LMFDB - Embedded newform 370.2.l.c.101.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(11,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("370.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.l (of order $6$, 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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.116304318664704.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{11} + x^{10} + 6x^{9} - 9x^{8} - 2x^{7} + 18x^{6} - 4x^{5} - 36x^{4} + 48x^{3} + 16x^{2} - 64x + 64 $ x^12 - 2x^11 + x^10 + 6x^9 - 9x^8 - 2x^7 + 18x^6 - 4x^5 - 36x^4 + 48x^3 + 16x^2 - 64x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.4
Root			$0.742163 + 1.20382i$ of defining polynomial
Character	$\chi$	$=$	370.101
Dual form			370.2.l.c.11.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(-0.671462 - 1.16301i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} -1.34292i q^{6} +(-1.45444 - 2.51917i) q^{7} +1.00000i q^{8} +(0.598279 - 1.03625i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(-0.671462 - 1.16301i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} -1.34292i q^{6} +(-1.45444 - 2.51917i) q^{7} +1.00000i q^{8} +(0.598279 - 1.03625i) q^{9} +1.00000 q^{10} -0.580401 q^{11} +(0.671462 - 1.16301i) q^{12} +(3.38520 - 1.95444i) q^{13} -2.90889i q^{14} +(-1.16301 - 0.671462i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.0603530 + 0.0348448i) q^{17} +(1.03625 - 0.598279i) q^{18} +(1.82413 - 1.05316i) q^{19} +(0.866025 + 0.500000i) q^{20} +(-1.95321 + 3.38305i) q^{21} +(-0.502642 - 0.290201i) q^{22} -2.38825i q^{23} +(1.16301 - 0.671462i) q^{24} +(0.500000 - 0.866025i) q^{25} +3.90889 q^{26} -5.63565 q^{27} +(1.45444 - 2.51917i) q^{28} +1.17137i q^{29} +(-0.671462 - 1.16301i) q^{30} +7.68209i q^{31} +(-0.866025 + 0.500000i) q^{32} +(0.389717 + 0.675010i) q^{33} +(0.0348448 + 0.0603530i) q^{34} +(-2.51917 - 1.45444i) q^{35} +1.19656 q^{36} +(5.40900 - 2.78257i) q^{37} +2.10632 q^{38} +(-4.54606 - 2.62467i) q^{39} +(0.500000 + 0.866025i) q^{40} +(5.13662 + 8.89689i) q^{41} +(-3.38305 + 1.95321i) q^{42} -0.658184i q^{43} +(-0.290201 - 0.502642i) q^{44} -1.19656i q^{45} +(1.19413 - 2.06829i) q^{46} -4.39031 q^{47} +1.34292 q^{48} +(-0.730813 + 1.26581i) q^{49} +(0.866025 - 0.500000i) q^{50} -0.0935879i q^{51} +(3.38520 + 1.95444i) q^{52} +(-0.701343 + 1.21476i) q^{53} +(-4.88062 - 2.81783i) q^{54} +(-0.502642 + 0.290201i) q^{55} +(2.51917 - 1.45444i) q^{56} +(-2.44966 - 1.41431i) q^{57} +(-0.585685 + 1.01444i) q^{58} +(-5.65114 - 3.26269i) q^{59} -1.34292i q^{60} +(-11.5509 + 6.66893i) q^{61} +(-3.84104 + 6.65288i) q^{62} -3.48065 q^{63} -1.00000 q^{64} +(1.95444 - 3.38520i) q^{65} +0.779434i q^{66} +(5.97361 + 10.3466i) q^{67} +0.0696897i q^{68} +(-2.77755 + 1.60362i) q^{69} +(-1.45444 - 2.51917i) q^{70} +(5.69900 + 9.87096i) q^{71} +(1.03625 + 0.598279i) q^{72} -0.566789 q^{73} +(6.07562 + 0.294725i) q^{74} -1.34292 q^{75} +(1.82413 + 1.05316i) q^{76} +(0.844161 + 1.46213i) q^{77} +(-2.62467 - 4.54606i) q^{78} +(-2.04694 + 1.18180i) q^{79} +1.00000i q^{80} +(1.98929 + 3.44555i) q^{81} +10.2732i q^{82} +(-4.57125 + 7.91763i) q^{83} -3.90641 q^{84} +0.0696897 q^{85} +(0.329092 - 0.570004i) q^{86} +(1.36231 - 0.786530i) q^{87} -0.580401i q^{88} +(3.16126 + 1.82516i) q^{89} +(0.598279 - 1.03625i) q^{90} +(-9.84715 - 5.68526i) q^{91} +(2.06829 - 1.19413i) q^{92} +(8.93431 - 5.15823i) q^{93} +(-3.80212 - 2.19515i) q^{94} +(1.05316 - 1.82413i) q^{95} +(1.16301 + 0.671462i) q^{96} -0.619286i q^{97} +(-1.26581 + 0.730813i) q^{98} +(-0.347242 + 0.601440i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{3} + 6 q^{4} + 2 q^{7} - 2 q^{9}+O(q^{10}) $ 12 * q + 4 * q^3 + 6 * q^4 + 2 * q^7 - 2 * q^9	$ 12 q + 4 q^{3} + 6 q^{4} + 2 q^{7} - 2 q^{9} + 12 q^{10} - 16 q^{11} - 4 q^{12} + 6 q^{13} - 6 q^{16} - 6 q^{17} + 18 q^{19} - 14 q^{21} + 6 q^{22} + 6 q^{25} + 8 q^{26} - 32 q^{27} - 2 q^{28} + 4 q^{30} - 10 q^{33} - 10 q^{34} - 6 q^{35} - 4 q^{36} - 26 q^{37} + 8 q^{38} + 18 q^{39} + 6 q^{40} + 4 q^{41} + 18 q^{42} - 8 q^{44} - 4 q^{46} - 20 q^{47} - 8 q^{48} + 2 q^{49} + 6 q^{52} - 2 q^{53} + 6 q^{55} + 6 q^{56} + 36 q^{57} + 8 q^{58} + 12 q^{59} + 24 q^{61} + 10 q^{62} - 16 q^{63} - 12 q^{64} + 4 q^{65} + 28 q^{67} - 6 q^{69} + 2 q^{70} - 40 q^{71} - 12 q^{73} + 14 q^{74} + 8 q^{75} + 18 q^{76} - 24 q^{77} - 10 q^{78} + 24 q^{79} - 6 q^{81} - 16 q^{83} - 28 q^{84} - 20 q^{85} - 16 q^{86} - 24 q^{87} + 6 q^{89} - 2 q^{90} - 18 q^{91} + 6 q^{92} + 78 q^{93} + 4 q^{95} - 12 q^{98} + 22 q^{99}+O(q^{100}) $ 12 * q + 4 * q^3 + 6 * q^4 + 2 * q^7 - 2 * q^9 + 12 * q^10 - 16 * q^11 - 4 * q^12 + 6 * q^13 - 6 * q^16 - 6 * q^17 + 18 * q^19 - 14 * q^21 + 6 * q^22 + 6 * q^25 + 8 * q^26 - 32 * q^27 - 2 * q^28 + 4 * q^30 - 10 * q^33 - 10 * q^34 - 6 * q^35 - 4 * q^36 - 26 * q^37 + 8 * q^38 + 18 * q^39 + 6 * q^40 + 4 * q^41 + 18 * q^42 - 8 * q^44 - 4 * q^46 - 20 * q^47 - 8 * q^48 + 2 * q^49 + 6 * q^52 - 2 * q^53 + 6 * q^55 + 6 * q^56 + 36 * q^57 + 8 * q^58 + 12 * q^59 + 24 * q^61 + 10 * q^62 - 16 * q^63 - 12 * q^64 + 4 * q^65 + 28 * q^67 - 6 * q^69 + 2 * q^70 - 40 * q^71 - 12 * q^73 + 14 * q^74 + 8 * q^75 + 18 * q^76 - 24 * q^77 - 10 * q^78 + 24 * q^79 - 6 * q^81 - 16 * q^83 - 28 * q^84 - 20 * q^85 - 16 * q^86 - 24 * q^87 + 6 * q^89 - 2 * q^90 - 18 * q^91 + 6 * q^92 + 78 * q^93 + 4 * q^95 - 12 * q^98 + 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	−0.671462	−	1.16301i	−0.387669	−	0.671462i	0.604467	−	0.796630i	$-0.293386\pi$
$3$	−0.671462	−	1.16301i	−0.387669	−	0.671462i	−0.992135	+	0.125169i	$0.960053\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$6$		−	1.34292i		−	0.548246i
$7$	−1.45444	−	2.51917i	−0.549728	−	0.952157i	−0.998293	−	0.0584066i	$-0.981398\pi$
$7$	−1.45444	−	2.51917i	−0.549728	−	0.952157i	0.448565	−	0.893750i	$-0.351935\pi$
$8$			1.00000i			0.353553i
$9$	0.598279	−	1.03625i	0.199426	−	0.345416i
$10$	1.00000			0.316228
$11$	−0.580401			−0.174998			−0.0874988	−	0.996165i	$-0.527887\pi$
$11$	−0.580401			−0.174998			−0.0874988	+	0.996165i	$0.527887\pi$
$12$	0.671462	−	1.16301i	0.193834	−	0.335731i
$13$	3.38520	−	1.95444i	0.938884	−	0.542065i	0.0492740	−	0.998785i	$-0.484309\pi$
$13$	3.38520	−	1.95444i	0.938884	−	0.542065i	0.889610	+	0.456720i	$0.150976\pi$
$14$		−	2.90889i		−	0.777433i
$15$	−1.16301	−	0.671462i	−0.300287	−	0.173371i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.0603530	+	0.0348448i	0.0146378	+	0.00845112i	0.507301	−	0.861769i	$-0.330643\pi$
$17$	0.0603530	+	0.0348448i	0.0146378	+	0.00845112i	−0.492663	+	0.870220i	$0.663977\pi$
$18$	1.03625	−	0.598279i	0.244246	−	0.141016i
$19$	1.82413	−	1.05316i	0.418484	−	0.241612i	−0.275945	−	0.961174i	$-0.588991\pi$
$19$	1.82413	−	1.05316i	0.418484	−	0.241612i	0.694428	+	0.719562i	$0.255657\pi$
$20$	0.866025	+	0.500000i	0.193649	+	0.111803i
$21$	−1.95321	+	3.38305i	−0.426225	+	0.738242i
$22$	−0.502642	−	0.290201i	−0.107164	−	0.0618710i
$23$		−	2.38825i		−	0.497985i	−0.968505	−	0.248992i	$-0.919901\pi$
$23$		−	2.38825i		−	0.497985i	0.968505	−	0.248992i	$-0.0800994\pi$
$24$	1.16301	−	0.671462i	0.237398	−	0.137062i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	3.90889			0.766596
$27$	−5.63565			−1.08458
$28$	1.45444	−	2.51917i	0.274864	−	0.476078i
$29$			1.17137i			0.217518i	0.994068	+	0.108759i	$0.0346877\pi$
$29$			1.17137i			0.217518i	−0.994068	+	0.108759i	$0.965312\pi$
$30$	−0.671462	−	1.16301i	−0.122592	−	0.212335i
$31$			7.68209i			1.37974i	0.723931	+	0.689872i	$0.242333\pi$
