	$0.316993\pi$
$878$	35.7249	+	61.8773i	1.20566	+	2.08826i
$879$	6.80764	+	11.7912i	0.229616	+	0.397707i
$880$	−1.01013	+	1.74959i	−0.0340514	+	0.0589788i
$881$	−36.5231			−1.23050			−0.615248	−	0.788334i	$-0.710944\pi$
$881$	−36.5231			−1.23050			−0.615248	+	0.788334i	$0.710944\pi$
$882$	−13.5903	+	8.30153i	−0.457608	+	0.279527i
$883$	−54.7823			−1.84357			−0.921785	−	0.387702i	$-0.873269\pi$
$883$	−54.7823			−1.84357			−0.921785	+	0.387702i	$0.873269\pi$
$884$	−7.09602	+	12.2907i	−0.238665	+	0.413380i
$885$	0.467112	+	0.809061i	0.0157018	+	0.0271963i
$886$	10.3273	+	17.8874i	0.346953	+	0.600940i
$887$	6.87188	−	11.9024i	0.230735	−	0.399645i	−0.727289	−	0.686331i	$-0.759220\pi$
$887$	6.87188	−	11.9024i	0.230735	−	0.399645i	0.958025	+	0.286686i	$0.0925535\pi$
$888$	−17.5110			−0.587632
$889$	−7.75605	+	7.95047i	−0.260130	+	0.266650i
$890$	−1.57632			−0.0528383
$891$	−3.06335	+	5.30587i	−0.102626	+	0.177753i
$892$	−3.94056	−	6.82526i	−0.131940	−	0.228527i
$893$	46.1091	+	79.8633i	1.54298	+	2.67252i
$894$	−12.4265	+	21.5233i	−0.415604	+	0.719847i
$895$	−10.3442			−0.345767
$896$	−12.6801	−	45.0831i	−0.423613	−	1.50612i
$897$	−0.910400			−0.0303974
$898$	−27.2284	+	47.1611i	−0.908625	+	1.57378i
$899$	−9.13486	−	15.8220i	−0.304665	−	0.527695i
$900$	5.50296	+	9.53141i	0.183432	+	0.317714i
$901$	−10.3741	+	17.9685i	−0.345612	+	0.598618i
$902$	−35.1536			−1.17049
$903$	−0.593201	−	0.151104i	−0.0197405	−	0.00502842i
$904$	−49.7366			−1.65422
$905$	−1.50415	+	2.60526i	−0.0499996	+	0.0866019i
$906$	−18.0336	−	31.2351i	−0.599126	−	1.03772i
$907$	10.9920	+	19.0388i	0.364985	+	0.632172i	0.988774	−	0.149421i	$-0.0477409\pi$
$907$	10.9920	+	19.0388i	0.364985	+	0.632172i	−0.623789	+	0.781593i	$0.714408\pi$
$908$	35.0116	−	60.6418i	1.16190	−	2.01247i
$909$	−8.13075			−0.269680
$910$	6.57778	+	1.67553i	0.218051	+	0.0555433i
$911$	−17.3602			−0.575170			−0.287585	−	0.957755i	$-0.592852\pi$
$911$	−17.3602			−0.575170			−0.287585	+	0.957755i	$0.592852\pi$
$912$	0.918900	−	1.59158i	0.0304278	−	0.0527026i
$913$	−47.5421	−	82.3454i	−1.57341	−	2.72523i
$914$	5.47183	+	9.47750i	0.180992	+	0.313488i
$915$	−2.21518	+	3.83681i	−0.0732317	+	0.126841i
$916$	46.8315			1.54735
$917$	2.74750	+	9.76853i	0.0907305	+	0.322585i
$918$	−11.1675			−0.368581
$919$	−2.57423	+	4.45869i	−0.0849159	+	0.147079i	−0.905355	−	0.424655i	$-0.860395\pi$
$919$	−2.57423	+	4.45869i	−0.0849159	+	0.147079i	0.820439	+	0.571733i	$0.193729\pi$
$920$	1.65663	+	2.86938i	0.0546176	+	0.0946005i
$921$	−0.972468	−	1.68436i	−0.0320439	−	0.0555017i