$31$			7.68209i			1.37974i	−0.723931	+	0.689872i	$0.757667\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	0.389717	+	0.675010i	0.0678410	+	0.117504i
$34$	0.0348448	+	0.0603530i	0.00597584	+	0.0103505i
$35$	−2.51917	−	1.45444i	−0.425818	−	0.245846i
$36$	1.19656			0.199426
$37$	5.40900	−	2.78257i	0.889234	−	0.457452i
$37$	5.40900	−	2.78257i	0.889234	−	0.457452i
$38$	2.10632			0.341691
$39$	−4.54606	−	2.62467i	−0.727952	−	0.420283i
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	5.13662	+	8.89689i	0.802205	+	1.38946i	0.918162	+	0.396206i	$0.129673\pi$
$41$	5.13662	+	8.89689i	0.802205	+	1.38946i	−0.115956	+	0.993254i	$0.536993\pi$
$42$	−3.38305	+	1.95321i	−0.522016	+	0.301386i
$43$		−	0.658184i		−	0.100372i	−0.998740	−	0.0501860i	$-0.984019\pi$
$43$		−	0.658184i		−	0.100372i	0.998740	−	0.0501860i	$-0.0159814\pi$
$44$	−0.290201	−	0.502642i	−0.0437494	−	0.0757761i
$45$		−	1.19656i		−	0.178372i
$46$	1.19413	−	2.06829i	0.176064	−	0.304952i
$47$	−4.39031			−0.640392			−0.320196	−	0.947351i	$-0.603749\pi$
$47$	−4.39031			−0.640392			−0.320196	+	0.947351i	$0.603749\pi$
$48$	1.34292			0.193834
$49$	−0.730813	+	1.26581i	−0.104402	+	0.180829i
$50$	0.866025	−	0.500000i	0.122474	−	0.0707107i
$51$		−	0.0935879i		−	0.0131049i
$52$	3.38520	+	1.95444i	0.469442	+	0.271033i
$53$	−0.701343	+	1.21476i	−0.0963369	+	0.166860i	−0.910166	−	0.414244i	$-0.864046\pi$
$53$	−0.701343	+	1.21476i	−0.0963369	+	0.166860i	0.813829	+	0.581105i	$0.197379\pi$
$54$	−4.88062	−	2.81783i	−0.664168	−	0.383458i
$55$	−0.502642	+	0.290201i	−0.0677762	+	0.0391306i
$56$	2.51917	−	1.45444i	0.336638	−	0.194358i
$57$	−2.44966	−	1.41431i	−0.324466	−	0.187331i
$58$	−0.585685	+	1.01444i	−0.0769042	+	0.133202i
$59$	−5.65114	−	3.26269i	−0.735716	−	0.424766i	0.0847936	−	0.996399i	$-0.472977\pi$
$59$	−5.65114	−	3.26269i	−0.735716	−	0.424766i	−0.820510	+	0.571633i	$0.806310\pi$
$60$		−	1.34292i		−	0.173371i
$61$	−11.5509	+	6.66893i	−1.47895	+	0.853870i	−0.999716	−	0.0238203i	$-0.992417\pi$
$61$	−11.5509	+	6.66893i	−1.47895	+	0.853870i	−0.479229	+	0.877690i	$0.659084\pi$
$62$	−3.84104	+	6.65288i	−0.487813	+	0.844917i
$63$	−3.48065			−0.438521
$64$	−1.00000			−0.125000
$65$	1.95444	−	3.38520i	0.242419	−	0.419882i
$66$			0.779434i			0.0959417i
$67$	5.97361	+	10.3466i	0.729793	+	1.26404i	0.956970	+	0.290185i	$0.0937170\pi$
$67$	5.97361	+	10.3466i	0.729793	+	1.26404i	−0.227177	+	0.973853i	$0.572950\pi$
$68$			0.0696897i			0.00845112i
$69$	−2.77755	+	1.60362i	−0.334377	+	0.193053i
$70$	−1.45444	−	2.51917i	−0.173839	−	0.301098i
$71$	5.69900	+	9.87096i	0.676347	+	1.17147i	0.976073	+	0.217442i	$0.0697713\pi$
$71$	5.69900	+	9.87096i	0.676347	+	1.17147i	−0.299726	+	0.954025i	$0.596895\pi$
$72$	1.03625	+	0.598279i	0.122123	+	0.0705078i
$73$	−0.566789			−0.0663376			−0.0331688	−	0.999450i	$-0.510560\pi$
$73$	−0.566789			−0.0663376			−0.0331688	+	0.999450i	$0.510560\pi$
$74$	6.07562	+	0.294725i	0.706276	+	0.0342611i
$75$	−1.34292			−0.155067
$76$	1.82413	+	1.05316i	0.209242	+	0.120806i
$77$	0.844161	+	1.46213i	0.0962010	+	0.166625i
$78$	−2.62467	−	4.54606i	−0.297185	−	0.514740i
$79$	−2.04694	+	1.18180i	−0.230298	+	0.132963i	−0.610710	−	0.791855i	$-0.709116\pi$
$79$	−2.04694	+	1.18180i	−0.230298	+	0.132963i	0.380411	+	0.924817i	$0.375782\pi$
$80$			1.00000i			0.111803i
$81$	1.98929	+	3.44555i	0.221032	+	0.382839i
$82$			10.2732i			1.13449i
$83$	−4.57125	+	7.91763i	−0.501760	+	0.869073i	0.498238	+	0.867040i	$0.333981\pi$
$83$	−4.57125	+	7.91763i	−0.501760	+	0.869073i	−0.999998	+	0.00203314i	$0.999353\pi$
$84$	−3.90641			−0.426225
$85$	0.0696897			0.00755891
$86$	0.329092	−	0.570004i	0.0354869	−	0.0614651i
$87$	1.36231	−	0.786530i	0.146055	−	0.0843249i
$88$		−	0.580401i		−	0.0618710i
$89$	3.16126	+	1.82516i	0.335093	+	0.193466i	0.658100	−	0.752930i	$-0.271360\pi$
$89$	3.16126	+	1.82516i	0.335093	+	0.193466i	−0.323007	+	0.946397i	$0.604694\pi$
$90$	0.598279	−	1.03625i	0.0630641	−	0.109230i
$91$	−9.84715	−	5.68526i	−1.03226	−	0.595977i
$92$	2.06829	−	1.19413i	0.215634	−	0.124496i
$93$	8.93431	−	5.15823i	0.926445	−	0.534883i
$94$	−3.80212	−	2.19515i	−0.392158	−	0.226413i
$95$	1.05316	−	1.82413i	0.108052	−	0.187152i
$96$	1.16301	+	0.671462i	0.118699	+	0.0685308i
$97$		−	0.619286i		−	0.0628790i	−0.999506	−	0.0314395i	$-0.989991\pi$
$97$		−	0.619286i		−	0.0628790i	0.999506	−	0.0314395i	$-0.0100091\pi$
$98$	−1.26581	+	0.730813i	−0.127866	+	0.0738233i
$99$	−0.347242	+	0.601440i	−0.0348991	+	0.0604470i
$100$	1.00000			0.100000
$101$	−4.00939			−0.398949			−0.199475	−	0.979903i	$-0.563924\pi$
$101$	−4.00939			−0.398949			−0.199475	+	0.979903i	$0.563924\pi$
$102$	0.0467939	−	0.0810495i	0.00463329	−	0.00802509i
$103$		−	17.9370i		−	1.76739i	−0.468067	−	0.883693i	$-0.655049\pi$
$103$		−	17.9370i		−	1.76739i	0.468067	−	0.883693i	$-0.344951\pi$
$104$	1.95444	+	3.38520i	0.191649	+	0.331946i
$105$			3.90641i			0.381227i
$106$	−1.21476	+	0.701343i	−0.117988	+	0.0681205i
$107$	1.86802	+	3.23550i	0.180588	+	0.312788i	0.942081	−	0.335385i	$-0.108867\pi$
$107$	1.86802	+	3.23550i	0.180588	+	0.312788i	−0.761493	+	0.648173i	$0.775533\pi$
$108$	−2.81783	−	4.88062i	−0.271146	−	0.469638i
$109$	11.0292	+	6.36770i	1.05640	+	0.609916i	0.924436	−	0.381338i	$-0.124537\pi$
$109$	11.0292	+	6.36770i	1.05640	+	0.609916i	0.131969	+	0.991254i	$0.457870\pi$
$110$	−0.580401			−0.0553391
$111$	−6.86808	−	4.42231i	−0.651889	−	0.419747i
$112$	2.90889			0.274864
$113$	1.78483	+	1.03047i	0.167903	+	0.0969386i	0.581596	−	0.813477i	$-0.302428\pi$
$113$	1.78483	+	1.03047i	0.167903	+	0.0969386i	−0.413694	+	0.910416i	$0.635762\pi$
$114$	−1.41431	−	2.44966i	−0.132463	−	0.229432i
$115$	−1.19413	−	2.06829i	−0.111353	−	0.192869i
$116$	−1.01444	+	0.585685i	−0.0941881	+	0.0543795i
$117$		−	4.67721i		−	0.432408i
$118$	−3.26269	−	5.65114i	−0.300355	−	0.520230i
$119$		−	0.202719i		−	0.0185833i
$120$	0.671462	−	1.16301i	0.0612958	−	0.106167i
$121$	−10.6631			−0.969376
$122$	−13.3379			−1.20755
$123$	6.89809	−	11.9478i	0.621979	−	1.07730i
$124$	−6.65288	+	3.84104i	−0.597447	+	0.344936i
$125$		−	1.00000i		−	0.0894427i
$126$	−3.01433	−	1.74033i	−0.268538	−	0.155041i
$127$	7.83711	−	13.5743i	0.695431	−	1.20452i	−0.274604	−	0.961557i	$-0.588547\pi$
$127$	7.83711	−	13.5743i	0.695431	−	1.20452i	0.970035	−	0.242965i	$-0.0781200\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−0.765471	+	0.441945i	−0.0673960	+	0.0389111i
$130$	3.38520	−	1.95444i	0.296901	−	0.171416i
$131$	4.21293	+	2.43233i	0.368085	+	0.212514i	0.672622	−	0.739987i	$-0.265168\pi$
$131$	4.21293	+	2.43233i	0.368085	+	0.212514i	−0.304537	+	0.952501i	$0.598502\pi$
$132$	−0.389717	+	0.675010i	−0.0339205	+	0.0587521i
$133$	−5.30619	−	3.06353i	−0.460105	−	0.265642i
$134$			11.9472i			1.03208i
$135$	−4.88062	+	2.81783i	−0.420057	+	0.242520i
$136$	−0.0348448	+	0.0603530i	−0.00298792	+	0.00517523i
$137$	12.4686			1.06527			0.532633	−	0.846346i	$-0.321203\pi$
$137$	12.4686			1.06527			0.532633	+	0.846346i	$0.321203\pi$
$138$	−3.20724			−0.273018
$139$	8.60343	−	14.9016i	0.729733	−	1.26393i	−0.227263	−	0.973833i	$-0.572978\pi$
$139$	8.60343	−	14.9016i	0.729733	−	1.26393i	0.956996	−	0.290101i	$-0.0936890\pi$
$140$		−	2.90889i		−	0.245846i
$141$	2.94792	+	5.10595i	0.248260	+	0.429999i
$142$			11.3980i			0.956499i
$143$	−1.96477	+	1.13436i	−0.164302	+	0.0948601i
$144$	0.598279	+	1.03625i	0.0498566	+	0.0863541i
$145$	0.585685	+	1.01444i	0.0486385	+	0.0842444i
$146$	−0.490853	−	0.283394i	−0.0406233	−	0.0234539i
$147$	1.96285			0.161893
$148$	5.11428	+	3.29305i	0.420391	+	0.270687i
$149$	14.0790			1.15340			0.576700	−	0.816956i	$-0.304340\pi$
$149$	14.0790			1.15340			0.576700	+	0.816956i	$0.304340\pi$
$150$	−1.16301	−	0.671462i	−0.0949590	−	0.0548246i
$151$	−8.99084	−	15.5726i	−0.731664	−	1.26728i	−0.956171	−	0.292808i	$-0.905410\pi$
$151$	−8.99084	−	15.5726i	−0.731664	−	1.26728i	0.224507	−	0.974472i	$-0.427923\pi$
$152$	1.05316	+	1.82413i	0.0854227	+	0.147956i
$153$	0.0722159	−	0.0416939i	0.00583831	−	0.00337075i
$154$			1.68832i			0.136049i
$155$	3.84104	+	6.65288i	0.308520	+	0.534372i
$156$		−	5.24934i		−	0.420283i
$157$	−0.124789	+	0.216141i	−0.00995926	+	0.0172499i	−0.870962	−	0.491350i	$-0.836504\pi$
$157$	−0.124789	+	0.216141i	−0.00995926	+	0.0172499i	0.861003	+	0.508600i	$0.169837\pi$
$158$	−2.36360			−0.188038
$159$	1.88370			0.149387
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	−6.01641	+	3.47358i	−0.474159	+	0.273756i
$162$			3.97858i			0.312587i
$163$	3.18177	+	1.83699i	0.249215	+	0.143885i	0.619405	−	0.785072i	$-0.287374\pi$
$163$	3.18177	+	1.83699i	0.249215	+	0.143885i	−0.370190	+	0.928956i	$0.620707\pi$
$164$	−5.13662	+	8.89689i	−0.401103	+	0.694730i
$165$	0.675010	+	0.389717i	0.0525494	+	0.0303394i
$166$	−7.91763	+	4.57125i	−0.614528	+	0.354798i
$167$	2.09975	−	1.21229i	0.162484	−	0.0938099i	−0.416553	−	0.909111i	$-0.636762\pi$
$167$	2.09975	−	1.21229i	0.162484	−	0.0938099i	0.579037	+	0.815301i	$0.303429\pi$
$168$	−3.38305	−	1.95321i	−0.261008	−	0.150693i
$169$	1.13970	−	1.97402i	0.0876693	−	0.151848i
$170$	0.0603530	+	0.0348448i	0.00462887	+	0.00267248i
$171$		−	2.52034i		−	0.192735i
$172$	0.570004	−	0.329092i	0.0434624	−	0.0250930i
$173$	1.15287	−	1.99683i	0.0876511	−	0.151816i	−0.818867	−	0.573984i	$-0.805397\pi$
$173$	1.15287	−	1.99683i	0.0876511	−	0.151816i	0.906518	+	0.422168i	$0.138731\pi$
$174$	1.57306			0.119253
$175$	−2.90889			−0.219891
$176$	0.290201	−	0.502642i	0.0218747	−	0.0378881i
$177$			8.76308i			0.658673i
$178$	1.82516	+	3.16126i	0.136801	+	0.236947i
$179$			17.2172i			1.28687i	0.765499	+	0.643437i	$0.222492\pi$
$179$			17.2172i			1.28687i	−0.765499	+	0.643437i	$0.777508\pi$
$180$	1.03625	−	0.598279i	0.0772375	−	0.0445931i
$181$	6.26813	+	10.8567i	0.465907	+	0.806974i	0.999242	−	0.0389299i	$-0.0123949\pi$
$181$	6.26813	+	10.8567i	0.465907	+	0.806974i	−0.533335	+	0.845904i	$0.679062\pi$
$182$	−5.68526	−	9.84715i	−0.421419	−	0.729920i
$183$	15.5120	+	8.95587i	1.14668	+	0.662037i
$184$	2.38825			0.176064
$185$	3.29305	−	5.11428i	0.242110	−	0.376009i
$186$	10.3165			0.756439
$187$	−0.0350290	−	0.0202240i	−0.00256157	−	0.00147892i
$188$	−2.19515	−	3.80212i	−0.160098	−	0.277298i
$189$	8.19674	+	14.1972i	0.596225	+	1.03269i
$190$	1.82413	−	1.05316i	0.132336	−	0.0764044i
$191$			4.71519i			0.341179i	0.985342	+	0.170590i	$0.0545673\pi$
$191$			4.71519i			0.341179i	−0.985342	+	0.170590i	$0.945433\pi$
$192$	0.671462	+	1.16301i	0.0484586	+	0.0839327i
$193$		−	20.3911i		−	1.46778i	−0.679267	−	0.733891i	$-0.737702\pi$
$193$		−	20.3911i		−	1.46778i	0.679267	−	0.733891i	$-0.262298\pi$
$194$	0.309643	−	0.536317i	0.0222311	−	0.0385054i
$195$	−5.24934			−0.375913
$196$	−1.46163			−0.104402
$197$	−4.95315	+	8.57911i	−0.352898	+	0.611237i	−0.986756	−	0.162213i	$-0.948137\pi$
$197$	−4.95315	+	8.57911i	−0.352898	+	0.611237i	0.633858	+	0.773449i	$0.281470\pi$
$198$	−0.601440	+	0.347242i	−0.0427425	+	0.0246774i
$199$		−	10.1355i		−	0.718487i	−0.933244	−	0.359243i	$-0.883035\pi$
$199$		−	10.1355i		−	0.718487i	0.933244	−	0.359243i	$-0.116965\pi$
$200$	0.866025	+	0.500000i	0.0612372	+	0.0353553i
$201$	8.02210	−	13.8947i	0.565836	−	0.980056i
$202$	−3.47223	−	2.00469i	−0.244305	−	0.141050i
$203$	2.95088	−	1.70369i	0.207111	−	0.119576i
$204$	0.0810495	−	0.0467939i	0.00567460	−	0.00327623i
$205$	8.89689	+	5.13662i	0.621385	+	0.358757i
$206$	8.96850	−	15.5339i	0.624865	−	1.08230i
$207$	−2.47482	−	1.42884i	−0.172012	−	0.0993112i
$208$			3.90889i			0.271033i
$209$	−1.05873	+	0.611256i	−0.0732336	+	0.0422815i
$210$	−1.95321	+	3.38305i	−0.134784	+	0.233453i
$211$	9.19575			0.633061			0.316531	−	0.948582i	$-0.397482\pi$
$211$	9.19575			0.633061			0.316531	+	0.948582i	$0.397482\pi$
$212$	−1.40269			−0.0963369
$213$	7.65332	−	13.2559i	0.524397	−	0.908282i
$214$			3.73604i			0.255390i
$215$	−0.329092	−	0.570004i	−0.0224439	−	0.0388739i
$216$		−	5.63565i		−	0.383458i
$217$	19.3525	−	11.1732i	1.31373	−	0.758484i
$218$	6.36770	+	11.0292i	0.431275	+	0.746991i
$219$	0.380577	+	0.659178i	0.0257170	+	0.0445431i
$220$	−0.502642	−	0.290201i	−0.0338881	−	0.0195653i
$221$	0.272409			0.0183242
$222$	−3.73678	−	7.26387i	−0.250796	−	0.487519i
$223$	11.5567			0.773896			0.386948	−	0.922102i	$-0.373529\pi$
$223$	11.5567			0.773896			0.386948	+	0.922102i	$0.373529\pi$
$224$	2.51917	+	1.45444i	0.168319	+	0.0971791i
$225$	−0.598279	−	1.03625i	−0.0398853	−	0.0690833i
$226$	1.03047	+	1.78483i	0.0685459	+	0.118725i
$227$	−9.72869	+	5.61686i	−0.645716	+	0.372804i	−0.786813	−	0.617192i	$-0.788270\pi$
$227$	−9.72869	+	5.61686i	−0.645716	+	0.372804i	0.141097	+	0.989996i	$0.454937\pi$
$228$		−	2.82863i		−	0.187331i
$229$	−2.99531	−	5.18802i	−0.197935	−	0.342834i	0.749923	−	0.661525i	$-0.230090\pi$
$229$	−2.99531	−	5.18802i	−0.197935	−	0.342834i	−0.947859	+	0.318691i	$0.896757\pi$
$230$		−	2.38825i		−	0.157477i
$231$	1.13364	−	1.96353i	0.0745882	−	0.129191i
$232$	−1.17137			−0.0769042
$233$	−24.2435			−1.58825			−0.794123	−	0.607757i	$-0.792070\pi$
$233$	−24.2435			−1.58825			−0.794123	+	0.607757i	$0.792070\pi$
$234$	2.33860	−	4.05058i	0.152879	−	0.264795i
$235$	−3.80212	+	2.19515i	−0.248023	+	0.143196i
$236$		−	6.52538i		−	0.424766i
$237$	2.74888	+	1.58707i	0.178559	+	0.103091i
$238$	0.101360	−	0.175560i	0.00657017	−	0.0113799i
$239$	−15.1557	−	8.75017i	−0.980343	−	0.566001i	−0.0779693	−	0.996956i	$-0.524844\pi$
$239$	−15.1557	−	8.75017i	−0.980343	−	0.566001i	−0.902374	+	0.430954i	$0.858177\pi$
$240$	1.16301	−	0.671462i	0.0750717	−	0.0433427i
$241$	−13.8035	+	7.96945i	−0.889161	+	0.513357i	−0.873668	−	0.486523i	$-0.838265\pi$
$241$	−13.8035	+	7.96945i	−0.889161	+	0.513357i	−0.0154928	+	0.999880i	$0.504932\pi$
$242$	−9.23455	−	5.33157i	−0.593619	−	0.342726i
$243$	−5.78202	+	10.0148i	−0.370917	+	0.642447i
$244$	−11.5509	−	6.66893i	−0.739473	−	0.426935i
$245$			1.46163i			0.0933799i
$246$	11.9478	−	6.89809i	0.761766	−	0.439806i
$247$	4.11669	−	7.13031i	0.261939	−	0.453691i
$248$	−7.68209			−0.487813
$249$	12.2777			0.778066
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$			17.7072i			1.11767i	0.829279	+	0.558835i	$0.188752\pi$
$251$			17.7072i			1.11767i	−0.829279	+	0.558835i	$0.811248\pi$
$252$	−1.74033	−	3.01433i	−0.109630	−	0.189885i
$253$			1.38614i			0.0871461i
$254$	13.5743	−	7.83711i	0.851726	−	0.491744i
$255$	−0.0467939	−	0.0810495i	−0.00293035	−	0.00507552i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−21.0090	−	12.1295i	−1.31050	−	0.756620i	−0.328325	−	0.944565i	$-0.606484\pi$
$257$	−21.0090	−	12.1295i	−1.31050	−	0.756620i	−0.982180	+	0.187945i	$0.939817\pi$
$258$	−0.883890			−0.0550286
$259$	−14.8769	−	9.57911i	−0.924403	−	0.595217i
$260$	3.90889			0.242419
$261$	1.21383	+	0.700806i	0.0751343	+	0.0433788i
$262$	2.43233	+	4.21293i	0.150270	+	0.260275i
$263$	0.767685	+	1.32967i	0.0473375	+	0.0819909i	0.888723	−	0.458444i	$-0.151593\pi$
$263$	0.767685	+	1.32967i	0.0473375	+	0.0819909i	−0.841386	+	0.540435i	$0.818260\pi$
$264$	−0.675010	+	0.389717i	−0.0415440	+	0.0239854i
$265$			1.40269i			0.0861664i
$266$	−3.06353	−	5.30619i	−0.187837	−	0.325343i
$267$		−	4.90209i		−	0.300003i
$268$	−5.97361	+	10.3466i	−0.364897	+	0.632019i
$269$	6.65579			0.405811			0.202905	−	0.979198i	$-0.434962\pi$
$269$	6.65579			0.405811			0.202905	+	0.979198i	$0.434962\pi$