$922$	−26.6967	+	46.2401i	−0.879210	+	1.52284i
$923$	14.4367			0.475188
$924$	−35.9468	+	36.8479i	−1.18256	+	1.21221i
$925$	−22.6883			−0.745988
$926$	−26.6568	+	46.1709i	−0.875996	+	1.51727i
$927$	7.13975	+	12.3664i	0.234500	+	0.406166i
$928$	10.0049	+	17.3290i	0.328428	+	0.568854i
$929$	−6.23246	+	10.7949i	−0.204480	+	0.354170i	−0.949967	−	0.312350i	$-0.898884\pi$
$929$	−6.23246	+	10.7949i	−0.204480	+	0.354170i	0.745487	+	0.666520i	$0.232217\pi$
$930$	15.3228			0.502453
$931$	−42.4367	−	23.1196i	−1.39081	−	0.757714i
$932$	−10.8488			−0.355363
$933$	−7.10098	+	12.2993i	−0.232476	+	0.402660i
$934$	−15.3002	−	26.5007i	−0.500636	−	0.867128i
$935$	18.6264	+	32.2619i	0.609148	+	1.05508i
$936$	−1.21757	+	2.10890i	−0.0397976	+	0.0689315i
$937$	−1.66532			−0.0544038			−0.0272019	−	0.999630i	$-0.508660\pi$
$937$	−1.66532			−0.0544038			−0.0272019	+	0.999630i	$0.508660\pi$
$938$	−18.8893	+	19.3628i	−0.616757	+	0.632217i
$939$	4.20457			0.137211
$940$	26.2731	−	45.5064i	0.856935	−	1.48426i
$941$	17.0831	+	29.5887i	0.556892	+	0.964565i	0.997754	+	0.0669898i	$0.0213395\pi$
$941$	17.0831	+	29.5887i	0.556892	+	0.964565i	−0.440862	+	0.897575i	$0.645327\pi$
$942$	−10.4651	−	18.1260i	−0.340970	−	0.590577i
$943$	1.26104	−	2.18418i	0.0410650	−	0.0711267i
$944$	0.200772			0.00653457
$945$	0.887339	+	3.15486i	0.0288651	+	0.102628i
$946$	−3.22490			−0.104851
$947$	−26.1581	+	45.3071i	−0.850024	+	1.47228i	0.0311620	+	0.999514i	$0.490079\pi$
$947$	−26.1581	+	45.3071i	−0.850024	+	1.47228i	−0.881186	+	0.472770i	$0.843254\pi$
$948$	−0.352530	−	0.610601i	−0.0114497	−	0.0198314i
$949$	1.94724	+	3.37272i	0.0632100	+	0.109483i
$950$	−27.2158	+	47.1391i	−0.882997	+	1.52940i
$951$	−0.738433			−0.0239453
$952$	−33.6635	−	8.57497i	−1.09104	−	0.277916i
$953$	−35.3873			−1.14631			−0.573154	−	0.819448i	$-0.694280\pi$
$953$	−35.3873			−1.14631			−0.573154	+	0.819448i	$0.694280\pi$
$954$	−4.80804	+	8.32778i	−0.155666	+	0.269622i
$955$	−8.85240	−	15.3328i	−0.286457	−	0.496158i
$956$	17.2682	+	29.9094i	0.558494	+	0.967340i
$957$	10.2930	−	17.8279i	0.332724	−	0.576295i
$958$	15.3829			0.496998
$959$	−18.6047	−	4.73910i	−0.600777	−	0.153033i
$960$	−16.1227			−0.520358
$961$	0.717600	−	1.24292i	0.0231484	−	0.0400942i
$962$	−6.77965	−	11.7427i	−0.218585	−	0.378600i
$963$	3.27882	+	5.67908i	0.105658	+	0.183006i
$964$	33.9747	−	58.8459i	1.09425	−	1.89530i
$965$	−2.58893			−0.0833406
$966$	−1.62971	−	5.79432i	−0.0524352	−	0.186429i
$967$	−1.97543			−0.0635254			−0.0317627	−	0.999495i	$-0.510112\pi$
$967$	−1.97543			−0.0635254			−0.0317627	+	0.999495i	$0.510112\pi$