$270$	−5.63565			−0.342975
$271$	14.4794	−	25.0791i	0.879561	−	1.52344i	0.0277382	−	0.999615i	$-0.491170\pi$
$271$	14.4794	−	25.0791i	0.879561	−	1.52344i	0.851823	−	0.523830i	$-0.175497\pi$
$272$	−0.0603530	+	0.0348448i	−0.00365944	+	0.00211278i
$273$			15.2697i			0.924166i
$274$	10.7981	+	6.23431i	0.652340	+	0.376628i
$275$	−0.290201	+	0.502642i	−0.0174998	+	0.0303105i
$276$	−2.77755	−	1.60362i	−0.167189	−	0.0965265i
$277$	3.84668	−	2.22088i	0.231125	−	0.133440i	−0.379966	−	0.925000i	$-0.624064\pi$
$277$	3.84668	−	2.22088i	0.231125	−	0.133440i	0.611091	+	0.791560i	$0.290731\pi$
$278$	14.9016	−	8.60343i	0.893737	−	0.515999i
$279$	7.96056	+	4.59603i	0.476586	+	0.275157i
$280$	1.45444	−	2.51917i	0.0869196	−	0.150549i
$281$	7.27571	+	4.20063i	0.434032	+	0.250589i	0.701063	−	0.713099i	$-0.252709\pi$
$281$	7.27571	+	4.20063i	0.434032	+	0.250589i	−0.267031	+	0.963688i	$0.586042\pi$
$282$			5.89584i			0.351092i
$283$	−17.4057	+	10.0492i	−1.03466	+	0.597362i	−0.918316	−	0.395847i	$-0.870451\pi$
$283$	−17.4057	+	10.0492i	−1.03466	+	0.597362i	−0.116345	+	0.993209i	$0.537118\pi$
$284$	−5.69900	+	9.87096i	−0.338173	+	0.585734i
$285$	−2.82863			−0.167554
$286$	−2.26872			−0.134152
$287$	14.9418	−	25.8800i	0.881989	−	1.52765i
$288$			1.19656i			0.0705078i
$289$	−8.49757	−	14.7182i	−0.499857	−	0.865778i
$290$			1.17137i			0.0687853i
$291$	−0.720233	+	0.415827i	−0.0422208	+	0.0243762i
$292$	−0.283394	−	0.490853i	−0.0165844	−	0.0287250i
$293$	5.53514	+	9.58715i	0.323367	+	0.560087i	0.981180	−	0.193093i	$-0.0618520\pi$
$293$	5.53514	+	9.58715i	0.323367	+	0.560087i	−0.657814	+	0.753181i	$0.728519\pi$
$294$	1.69988	+	0.981426i	0.0991390	+	0.0572379i
$295$	−6.52538			−0.379922
$296$	2.78257	+	5.40900i	0.161734	+	0.314392i
$297$	3.27094			0.189799
$298$	12.1928	+	7.03952i	0.706310	+	0.407788i
$299$	−4.66770	−	8.08469i	−0.269940	−	0.467550i
$300$	−0.671462	−	1.16301i	−0.0387669	−	0.0671462i
$301$	−1.65808	+	0.957291i	−0.0955700	+	0.0551774i
$302$		−	17.9817i		−	1.03473i
$303$	2.69215	+	4.66294i	0.154660	+	0.267879i
$304$			2.10632i			0.120806i
$305$	−6.66893	+	11.5509i	−0.381862	+	0.661404i
$306$	0.0833877			0.00476696
$307$	−10.4723			−0.597683			−0.298842	−	0.954303i	$-0.596600\pi$
$307$	−10.4723			−0.597683			−0.298842	+	0.954303i	$0.596600\pi$
$308$	−0.844161	+	1.46213i	−0.0481005	+	0.0833125i
$309$	−20.8608	+	12.0440i	−1.18673	+	0.685160i
$310$			7.68209i			0.436313i
$311$	11.2295	+	6.48336i	0.636767	+	0.367638i	0.783368	−	0.621558i	$-0.213500\pi$
$311$	11.2295	+	6.48336i	0.636767	+	0.367638i	−0.146601	+	0.989196i	$0.546833\pi$
$312$	2.62467	−	4.54606i	0.148593	−	0.257370i
$313$	−27.3532	−	15.7924i	−1.54610	−	0.892639i	−0.998434	−	0.0559396i	$-0.982185\pi$
$313$	−27.3532	−	15.7924i	−1.54610	−	0.892639i	−0.547662	−	0.836700i	$-0.684482\pi$
$314$	−0.216141	+	0.124789i	−0.0121976	+	0.00704226i
$315$	−3.01433	+	1.74033i	−0.169838	+	0.0980562i
$316$	−2.04694	−	1.18180i	−0.115149	−	0.0664814i
$317$	−5.62163	+	9.73694i	−0.315742	+	0.546881i	−0.979595	−	0.200982i	$-0.935587\pi$
$317$	−5.62163	+	9.73694i	−0.315742	+	0.546881i	0.663853	+	0.747863i	$0.268920\pi$
$318$	1.63133	+	0.941850i	0.0914806	+	0.0528163i
$319$		−	0.679865i		−	0.0380651i
$320$	−0.866025	+	0.500000i	−0.0484123	+	0.0279508i
$321$	2.50861	−	4.34503i	0.140017	−	0.242516i
$322$	−6.94715			−0.387150
$323$	0.146789			0.00816756
$324$	−1.98929	+	3.44555i	−0.110516	+	0.191419i
$325$		−	3.90889i		−	0.216826i
$326$	1.83699	+	3.18177i	0.101742	+	0.176222i
$327$		−	17.1027i		−	0.945780i
$328$	−8.89689	+	5.13662i	−0.491248	+	0.283622i
$329$	6.38545	+	11.0599i	0.352041	+	0.609754i
$330$	0.389717	+	0.675010i	0.0214532	+	0.0371581i
$331$	−3.21867	−	1.85830i	−0.176914	−	0.102141i	0.408928	−	0.912567i	$-0.365903\pi$
$331$	−3.21867	−	1.85830i	−0.176914	−	0.102141i	−0.585842	+	0.810425i	$0.699236\pi$
$332$	−9.14250			−0.501760
$333$	0.352655	−	7.26983i	0.0193254	−	0.398384i
$334$	2.42458			0.132667
$335$	10.3466	+	5.97361i	0.565295	+	0.326373i
$336$	−1.95321	−	3.38305i	−0.106556	−	0.184561i
$337$	14.2644	+	24.7067i	0.777032	+	1.34586i	0.933645	+	0.358200i	$0.116609\pi$
$337$	14.2644	+	24.7067i	0.777032	+	1.34586i	−0.156613	+	0.987660i	$0.550057\pi$
$338$	1.97402	−	1.13970i	0.107372	−	0.0619915i
$339$		−	2.76769i		−	0.150320i
$340$	0.0348448	+	0.0603530i	0.00188973	+	0.00327310i
$341$		−	4.45869i		−	0.241452i
$342$	1.26017	−	2.18268i	0.0681421	−	0.118026i
$343$	−16.1105			−0.869886
$344$	0.658184			0.0354869
$345$	−1.60362	+	2.77755i	−0.0863359	+	0.149538i
$346$	1.99683	−	1.15287i	0.107350	−	0.0619787i
$347$			20.4797i			1.09941i	0.835359	+	0.549705i	$0.185260\pi$
$347$			20.4797i			1.09941i	−0.835359	+	0.549705i	$0.814740\pi$
$348$	1.36231	+	0.786530i	0.0730275	+	0.0421625i
$349$	−3.89519	+	6.74667i	−0.208505	+	0.361141i	−0.951244	−	0.308440i	$-0.900193\pi$
$349$	−3.89519	+	6.74667i	−0.208505	+	0.361141i	0.742739	+	0.669581i	$0.233526\pi$
$350$	−2.51917	−	1.45444i	−0.134655	−	0.0777433i
$351$	−19.0778	+	11.0146i	−1.01830	+	0.587914i
$352$	0.502642	−	0.290201i	0.0267909	−	0.0154677i
$353$	6.09299	+	3.51779i	0.324297	+	0.187233i	0.653306	−	0.757094i	$-0.273381\pi$
$353$	6.09299	+	3.51779i	0.324297	+	0.187233i	−0.329009	+	0.944327i	$0.606715\pi$
$354$	−4.38154	+	7.58905i	−0.232876	+	0.403353i
$355$	9.87096	+	5.69900i	0.523896	+	0.302472i
$356$			3.65031i			0.193466i
$357$	−0.235764	+	0.136118i	−0.0124779	+	0.00720414i
$358$	−8.60860	+	14.9105i	−0.454979	+	0.788047i
$359$	−17.5762			−0.927639			−0.463819	−	0.885930i	$-0.653521\pi$
$359$	−17.5762			−0.927639			−0.463819	+	0.885930i	$0.653521\pi$
$360$	1.19656			0.0630641
$361$	−7.28170	+	12.6123i	−0.383247	+	0.663804i
$362$			12.5363i			0.658892i
$363$	7.15988	+	12.4013i	0.375796	+	0.650899i
$364$		−	11.3705i		−	0.595977i
$365$	−0.490853	+	0.283394i	−0.0256924	+	0.0148335i
$366$	8.95587	+	15.5120i	0.468131	+	0.810826i
$367$	−3.05679	−	5.29452i	−0.159563	−	0.276372i	0.775148	−	0.631780i	$-0.217675\pi$
$367$	−3.05679	−	5.29452i	−0.159563	−	0.276372i	−0.934711	+	0.355408i	$0.884342\pi$
$368$	2.06829	+	1.19413i	0.107817	+	0.0622481i
$369$	12.2925			0.639923
$370$	5.40900	−	2.78257i	0.281201	−	0.144659i
$371$	4.08026			0.211836
$372$	8.93431	+	5.15823i	0.463222	+	0.267442i
$373$	11.4160	+	19.7731i	0.591098	+	1.02381i	0.994085	+	0.108606i	$0.0346386\pi$
$373$	11.4160	+	19.7731i	0.591098	+	1.02381i	−0.402987	+	0.915206i	$0.632028\pi$
$374$	−0.0202240	−	0.0350290i	−0.00104576	−	0.00181130i
$375$	−1.16301	+	0.671462i	−0.0600573	+	0.0346741i
$376$		−	4.39031i		−	0.226413i
$377$	2.28938	+	3.96532i	0.117909	+	0.204224i
$378$			16.3935i			0.843190i
$379$	−2.02239	+	3.50289i	−0.103883	+	0.179931i	−0.913281	−	0.407329i	$-0.866460\pi$
$379$	−2.02239	+	3.50289i	−0.103883	+	0.179931i	0.809398	+	0.587260i	$0.199794\pi$
$380$	2.10632			0.108052
$381$	−21.0493			−1.07839
$382$	−2.35760	+	4.08348i	−0.120625	+	0.208929i
$383$	−21.6214	+	12.4831i	−1.10480	+	0.637857i	−0.937478	−	0.348046i	$-0.886845\pi$
$383$	−21.6214	+	12.4831i	−1.10480	+	0.637857i	−0.167322	+	0.985902i	$0.553512\pi$
$384$			1.34292i			0.0685308i
$385$	1.46213	+	0.844161i	0.0745170	+	0.0430224i
$386$	10.1955	−	17.6592i	0.518939	−	0.898830i
$387$	−0.682043	−	0.393777i	−0.0346702	−	0.0200168i
$388$	0.536317	−	0.309643i	0.0272274	−	0.0157197i
$389$	30.0971	−	17.3766i	1.52598	−	0.881027i	0.526459	−	0.850201i	$-0.323519\pi$
$389$	30.0971	−	17.3766i	1.52598	−	0.881027i	0.999525	−	0.0308266i	$-0.00981398\pi$
$390$	−4.54606	−	2.62467i	−0.230199	−	0.132905i
$391$	0.0832182	−	0.144138i	0.00420852	−	0.00728938i