$968$	−35.4898	+	61.4702i	−1.14069	+	1.97573i
$969$	−16.9442	−	29.3482i	−0.544326	−	0.942801i
$970$	24.8660	+	43.0692i	0.798400	+	1.38287i
$971$	14.3768	−	24.9013i	0.461373	−	0.799122i	−0.537657	−	0.843164i	$-0.680690\pi$
$971$	14.3768	−	24.9013i	0.461373	−	0.799122i	0.999030	+	0.0440423i	$0.0140236\pi$
$972$	−3.17573			−0.101862
$973$	6.50644	−	6.66954i	0.208587	−	0.213816i
$974$	45.1969			1.44820
$975$	−1.57756	+	2.73241i	−0.0505223	+	0.0875072i
$976$	0.476061	+	0.824561i	0.0152383	+	0.0263936i
$977$	5.36870	+	9.29886i	0.171760	+	0.297497i	0.939035	−	0.343821i	$-0.111721\pi$
$977$	5.36870	+	9.29886i	0.171760	+	0.297497i	−0.767275	+	0.641318i	$0.778388\pi$
$978$	−1.87550	+	3.24846i	−0.0599718	+	0.103874i
$979$	3.42705			0.109529
$980$	0.681610	+	27.5278i	0.0217732	+	0.879345i
$981$	18.2358			0.582226
$982$	−4.78141	+	8.28164i	−0.152581	+	0.264278i
$983$	23.1383	+	40.0767i	0.737997	+	1.27825i	0.953396	+	0.301722i	$0.0975616\pi$
$983$	23.1383	+	40.0767i	0.737997	+	1.27825i	−0.215399	+	0.976526i	$0.569105\pi$
$984$	−3.37303	−	5.84226i	−0.107528	−	0.186245i
$985$	6.74238	−	11.6781i	0.214830	−	0.372096i
$986$	37.5232			1.19498
$987$	−24.6789	+	25.2975i	−0.785538	+	0.805229i
$988$	−19.9599			−0.635008
$989$	0.115684	−	0.200371i	0.00367855	−	0.00637143i
$990$	8.63268	+	14.9522i	0.274365	+	0.475213i
$991$	21.4876	+	37.2176i	0.682576	+	1.18226i	0.974192	+	0.225721i	$0.0724739\pi$
$991$	21.4876	+	37.2176i	0.682576	+	1.18226i	−0.291616	+	0.956536i	$0.594193\pi$
$992$	16.1904	−	28.0425i	0.514045	−	0.890352i
$993$	20.5989			0.653686
$994$	25.8431	+	91.8833i	0.819695	+	2.91436i
$995$	−4.26176			−0.135107
$996$	24.6431	−	42.6832i	0.780848	−	1.35247i
$997$	6.04080	+	10.4630i	0.191314	+	0.331365i	0.945686	−	0.325082i	$-0.105392\pi$
$997$	6.04080	+	10.4630i	0.191314	+	0.331365i	−0.754372	+	0.656447i	$0.772058\pi$
$998$	−7.90388	−	13.6899i	−0.250193	−	0.433347i
$999$	3.27333	−	5.66957i	0.103563	−	0.179377i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.i.h.415.3	yes	20
7.2	even	3		3381.2.a.bi.1.8		10
7.4	even	3	inner	483.2.i.h.277.3	✓	20
7.5	odd	6		3381.2.a.bj.1.8		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.i.h.277.3	✓	20	7.4	even	3	inner
483.2.i.h.415.3	yes	20	1.1	even	1	trivial
3381.2.a.bi.1.8		10	7.2	even	3
3381.2.a.bj.1.8		10	7.5	odd	6

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.13751 + 1.97023i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.58786 - 2.75026i) q^{4} +(0.619347 - 1.07274i) q^{5} -2.27502 q^{6} +(1.84753 - 1.89384i) q^{7} +2.67481 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.13751 + 1.97023i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.58786 - 2.75026i) q^{4} +(0.619347 - 1.07274i) q^{5} -2.27502 q^{6} +(1.84753 - 1.89384i) q^{7} +2.67481 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.40903 + 2.44051i) q^{10} +(-3.06335 - 5.30587i) q^{11} +(1.58786 - 2.75026i) q^{12} +0.910400 q^{13} +(1.62971 + 5.79432i) q^{14} +1.23869 q^{15} +(0.133103 - 0.230540i) q^{16} +(-2.45436 - 4.25108i) q^{17} +(-1.13751 - 1.97023i) q^{18} +(3.45185 - 5.97878i) q^{19} -3.93376 q^{20} +(2.56388 + 0.653086i) q^{21} +13.9384 q^{22} +(-0.500000 + 0.866025i) q^{23} +(1.33740 + 2.31645i) q^{24} +(1.73282 + 3.00133i) q^{25} +(-1.03559 + 1.79370i) q^{26} -1.00000 q^{27} +(-8.14219 - 2.07403i) q^{28} +3.36004 q^{29} +(-1.40903 + 2.44051i) q^{30} +(-2.71868 - 4.70889i) q^{31} +(2.97762 + 5.15739i) q^{32} +(3.06335 - 5.30587i) q^{33} +11.1675 q^{34} +(-0.887339 - 3.15486i) q^{35} +3.17573 q^{36} +(-3.27333 + 5.66957i) q^{37} +(7.85304 + 13.6019i) q^{38} +(0.455200 + 0.788430i) q^{39} +(1.65663 - 2.86938i) q^{40} -2.52207 q^{41} +(-4.20317 + 4.30853i) q^{42} -0.231369 q^{43} +(-9.72835 + 16.8500i) q^{44} +(0.619347 + 1.07274i) q^{45} +(-1.13751 - 1.97023i) q^{46} +(-6.67889 + 11.5682i) q^{47} +0.266205 q^{48} +(-0.173272 - 6.99786i) q^{49} -7.88440 q^{50} +(2.45436 - 4.25108i) q^{51} +(-1.44559 - 2.50384i) q^{52} +(-2.11340 - 3.66052i) q^{53} +(1.13751 - 1.97023i) q^{54} -7.58909 q^{55} +(4.94179 - 5.06567i) q^{56} +6.90370 q^{57} +(-3.82209 + 6.62005i) q^{58} +(0.377100 + 0.653157i) q^{59} +(-1.96688 - 3.40673i) q^{60} +(-1.78832 + 3.09747i) q^{61} +12.3701 q^{62} +(0.716350 + 2.54693i) q^{63} -13.0159 q^{64} +(0.563853 - 0.976623i) q^{65} +(6.96918 + 12.0710i) q^{66} +(2.24703 + 3.89197i) q^{67} +(-7.79440 + 13.5003i) q^{68} -1.00000 q^{69} +(7.22516 + 1.84043i) q^{70} +15.8575 q^{71} +(-1.33740 + 2.31645i) q^{72} +(2.13888 + 3.70465i) q^{73} +(-7.44689 - 12.8984i) q^{74} +(-1.73282 + 3.00133i) q^{75} -21.9243 q^{76} +(-15.7081 - 4.00126i) q^{77} -2.07118 q^{78} +(0.111008 - 0.192271i) q^{79} +(-0.164873 - 0.285569i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.86889 - 4.96906i) q^{82} +15.5197 q^{83} +(-2.27493 - 8.08835i) q^{84} -6.08041 q^{85} +(0.263184 - 0.455849i) q^{86} +(1.68002 + 2.90988i) q^{87} +(-8.19386 - 14.1922i) q^{88} +(-0.279682 + 0.484423i) q^{89} -2.81806 q^{90} +(1.68199 - 1.72415i) q^{91} +3.17573 q^{92} +(2.71868 - 4.70889i) q^{93} +(-15.1946 - 26.3179i) q^{94} +(-4.27579 - 7.40588i) q^{95} +(-2.97762 + 5.15739i) q^{96} +17.6476 q^{97} +(13.9845 + 7.61875i) q^{98} +6.12669 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 3 q^{2} + 10 q^{3} - 15 q^{4} + 5 q^{5} - 6 q^{6} + 18 q^{8} - 10 q^{9}+O(q^{10}) \) 20 * q - 3 * q^2 + 10 * q^3 - 15 * q^4 + 5 * q^5 - 6 * q^6 + 18 * q^8 - 10 * q^9	\( 20 q - 3 q^{2} + 10 q^{3} - 15 q^{4} + 5 q^{5} - 6 q^{6} + 18 q^{8} - 10 q^{9} - 11 q^{10} - 8 q^{11} + 15 q^{12} + 11 q^{14} + 10 q^{15} - 37 q^{16} + 11 q^{17} - 3 q^{18} - q^{19} - 30 q^{20} + 12 q^{22} - 10 q^{23} + 9 q^{24} - 21 q^{25} - q^{26} - 20 q^{27} + 44 q^{28} + 44 q^{29} + 11 q^{30} + 3 q^{31} - 11 q^{32} + 8 q^{33} - 6 q^{34} - 9 q^{35} + 30 q^{36} + 3 q^{37} - 16 q^{38} - 39 q^{40} - 52 q^{41} + 7 q^{42} + 54 q^{43} - 16 q^{44} + 5 q^{45} - 3 q^{46} - 11 q^{47} - 74 q^{48} + 22 q^{49} + 4 q^{50} - 11 q^{51} - 29 q^{52} - 5 q^{53} + 3 q^{54} - 36 q^{55} + 43 q^{56} - 2 q^{57} - 16 q^{58} + 10 q^{59} - 15 q^{60} - 22 q^{61} - 64 q^{62} + 138 q^{64} + 11 q^{65} + 6 q^{66} + 2 q^{67} + 21 q^{68} - 20 q^{69} + 84 q^{70} + 54 q^{71} - 9 q^{72} + 8 q^{73} - 14 q^{74} + 21 q^{75} - 44 q^{76} + 8 q^{77} - 2 q^{78} - 21 q^{79} + 53 q^{80} - 10 q^{81} - 36 q^{82} - 24 q^{83} + 25 q^{84} + 46 q^{85} - 18 q^{86} + 22 q^{87} + 10 q^{88} - 6 q^{89} + 22 q^{90} - 62 q^{91} + 30 q^{92} - 3 q^{93} - 35 q^{94} - 44 q^{95} + 11 q^{96} + 12 q^{97} + 2 q^{98} + 16 q^{99}+O(q^{100}) \) 20 * q - 3 * q^2 + 10 * q^3 - 15 * q^4 + 5 * q^5 - 6 * q^6 + 18 * q^8 - 10 * q^9 - 11 * q^10 - 8 * q^11 + 15 * q^12 + 11 * q^14 + 10 * q^15 - 37 * q^16 + 11 * q^17 - 3 * q^18 - q^19 - 30 * q^20 + 12 * q^22 - 10 * q^23 + 9 * q^24 - 21 * q^25 - q^26 - 20 * q^27 + 44 * q^28 + 44 * q^29 + 11 * q^30 + 3 * q^31 - 11 * q^32 + 8 * q^33 - 6 * q^34 - 9 * q^35 + 30 * q^36 + 3 * q^37 - 16 * q^38 - 39 * q^40 - 52 * q^41 + 7 * q^42 + 54 * q^43 - 16 * q^44 + 5 * q^45 - 3 * q^46 - 11 * q^47 - 74 * q^48 + 22 * q^49 + 4 * q^50 - 11 * q^51 - 29 * q^52 - 5 * q^53 + 3 * q^54 - 36 * q^55 + 43 * q^56 - 2 * q^57 - 16 * q^58 + 10 * q^59 - 15 * q^60 - 22 * q^61 - 64 * q^62 + 138 * q^64 + 11 * q^65 + 6 * q^66 + 2 * q^67 + 21 * q^68 - 20 * q^69 + 84 * q^70 + 54 * q^71 - 9 * q^72 + 8 * q^73 - 14 * q^74 + 21 * q^75 - 44 * q^76 + 8 * q^77 - 2 * q^78 - 21 * q^79 + 53 * q^80 - 10 * q^81 - 36 * q^82 - 24 * q^83 + 25 * q^84 + 46 * q^85 - 18 * q^86 + 22 * q^87 + 10 * q^88 - 6 * q^89 + 22 * q^90 - 62 * q^91 + 30 * q^92 - 3 * q^93 - 35 * q^94 - 44 * q^95 + 11 * q^96 + 12 * q^97 + 2 * q^98 + 16 * q^99

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