$392$	−1.26581	−	0.730813i	−0.0639328	−	0.0369116i
$393$		−	6.53287i		−	0.329540i
$394$	−8.57911	+	4.95315i	−0.432210	+	0.249536i
$395$	−1.18180	+	2.04694i	−0.0594628	+	0.102993i
$396$	−0.694483			−0.0348991
$397$	−32.0808			−1.61009			−0.805044	−	0.593215i	$-0.797859\pi$
$397$	−32.0808			−1.61009			−0.805044	+	0.593215i	$0.797859\pi$
$398$	5.06775	−	8.77760i	0.254023	−	0.439981i
$399$			8.22816i			0.411923i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$			9.59949i			0.479376i	0.970850	+	0.239688i	$0.0770451\pi$
$401$			9.59949i			0.479376i	−0.970850	+	0.239688i	$0.922955\pi$
$402$	13.8947	−	8.02210i	0.693004	−	0.400106i
$403$	15.0142	+	26.0054i	0.747911	+	1.29542i
$404$	−2.00469	−	3.47223i	−0.0997373	−	0.172750i
$405$	3.44555	+	1.98929i	0.171211	+	0.0988485i
$406$	3.40739			0.169106
$407$	−3.13939	+	1.61501i	−0.155614	+	0.0800529i
$408$	0.0935879			0.00463329
$409$	−23.2710	−	13.4355i	−1.15067	−	0.664342i	−0.201623	−	0.979463i	$-0.564622\pi$
$409$	−23.2710	−	13.4355i	−1.15067	−	0.664342i	−0.949051	+	0.315121i	$0.897955\pi$
$410$	5.13662	+	8.89689i	0.253680	+	0.439386i
$411$	−8.37220	−	14.5011i	−0.412970	−	0.715285i
$412$	15.5339	−	8.96850i	0.765301	−	0.441846i
$413$			18.9816i			0.934023i
$414$	−1.42884	−	2.47482i	−0.0702236	−	0.121631i
$415$			9.14250i			0.448788i
$416$	−1.95444	+	3.38520i	−0.0958245	+	0.165973i
$417$	−23.1075			−1.13158
$418$	−1.22251			−0.0597950
$419$	−12.2340	+	21.1900i	−0.597671	+	1.03520i	0.395493	+	0.918469i	$0.370574\pi$
$419$	−12.2340	+	21.1900i	−0.597671	+	1.03520i	−0.993164	+	0.116728i	$0.962759\pi$
$420$	−3.38305	+	1.95321i	−0.165076	+	0.0953067i
$421$		−	25.3121i		−	1.23364i	−0.787105	−	0.616819i	$-0.788421\pi$
$421$		−	25.3121i		−	1.23364i	0.787105	−	0.616819i	$-0.211579\pi$
$422$	7.96375	+	4.59787i	0.387669	+	0.223821i
$423$	−2.62663	+	4.54945i	−0.127711	+	0.221202i
$424$	−1.21476	−	0.701343i	−0.0589941	−	0.0340602i
$425$	0.0603530	−	0.0348448i	0.00292755	−	0.00169022i
$426$	13.2559	−	7.65332i	0.642252	−	0.370805i
$427$	33.6004	+	19.3992i	1.62604	+	0.938792i
$428$	−1.86802	+	3.23550i	−0.0902941	+	0.156394i
$429$	2.63854	+	1.52336i	0.127390	+	0.0735485i
$430$		−	0.658184i		−	0.0317404i
$431$	24.9093	−	14.3814i	1.19984	−	0.692727i	0.239320	−	0.970941i	$-0.423076\pi$
$431$	24.9093	−	14.3814i	1.19984	−	0.692727i	0.960519	+	0.278213i	$0.0897422\pi$
$432$	2.81783	−	4.88062i	0.135573	−	0.234819i
$433$	−36.0203			−1.73103			−0.865513	−	0.500887i	$-0.833007\pi$
$433$	−36.0203			−1.73103			−0.865513	+	0.500887i	$0.833007\pi$
$434$	22.3463			1.07266
$435$	0.786530	−	1.36231i	0.0377112	−	0.0653178i
$436$			12.7354i			0.609916i
$437$	−2.51521	−	4.35648i	−0.120319	−	0.208399i
$438$			0.761154i			0.0363693i
$439$	1.97086	−	1.13787i	0.0940639	−	0.0543078i	−0.452230	−	0.891901i	$-0.649371\pi$
$439$	1.97086	−	1.13787i	0.0940639	−	0.0543078i	0.546294	+	0.837593i	$0.316038\pi$
$440$	−0.290201	−	0.502642i	−0.0138348	−	0.0239625i
$441$	0.874460	+	1.51461i	0.0416410	+	0.0721242i
$442$	0.235913	+	0.136205i	0.0112212	+	0.00647859i
$443$	−3.78495			−0.179828			−0.0899141	−	0.995950i	$-0.528659\pi$
$443$	−3.78495			−0.179828			−0.0899141	+	0.995950i	$0.528659\pi$
$444$	0.395793	−	8.15909i	0.0187835	−	0.387213i
$445$	3.65031			0.173041
$446$	10.0084	+	5.77836i	0.473912	+	0.273613i
$447$	−9.45353	−	16.3740i	−0.447137	−	0.774464i
$448$	1.45444	+	2.51917i	0.0687160	+	0.119020i
$449$	3.20064	−	1.84789i	0.151048	−	0.0872075i	−0.422571	−	0.906330i	$-0.638872\pi$
$449$	3.20064	−	1.84789i	0.151048	−	0.0872075i	0.573619	+	0.819122i	$0.305539\pi$
$450$		−	1.19656i		−	0.0564063i
$451$	−2.98130	−	5.16376i	−0.140384	−	0.243152i
$452$			2.06094i			0.0969386i
$453$	−12.0740	+	20.9128i	−0.567287	+	0.982569i
$454$	−11.2337			−0.527225
$455$	−11.3705			−0.533058
$456$	1.41431	−	2.44966i	0.0662314	−	0.114716i
$457$	−19.3015	+	11.1437i	−0.902885	+	0.521281i	−0.878135	−	0.478413i	$-0.841212\pi$
$457$	−19.3015	+	11.1437i	−0.902885	+	0.521281i	−0.0247500	+	0.999694i	$0.507879\pi$
$458$		−	5.99061i		−	0.279923i
$459$	−0.340129	−	0.196373i	−0.0158759	−	0.00916593i
$460$	1.19413	−	2.06829i	0.0556764	−	0.0964343i
$461$	−26.9919	−	15.5838i	−1.25714	−	0.725810i	−0.284623	−	0.958640i	$-0.591868\pi$
$461$	−26.9919	−	15.5838i	−1.25714	−	0.725810i	−0.972518	+	0.232829i	$0.925202\pi$
$462$	1.96353	−	1.13364i	0.0913516	−	0.0527418i
$463$	14.2805	−	8.24484i	0.663670	−	0.383170i	−0.130004	−	0.991513i	$-0.541499\pi$
$463$	14.2805	−	8.24484i	0.663670	−	0.383170i	0.793674	+	0.608343i	$0.208166\pi$
$464$	−1.01444	−	0.585685i	−0.0470940	−	0.0271898i
$465$	5.15823	−	8.93431i	0.239207	−	0.414319i
$466$	−20.9955	−	12.1218i	−0.972599	−	0.561530i
$467$		−	3.11961i		−	0.144359i	−0.997392	−	0.0721793i	$-0.977005\pi$
$467$		−	3.11961i		−	0.144359i	0.997392	−	0.0721793i	$-0.0229954\pi$
$468$	4.05058	−	2.33860i	0.187238	−	0.108102i
$469$	17.3766	−	30.0971i	0.802376	−	1.38976i
$470$	−4.39031			−0.202510
$471$	0.335165			0.0154436
$472$	3.26269	−	5.65114i	0.150177	−	0.260115i
$473$			0.382011i			0.0175649i
$474$	1.58707	+	2.74888i	0.0728964	+	0.126260i
$475$		−	2.10632i		−	0.0966447i
$476$	0.175560	−	0.101360i	0.00804679	−	0.00464582i
$477$	0.839198	+	1.45353i	0.0384242	+	0.0665527i
$478$	−8.75017	−	15.1557i	−0.400223	−	0.693207i
$479$	−22.0029	−	12.7034i	−1.00534	−	0.580433i	−0.0955162	−	0.995428i	$-0.530450\pi$
$479$	−22.0029	−	12.7034i	−1.00534	−	0.580433i	−0.909824	+	0.414994i	$0.863784\pi$
$480$	1.34292			0.0612958
$481$	12.8722	−	19.9911i	0.586920	−	0.911517i
$482$	−15.9389			−0.725997
$483$	8.07957	+	4.66474i	0.367633	+	0.212253i
$484$	−5.33157	−	9.23455i	−0.242344	−	0.419752i
$485$	−0.309643	−	0.536317i	−0.0140602	−	0.0243529i
$486$	−10.0148	+	5.78202i	−0.454278	+	0.262278i
$487$		−	1.71715i		−	0.0778117i	−0.999243	−	0.0389058i	$-0.987613\pi$
$487$		−	1.71715i		−	0.0778117i	0.999243	−	0.0389058i	$-0.0123872\pi$
$488$	−6.66893	−	11.5509i	−0.301888	−	0.522886i
$489$		−	4.93388i		−	0.223118i
$490$	−0.730813	+	1.26581i	−0.0330148	+	0.0571833i
$491$	41.2269			1.86054			0.930272	−	0.366870i	$-0.119571\pi$
$491$	41.2269			1.86054			0.930272	+	0.366870i	$0.119571\pi$
$492$	13.7962			0.621979
$493$	−0.0408162	+	0.0706958i	−0.00183827	+	0.00318398i
$494$	7.13031	−	4.11669i	0.320808	−	0.185219i
$495$			0.694483i			0.0312147i
$496$	−6.65288	−	3.84104i	−0.298723	−	0.172468i
$497$	16.5777	−	28.7135i	0.743614	−	1.28798i
$498$	10.6328	+	6.13884i	0.476466	+	0.275088i
$499$	−8.78026	+	5.06928i	−0.393058	+	0.226932i	−0.683484	−	0.729965i	$-0.739536\pi$
$499$	−8.78026	+	5.06928i	−0.393058	+	0.226932i	0.290426	+	0.956897i	$0.406203\pi$
$500$	0.866025	−	0.500000i	0.0387298	−	0.0223607i
$501$	−2.81980	−	1.62801i	−0.125979	−	0.0727343i
$502$	−8.85362	+	15.3349i	−0.395156	+	0.684431i
$503$	33.0072	+	19.0567i	1.47172	+	0.849697i	0.999495	−	0.0317811i	$-0.0101179\pi$
$503$	33.0072	+	19.0567i	1.47172	+	0.849697i	0.472224	+	0.881478i	$0.343451\pi$
$504$		−	3.48065i		−	0.155041i
$505$	−3.47223	+	2.00469i	−0.154512	+	0.0892078i
$506$	−0.693072	+	1.20044i	−0.0308108	+	0.0533658i
$507$	−3.06106			−0.135946
$508$	15.6742			0.695431
$509$	17.6928	−	30.6449i	0.784221	−	1.35831i	−0.145242	−	0.989396i	$-0.546396\pi$
$509$	17.6928	−	30.6449i	0.784221	−	1.35831i	0.929463	−	0.368915i	$-0.120271\pi$
$510$		−	0.0935879i		−	0.00414414i
$511$	0.824362	+	1.42784i	0.0364676	+	0.0631638i
$512$		−	1.00000i		−	0.0441942i
$513$	−10.2802	+	5.93525i	−0.453880	+	0.262048i
$514$	−12.1295	−	21.0090i	−0.535011	−	0.926667i
$515$	−8.96850	−	15.5339i	−0.395200	−	0.684506i
$516$	−0.765471	−	0.441945i	−0.0336980	−	0.0194556i
$517$	2.54814			0.112067
$518$	−8.09418	−	15.7342i	−0.355638	−	0.691320i
$519$	−3.09643			−0.135918
$520$	3.38520	+	1.95444i	0.148451	+	0.0857080i
$521$	−15.8218	−	27.4042i	−0.693167	−	1.20060i	−0.970795	−	0.239912i	$-0.922882\pi$
$521$	−15.8218	−	27.4042i	−0.693167	−	1.20060i	0.277628	−	0.960689i	$-0.410452\pi$
$522$	0.700806	+	1.21383i	0.0306735	+	0.0531280i
$523$	9.26957	−	5.35179i	0.405330	−	0.234017i	−0.283451	−	0.958987i	$-0.591479\pi$
$523$	9.26957	−	5.35179i	0.405330	−	0.234017i	0.688781	+	0.724969i	$0.258146\pi$
$524$			4.86467i			0.212514i
$525$	1.95321	+	3.38305i	0.0852449	+	0.147648i
$526$			1.53537i			0.0669453i
$527$	−0.267681	+	0.463637i	−0.0116604	+	0.0201964i
$528$	−0.779434			−0.0339205
$529$	17.2963			0.752011
$530$	−0.701343	+	1.21476i	−0.0304644	+	0.0527659i
$531$	−6.76192	+	3.90399i	−0.293442	+	0.169419i
$532$		−	6.12706i		−	0.265642i
$533$	34.7769	+	20.0785i	1.50636	+	0.869695i
$534$	2.45105	−	4.24534i	0.106067	−	0.183714i
$535$	3.23550	+	1.86802i	0.139883	+	0.0807615i
$536$	−10.3466	+	5.97361i	−0.446905	+	0.258021i
$537$	20.0237	−	11.5607i	0.864087	−	0.498881i
$538$	5.76409	+	3.32790i	0.248507	+	0.143476i
$539$	0.424165	−	0.734675i	0.0182701	−	0.0316447i
$540$	−4.88062	−	2.81783i	−0.210028	−	0.121260i
$541$		−	27.6302i		−	1.18792i	−0.804496	−	0.593958i	$-0.797564\pi$
$541$		−	27.6302i		−	1.18792i	0.804496	−	0.593958i	$-0.202436\pi$
$542$	25.0791	−	14.4794i	1.07724	−	0.621944i
$543$	8.41762	−	14.5797i	0.361235	−	0.625677i
$544$	−0.0696897			−0.00298792
$545$	12.7354			0.545525
$546$	−7.63486	+	13.2240i	−0.326742	+	0.565934i
$547$			14.3498i			0.613552i	0.951782	+	0.306776i	$0.0992502\pi$
$547$			14.3498i			0.613552i	−0.951782	+	0.306776i	$0.900750\pi$
$548$	6.23431	+	10.7981i	0.266316	+	0.461274i
$549$			15.9595i			0.681136i
$550$	−0.502642	+	0.290201i	−0.0214327	+	0.0123742i
$551$	1.23364	+	2.13673i	0.0525549	+	0.0910278i
$552$	−1.60362	−	2.77755i	−0.0682545	−	0.118220i
$553$	5.95431	+	3.43772i	0.253203	+	0.146187i
$554$	4.44177			0.188713
$555$	−8.15909	−	0.395793i	−0.346334	−	0.0168005i
$556$	17.2069			0.729733
$557$	−40.6459	−	23.4669i	−1.72222	−	0.994326i	−0.914298	−	0.405042i	$-0.867257\pi$
$557$	−40.6459	−	23.4669i	−1.72222	−	0.994326i	−0.807925	−	0.589285i	$-0.799410\pi$
$558$	4.59603	+	7.96056i	0.194565	+	0.336997i
$559$	−1.28638	−	2.22808i	−0.0544082	−	0.0942378i
$560$	2.51917	−	1.45444i	0.106454	−	0.0614615i
$561$			0.0543185i			0.00229333i
$562$	4.20063	+	7.27571i	0.177193	+	0.306907i
$563$			26.2205i			1.10506i	0.833493	+	0.552530i	$0.186338\pi$
$563$			26.2205i			1.10506i	−0.833493	+	0.552530i	$0.813662\pi$
$564$	−2.94792	+	5.10595i	−0.124130	+	0.214999i
$565$	2.06094			0.0867045
$566$	−20.0984			−0.844797
$567$	5.78662	−	10.0227i	0.243015	−	0.420914i
$568$	−9.87096	+	5.69900i	−0.414176	+	0.239125i
$569$			3.90960i			0.163899i	0.996636	+	0.0819495i	$0.0261146\pi$
$569$			3.90960i			0.163899i	−0.996636	+	0.0819495i	$0.973885\pi$
$570$	−2.44966	−	1.41431i	−0.102605	−	0.0592391i
$571$	0.398368	−	0.689994i	0.0166712	−	0.0288754i	−0.857569	−	0.514368i	$-0.828026\pi$
$571$	0.398368	−	0.689994i	0.0166712	−	0.0288754i	0.874241	+	0.485493i	$0.161360\pi$
$572$	−1.96477	−	1.13436i	−0.0821512	−	0.0474300i
$573$	5.48379	−	3.16607i	0.229089	−	0.132264i
$574$	25.8800	−	14.9418i	1.08021	−	0.623661i
$575$	−2.06829	−	1.19413i	−0.0862535	−	0.0497985i
$576$	−0.598279	+	1.03625i	−0.0249283	+	0.0431771i
$577$	38.5571	+	22.2609i	1.60515	+	0.926735i	0.990434	+	0.137989i	$0.0440638\pi$
$577$	38.5571	+	22.2609i	1.60515	+	0.926735i	0.614719	+	0.788746i	$0.289269\pi$
$578$		−	16.9951i		−	0.706905i
$579$	−23.7149	+	13.6918i	−0.985559	+	0.569013i
$580$	−0.585685	+	1.01444i	−0.0243193	+	0.0421222i
$581$	26.5945			1.10333
$582$	−0.831654			−0.0344732
$583$	0.407060	−	0.705049i	0.0168587	−	0.0292002i
$584$		−	0.566789i		−	0.0234539i
$585$	−2.33860	−	4.05058i	−0.0966894	−	0.167471i
$586$			11.0703i			0.457309i
$587$	18.8589	−	10.8882i	0.778388	−	0.449403i	−0.0574704	−	0.998347i	$-0.518303\pi$
$587$	18.8589	−	10.8882i	0.778388	−	0.449403i	0.835859	+	0.548944i	$0.184970\pi$
$588$	0.981426	+	1.69988i	0.0404733	+	0.0701018i
$589$	8.09048	+	14.0131i	0.333362	+	0.577401i
$590$	−5.65114	−	3.26269i	−0.232654	−	0.134323i
$591$	13.3034			0.547229
$592$	−0.294725	+	6.07562i	−0.0121131	+	0.249706i
$593$	−14.4956			−0.595264			−0.297632	−	0.954681i	$-0.596197\pi$
$593$	−14.4956			−0.595264			−0.297632	+	0.954681i	$0.596197\pi$
$594$	2.83272	+	1.63547i	0.116228	+	0.0671041i
$595$	−0.101360	−	0.175560i	−0.00415534	−	0.00719727i
$596$	7.03952	+	12.1928i	0.288350	+	0.499437i
$597$	−11.7876	+	6.80560i	−0.482436	+	0.278535i
$598$		−	9.33540i		−	0.381753i
$599$	−15.6699	−	27.1411i	−0.640255	−	1.10895i	−0.985376	−	0.170396i	$-0.945495\pi$
$599$	−15.6699	−	27.1411i	−0.640255	−	1.10895i	0.345121	−	0.938558i	$-0.387838\pi$
$600$		−	1.34292i		−	0.0548246i
$601$	2.21429	−	3.83526i	0.0903227	−	0.156444i	−0.817324	−	0.576178i	$-0.804543\pi$
$601$	2.21429	−	3.83526i	0.0903227	−	0.156444i	0.907647	+	0.419735i	$0.137877\pi$
$602$	−1.91458			−0.0780326
$603$	14.2955			0.582160
$604$	8.99084	−	15.5726i	0.365832	−	0.633640i
$605$	−9.23455	+	5.33157i	−0.375438	+	0.216759i
$606$			5.38430i			0.218722i
$607$	31.0325	+	17.9166i	1.25957	+	0.727213i	0.972991	−	0.230843i	$-0.0741485\pi$
$607$	31.0325	+	17.9166i	1.25957	+	0.727213i	0.286579	+	0.958057i	$0.407482\pi$
$608$	−1.05316	+	1.82413i	−0.0427113	+	0.0739782i
$609$	−3.96281	−	2.28793i	−0.160581	−	0.0927115i
$610$	−11.5509	+	6.66893i	−0.467684	+	0.270017i
$611$	−14.8620	+	8.58061i	−0.601254	+	0.347134i
$612$	0.0722159	+	0.0416939i	0.00291915	+	0.00168537i
$613$	9.65823	−	16.7286i	0.390092	−	0.675660i	−0.602369	−	0.798218i	$-0.705776\pi$
$613$	9.65823	−	16.7286i	0.390092	−	0.675660i	0.992461	+	0.122558i	$0.0391097\pi$
$614$	−9.06924	−	5.23613i	−0.366005	−	0.211313i
$615$		−	13.7962i		−	0.556315i
$616$	−1.46213	+	0.844161i	−0.0589109	+	0.0340122i
$617$	12.6793	−	21.9611i	0.510448	−	0.884122i	−0.489478	−	0.872015i	$-0.662813\pi$
$617$	12.6793	−	21.9611i	0.510448	−	0.884122i	0.999927	−	0.0121070i	$-0.00385387\pi$
$618$	−24.0880			−0.968962
$619$	−18.9569			−0.761941			−0.380970	−	0.924587i	$-0.624410\pi$
$619$	−18.9569			−0.761941			−0.380970	+	0.924587i	$0.624410\pi$
$620$	−3.84104	+	6.65288i	−0.154260	+	0.267186i
$621$			13.4594i			0.540105i
$622$	6.48336	+	11.2295i	0.259959	+	0.450262i
$623$		−	10.6184i		−	0.425415i
$624$	4.54606	−	2.62467i	0.181988	−	0.105071i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−15.7924	−	27.3532i	−0.631191	−	1.09326i
$627$	1.42179	+	0.820870i	0.0567808	+	0.0327824i
$628$	−0.249578			−0.00995926
$629$	0.423408	+	0.0205393i	0.0168824	+	0.000818954i
$630$	−3.48065			−0.138672
$631$	37.7017	+	21.7671i	1.50088	+	0.866533i	0.999999	+	0.00101706i	$0.000323742\pi$
$631$	37.7017	+	21.7671i	1.50088	+	0.866533i	0.500881	+	0.865516i	$0.333010\pi$
$632$	−1.18180	−	2.04694i	−0.0470095	−	0.0814228i
$633$	−6.17459	−	10.6947i	−0.245418	−	0.425076i
$634$	−9.73694	+	5.62163i	−0.386703	+	0.223263i
$635$		−	15.6742i		−	0.622013i
$636$	0.941850	+	1.63133i	0.0373468	+	0.0646865i
$637$			5.71333i			0.226370i
$638$	0.339932	−	0.588780i	0.0134581	−	0.0233100i
$639$	13.6384			0.539525
$640$	−1.00000			−0.0395285
$641$	8.46180	−	14.6563i	0.334221	−	0.578888i	−0.649114	−	0.760691i	$-0.724860\pi$
$641$	8.46180	−	14.6563i	0.334221	−	0.578888i	0.983335	+	0.181803i	$0.0581934\pi$
$642$	4.34503	−	2.50861i	0.171485	−	0.0990068i
$643$			43.0250i			1.69674i	0.529404	+	0.848370i	$0.322415\pi$
$643$			43.0250i			1.69674i	−0.529404	+	0.848370i	$0.677585\pi$
$644$	−6.01641	−	3.47358i	−0.237080	−	0.136878i
$645$	−0.441945	+	0.765471i	−0.0174016	+	0.0301404i
$646$	0.127123	+	0.0733945i	0.00500159	+	0.00288767i
$647$	−10.0510	+	5.80294i	−0.395145	+	0.228137i	−0.684387	−	0.729119i	$-0.739930\pi$
$647$	−10.0510	+	5.80294i	−0.395145	+	0.228137i	0.289242	+	0.957256i	$0.406597\pi$
$648$	−3.44555	+	1.98929i	−0.135354	+	0.0781466i
$649$	3.27993	+	1.89367i	0.128748	+	0.0743330i
$650$	1.95444	−	3.38520i	0.0766596	−	0.132778i
$651$	−25.9889	−	15.0047i	−1.01859	−	0.588081i
$652$			3.67399i			0.143885i
$653$	−12.7430	+	7.35718i	−0.498672	+	0.287909i	−0.728165	−	0.685402i	$-0.759627\pi$
$653$	−12.7430	+	7.35718i	−0.498672	+	0.287909i	0.229493	+	0.973310i	$0.426293\pi$
$654$	8.55134	−	14.8114i	0.334384	−	0.579170i
$655$	4.86467			0.190078
$656$	−10.2732			−0.401103
$657$	−0.339098	+	0.587334i	−0.0132295	+	0.0229141i
$658$			12.7709i			0.497862i
$659$	17.6796	+	30.6220i	0.688700	+	1.19286i	0.972259	+	0.233908i	$0.0751514\pi$
$659$	17.6796	+	30.6220i	0.688700	+	1.19286i	−0.283559	+	0.958955i	$0.591515\pi$
$660$			0.779434i			0.0303394i
$661$	23.3803	−	13.4986i	0.909388	−	0.525035i	0.0291538	−	0.999575i	$-0.490719\pi$
$661$	23.3803	−	13.4986i	0.909388	−	0.525035i	0.880234	+	0.474540i	$0.157385\pi$
$662$	−1.85830	−	3.21867i	−0.0722249	−	0.125097i
$663$	−0.182912	−	0.316813i	−0.00710372	−	0.0123040i
$664$	−7.91763	−	4.57125i	−0.307264	−	0.177399i
$665$	−6.12706			−0.237597
$666$	3.94032	−	6.11953i	0.152684	−	0.237127i
$667$	2.79753			0.108321
$668$	2.09975	+	1.21229i	0.0812418	+	0.0469049i
$669$	−7.75990	−	13.4405i	−0.300015	−	0.519641i
$670$	5.97361	+	10.3466i	0.230781	+	0.399724i
$671$	6.70417	−	3.87066i	0.258812	−	0.149425i
$672$		−	3.90641i		−	0.150693i
$673$	−20.2852	−	35.1350i	−0.781937	−	1.35435i	−0.930812	−	0.365499i	$-0.880898\pi$
$673$	−20.2852	−	35.1350i	−0.781937	−	1.35435i	0.148875	−	0.988856i	$-0.452435\pi$
$674$			28.5288i			1.09889i
$675$	−2.81783	+	4.88062i	−0.108458	+	0.187855i
$676$	2.27940			0.0876693
$677$	−24.5549			−0.943721			−0.471860	−	0.881673i	$-0.656417\pi$
$677$	−24.5549			−0.943721			−0.471860	+	0.881673i	$0.656417\pi$
$678$	1.38384	−	2.39689i	0.0531462	−	0.0920519i
$679$	−1.56009	+	0.900717i	−0.0598707	+	0.0345663i
$680$			0.0696897i			0.00267248i
$681$	13.0649	+	7.54301i	0.500647	+	0.289049i
$682$	2.22935	−	3.86134i	0.0853661	−	0.147858i
$683$	−23.6370	−	13.6468i	−0.904445	−	0.522182i	−0.0258054	−	0.999667i	$-0.508215\pi$
$683$	−23.6370	−	13.6468i	−0.904445	−	0.522182i	−0.878640	+	0.477485i	$0.841548\pi$
$684$	2.18268	−	1.26017i	0.0834567	−	0.0481837i
$685$	10.7981	−	6.23431i	0.412576	−	0.238201i
$686$	−13.9521	−	8.05525i	−0.532694	−	0.307551i
$687$	−4.02246	+	6.96711i	−0.153467	+	0.265812i
$688$	0.570004	+	0.329092i	0.0217312	+	0.0125465i
$689$			5.48294i			0.208884i
$690$	−2.77755	+	1.60362i	−0.105739	+	0.0610487i
$691$	−1.41495	+	2.45077i	−0.0538273	+	0.0932316i	−0.891684	−	0.452659i	$-0.850475\pi$
$691$	−1.41495	+	2.45077i	−0.0538273	+	0.0932316i	0.837856	+	0.545891i	$0.183809\pi$
$692$	2.30574			0.0876511
$693$	2.02017			0.0767401
$694$	−10.2399	+	17.7360i	−0.388700	+	0.673248i
$695$		−	17.2069i		−	0.652693i
$696$	0.786530	+	1.36231i	0.0298134	+	0.0516382i
$697$			0.715939i			0.0271181i
$698$	−6.74667	+	3.89519i	−0.255365	+	0.147435i
$699$	16.2786	+	28.1954i	0.615713	+	1.06645i
$700$	−1.45444	−	2.51917i	−0.0549728	−	0.0952157i
$701$	−24.9362	−	14.3969i	−0.941825	−	0.543763i	−0.0512933	−	0.998684i	$-0.516334\pi$
$701$	−24.9362	−	14.3969i	−0.941825	−	0.543763i	−0.890532	+	0.454920i	$0.849668\pi$
$702$	−22.0291			−0.831436
$703$	6.93622	−	10.7723i	0.261605	−	0.406286i
$704$	0.580401			0.0218747
$705$	5.10595	+	2.94792i	0.192301	+	0.111025i
$706$	3.51779	+	6.09299i	0.132394	+	0.229313i
$707$	5.83143	+	10.1003i	0.219314	+	0.379862i
$708$	−7.58905	+	4.38154i	−0.285214	+	0.164668i
$709$			33.7944i			1.26918i	0.772851	+	0.634588i	$0.218830\pi$
$709$			33.7944i			1.26918i	−0.772851	+	0.634588i	$0.781170\pi$
$710$	5.69900	+	9.87096i	0.213880	+	0.370450i
$711$			2.82818i			0.106065i
$712$	−1.82516	+	3.16126i	−0.0684007	+	0.118473i
$713$	18.3467			0.687091
$714$	−0.272237			−0.0101882
$715$	−1.13436	+	1.96477i	−0.0424227	+	0.0734783i
$716$	−14.9105	+	8.60860i	−0.557233	+	0.321719i
$717$			23.5016i			0.877683i
$718$	−15.2215	−	8.78812i	−0.568060	−	0.327970i
$719$	−0.226730	+	0.392707i	−0.00845559	+	0.0146455i	−0.870222	−	0.492659i	$-0.836025\pi$
$719$	−0.226730	+	0.392707i	−0.00845559	+	0.0146455i	0.861767	+	0.507305i	$0.169358\pi$
$720$	1.03625	+	0.598279i	0.0386187	+	0.0222965i
$721$	−45.1864	+	26.0884i	−1.68283	+	0.971582i
$722$	−12.6123	+	7.28170i	−0.469380	+	0.270997i
$723$	18.5370	+	10.7024i	0.689399	+	0.398025i
$724$	−6.26813	+	10.8567i	−0.232953	+	0.403487i
$725$	1.01444	+	0.585685i	0.0376752	+	0.0217518i
$726$			14.3198i			0.531456i
$727$	−2.97420	+	1.71716i	−0.110307	+	0.0636859i	−0.554139	−	0.832424i	$-0.686952\pi$
$727$	−2.97420	+	1.71716i	−0.110307	+	0.0636859i	0.443831	+	0.896110i	$0.353619\pi$
$728$	5.68526	−	9.84715i	0.210710	−	0.364960i
$729$	27.4653			1.01724
$730$	−0.566789			−0.0209778
$731$	0.0229343	−	0.0397234i	0.000848256	−	0.00146922i
$732$			17.9117i			0.662037i
$733$	−13.9570	−	24.1742i	−0.515513	−	0.892895i	−0.999838	−	0.0180069i	$-0.994268\pi$
$733$	−13.9570	−	24.1742i	−0.515513	−	0.892895i	0.484325	−	0.874888i	$-0.339065\pi$
$734$		−	6.11359i		−	0.225657i
$735$	1.69988	−	0.981426i	0.0627010	−	0.0362004i
$736$	1.19413	+	2.06829i	0.0440160	+	0.0762380i
$737$	−3.46709	−	6.00518i	−0.127712	−	0.221204i
$738$	10.6456	+	6.14626i	0.391871	+	0.226247i
$739$	0.628763			0.0231294			0.0115647	−	0.999933i	$-0.496319\pi$
$739$	0.628763			0.0231294			0.0115647	+	0.999933i	$0.496319\pi$
$740$	6.07562	+	0.294725i	0.223344	+	0.0108343i
$741$	−11.0568			−0.406181
$742$	3.53361	+	2.04013i	0.129723	+	0.0748955i
$743$	2.18734	+	3.78859i	0.0802458	+	0.138990i	0.903355	−	0.428893i	$-0.141096\pi$
$743$	2.18734	+	3.78859i	0.0802458	+	0.138990i	−0.823110	+	0.567882i	$0.807763\pi$
$744$	5.15823	+	8.93431i	0.189110	+	0.327548i
$745$	12.1928	−	7.03952i	0.446710	−	0.257908i
$746$			22.8320i			0.835938i
$747$	5.46976	+	9.47391i	0.200128	+	0.346632i
$748$		−	0.0404480i		−	0.00147892i
$749$	5.43386	−	9.41172i	0.198549	−	0.343897i
$750$	−1.34292			−0.0490366
$751$	13.0739			0.477075			0.238537	−	0.971133i	$-0.423332\pi$
$751$	13.0739			0.477075			0.238537	+	0.971133i	$0.423332\pi$
$752$	2.19515	−	3.80212i	0.0800490	−	0.138649i
$753$	20.5936	−	11.8897i	0.750473	−	0.433286i
$754$			4.57876i			0.166748i
$755$	−15.5726	−	8.99084i	−0.566745	−	0.327210i
$756$	−8.19674	+	14.1972i	−0.298113	+	0.516346i
$757$	−17.0083	−	9.81977i	−0.618179	−	0.356906i	0.157981	−	0.987442i	$-0.449502\pi$
$757$	−17.0083	−	9.81977i	−0.618179	−	0.356906i	−0.776160	+	0.630536i	$0.782835\pi$
$758$	−3.50289	+	2.02239i	−0.127231	+	0.0734566i
$759$	1.61209	−	0.930742i	0.0585152	−	0.0337838i
$760$	1.82413	+	1.05316i	0.0661681	+	0.0382022i
$761$	19.1951	−	33.2469i	0.695822	−	1.20520i	−0.274081	−	0.961707i	$-0.588374\pi$
$761$	19.1951	−	33.2469i	0.695822	−	1.20520i	0.969903	−	0.243493i	$-0.0782932\pi$
$762$	−18.2292	−	10.5246i	−0.660375	−	0.381267i
$763$		−	37.0459i		−	1.34115i
$764$	−4.08348	+	2.35760i	−0.147735	+	0.0852948i
$765$	0.0416939	−	0.0722159i	0.00150744	−	0.00261097i
$766$	−24.9662			−0.902065
$767$	−25.5070			−0.921003
$768$	−0.671462	+	1.16301i	−0.0242293	+	0.0419663i
$769$			51.1431i			1.84427i	0.386873	+	0.922133i	$0.373555\pi$
$769$			51.1431i			1.84427i	−0.386873	+	0.922133i	$0.626445\pi$
$770$	0.844161	+	1.46213i	0.0304214	+	0.0526915i
$771$			32.5781i			1.17327i
$772$	17.6592	−	10.1955i	0.635568	−	0.366946i
$773$	−24.0498	−	41.6556i	−0.865013	−	1.49825i	−0.867034	−	0.498248i	$-0.833977\pi$
$773$	−24.0498	−	41.6556i	−0.865013	−	1.49825i	0.00202142	−	0.999998i	$-0.499357\pi$
$774$	−0.393777	−	0.682043i	−0.0141540	−	0.0245155i
$775$	6.65288	+	3.84104i	0.238979	+	0.137974i
$776$	0.619286			0.0222311
$777$	−1.15132	+	23.7339i	−0.0413032	+	0.851448i
$778$	34.7531			1.24596
$779$	18.7397	+	10.8194i	0.671420	+	0.387644i
$780$	−2.62467	−	4.54606i	−0.0939782	−	0.162775i
$781$	−3.30771	−	5.72911i	−0.118359	−	0.205004i
$782$	0.144138	−	0.0832182i	0.00515437	−	0.00297588i
$783$		−	6.60144i		−	0.235916i
$784$	−0.730813	−	1.26581i	−0.0261005	−	0.0452073i
$785$			0.249578i			0.00890783i
$786$	3.26644	−	5.65763i	0.116510	−	0.201801i
$787$	13.4013			0.477704			0.238852	−	0.971056i	$-0.423229\pi$
$787$	13.4013			0.477704			0.238852	+	0.971056i	$0.423229\pi$
$788$	−9.90631			−0.352898
$789$	1.03094	−	1.78564i	0.0367025	−	0.0635706i
$790$	−2.04694	+	1.18180i	−0.0728268	+	0.0420465i
$791$		−	5.99505i		−	0.213159i
$792$	−0.601440	−	0.347242i	−0.0213712	−	0.0123387i
$793$	−26.0681	+	45.1513i	−0.925706	+	1.60337i
$794$	−27.7828	−	16.0404i	−0.985974	−	0.569252i
$795$	1.63133	−	0.941850i	0.0578574	−	0.0334040i
$796$	8.77760	−	5.06775i	0.311114	−	0.179622i
$797$	−39.7423	−	22.9452i	−1.40774	−	0.812761i	−0.412573	−	0.910924i	$-0.635370\pi$
$797$	−39.7423	−	22.9452i	−1.40774	−	0.812761i	−0.995170	+	0.0981633i	$0.968703\pi$
$798$	−4.11408	+	7.12580i	−0.145637	+	0.252251i
$799$	−0.264968	−	0.152980i	−0.00937390	−	0.00541203i
$800$			1.00000i			0.0353553i
$801$	3.78264	−	2.18391i	0.133653	−	0.0771645i
$802$	−4.79975	+	8.31341i	−0.169485	+	0.293557i
$803$	0.328965			0.0116089
$804$	16.0442			0.565836
$805$	−3.47358	+	6.01641i	−0.122427	+	0.212051i
$806$			30.0284i			1.05771i
$807$	−4.46911	−	7.74073i	−0.157320	−	0.272486i
$808$		−	4.00939i		−	0.141050i
$809$	−19.0291	+	10.9865i	−0.669028	+	0.386263i	−0.795708	−	0.605680i	$-0.792901\pi$
$809$	−19.0291	+	10.9865i	−0.669028	+	0.386263i	0.126680	+	0.991944i	$0.459568\pi$
$810$	1.98929	+	3.44555i	0.0698965	+	0.121064i
$811$	9.20780	+	15.9484i	0.323329	+	0.560023i	0.981173	−	0.193132i	$-0.0618645\pi$
$811$	9.20780	+	15.9484i	0.323329	+	0.560023i	−0.657843	+	0.753155i	$0.728531\pi$
$812$	2.95088	+	1.70369i	0.103556	+	0.0597879i
$813$	−38.8895			−1.36391
$814$	−3.52630	−	0.171059i	−0.123597	−	0.00599560i
$815$	3.67399			0.128694
$816$	0.0810495	+	0.0467939i	0.00283730	+	0.00163812i
$817$	−0.693174	−	1.20061i	−0.0242511	−	0.0420041i
$818$	−13.4355	−	23.2710i	−0.469761	−	0.813650i
$819$	−11.7827	+	6.80274i	−0.411720	+	0.237707i
$820$			10.2732i			0.358757i
$821$	14.6693	+	25.4080i	0.511962	+	0.886745i	0.999904	+	0.0138683i	$0.00441455\pi$
$821$	14.6693	+	25.4080i	0.511962	+	0.886745i	−0.487942	+	0.872876i	$0.662252\pi$
$822$		−	16.7444i		−	0.584028i
$823$	16.3669	−	28.3483i	0.570515	−	0.988161i	−0.425998	−	0.904724i	$-0.640077\pi$
$823$	16.3669	−	28.3483i	0.570515	−	0.988161i	0.996513	−	0.0834368i	$-0.0265897\pi$
$824$	17.9370			0.624865
$825$	0.779434			0.0271364
$826$	−9.49079	+	16.4385i	−0.330227	+	0.571970i
$827$	−47.4222	+	27.3792i	−1.64903	+	0.952069i	−0.671575	+	0.740936i	$0.734382\pi$
$827$	−47.4222	+	27.3792i	−1.64903	+	0.952069i	−0.977457	+	0.211133i	$0.932285\pi$
$828$		−	2.85768i		−	0.0993112i
$829$	25.5354	+	14.7429i	0.886882	+	0.512042i	0.872921	−	0.487861i	$-0.162223\pi$
$829$	25.5354	+	14.7429i	0.886882	+	0.512042i	0.0139608	+	0.999903i	$0.495556\pi$
$830$	−4.57125	+	7.91763i	−0.158670	+	0.274825i
$831$	−5.16580	−	2.98248i	−0.179200	−	0.103461i
$832$	−3.38520	+	1.95444i	−0.117361	+	0.0677581i
$833$	−0.0882136	+	0.0509301i	−0.00305642	+	0.00176462i
$834$	−20.0117	−	11.5537i	−0.692947	−	0.400073i
$835$	1.21229	−	2.09975i	0.0419531	−	0.0726648i
$836$	−1.05873	−	0.611256i	−0.0366168	−	0.0211407i
$837$		−	43.2936i		−	1.49645i
$838$	−21.1900	+	12.2340i	−0.731995	+	0.422617i
$839$	15.4100	−	26.6910i	0.532014	−	0.921475i	−0.467288	−	0.884105i	$-0.654769\pi$
$839$	15.4100	−	26.6910i	0.532014	−	0.921475i	0.999302	−	0.0373698i	$-0.0118980\pi$
$840$	−3.90641			−0.134784
$841$	27.6279			0.952686
$842$	12.6561	−	21.9209i	0.436157	−	0.755446i
$843$		−	11.2823i		−	0.388581i
$844$	4.59787	+	7.96375i	0.158265	+	0.274124i
$845$		−	2.27940i		−	0.0784138i
$846$	−4.54945	+	2.62663i	−0.156413	+	0.0903053i
$847$	15.5089	+	26.8623i	0.532893	+	0.922998i
$848$	−0.701343	−	1.21476i	−0.0240842	−	0.0417151i
$849$	23.3745	+	13.4953i	0.802211	+	0.463157i
$850$	0.0696897			0.00239034
$851$	−6.64547	−	12.9180i	−0.227804	−	0.442825i
$852$	15.3066			0.524397
$853$	−27.4808	−	15.8660i	−0.940925	−	0.543243i	−0.0506746	−	0.998715i	$-0.516137\pi$
$853$	−27.4808	−	15.8660i	−0.940925	−	0.543243i	−0.890250	+	0.455472i	$0.849470\pi$
$854$	19.3992	+	33.6004i	0.663826	+	1.14978i
$855$	−1.26017	−	2.18268i	−0.0430968	−	0.0746459i
$856$	−3.23550	+	1.86802i	−0.110587	+	0.0638476i
$857$			28.2882i			0.966308i	0.875535	+	0.483154i	$0.160509\pi$
$857$			28.2882i			0.966308i	−0.875535	+	0.483154i	$0.839491\pi$
$858$	1.52336	+	2.63854i	0.0520067	+	0.0900782i
$859$		−	14.0106i		−	0.478037i	−0.971015	−	0.239018i	$-0.923174\pi$
$859$		−	14.0106i		−	0.478037i	0.971015	−	0.239018i	$-0.0768256\pi$
$860$	0.329092	−	0.570004i	0.0112219	−	0.0194370i
$861$	−40.1315			−1.36768
$862$	28.7628			0.979665
$863$	20.6236	−	35.7211i	0.702035	−	1.21596i	−0.265716	−	0.964051i	$-0.585608\pi$
$863$	20.6236	−	35.7211i	0.702035	−	1.21596i	0.967751	−	0.251909i	$-0.0810584\pi$
$864$	4.88062	−	2.81783i	0.166042	−	0.0958644i
$865$		−	2.30574i		−	0.0783975i
$866$	−31.1945	−	18.0102i	−1.06003	−	0.612010i
$867$	−11.4116	+	19.7654i	−0.387558	+	0.671270i
$868$	19.3525	+	11.1732i	0.656866	+	0.379242i
$869$	1.18804	−	0.685918i	0.0403016	−	0.0232682i
$870$	1.36231	−	0.786530i	0.0461867	−	0.0266659i
$871$	40.4437	+	23.3502i	1.37038	+	0.791191i
$872$	−6.36770	+	11.0292i	−0.215638	+	0.373495i
$873$	−0.641735	−	0.370506i	−0.0217194	−	0.0125397i
$874$		−	5.03043i		−	0.170157i
$875$	−2.51917	+	1.45444i	−0.0851635	+	0.0491692i
$876$	−0.380577	+	0.659178i	−0.0128585	+	0.0222716i
$877$	10.9241			0.368881			0.184441	−	0.982844i	$-0.440953\pi$
$877$	10.9241			0.368881			0.184441	+	0.982844i	$0.440953\pi$
$878$	2.27575			0.0768028
$879$	7.43327	−	12.8748i	0.250718	−	0.434256i
$880$		−	0.580401i		−	0.0195653i
$881$	23.8970	+	41.3909i	0.805111	+	1.39449i	0.916216	+	0.400685i	$0.131228\pi$
$881$	23.8970	+	41.3909i	0.805111	+	1.39449i	−0.111105	+	0.993809i	$0.535439\pi$
$882$			1.74892i			0.0588892i
$883$	10.3632	−	5.98319i	0.348749	−	0.201350i	−0.315385	−	0.948964i	$-0.602134\pi$
$883$	10.3632	−	5.98319i	0.348749	−	0.201350i	0.664134	+	0.747613i	$0.268800\pi$
$884$	0.136205	+	0.235913i	0.00458106	+	0.00793462i
$885$	4.38154	+	7.58905i	0.147284	+	0.255103i
$886$	−3.27786	−	1.89247i	−0.110122	−	0.0635789i
$887$	−47.4989			−1.59486			−0.797428	−	0.603414i	$-0.793806\pi$
$887$	−47.4989			−1.59486			−0.797428	+	0.603414i	$0.793806\pi$
$888$	4.42231	−	6.86808i	0.148403	−	0.230478i
$889$	−45.5946			−1.52919
$890$	3.16126	+	1.82516i	0.105966	+	0.0611794i
$891$	−1.15459	−	1.99980i	−0.0386801	−	0.0669958i
$892$	5.77836	+	10.0084i	0.193474	+	0.335107i
$893$	−8.00848	+	4.62370i	−0.267994	+	0.154726i
$894$		−	18.9071i		−	0.632347i
$895$	8.60860	+	14.9105i	0.287754	+	0.498404i
$896$			2.90889i			0.0971791i
$897$	−6.26836	+	10.8571i	−0.209295	+	0.362509i
$898$	3.69579			0.123330
$899$	−8.99857			−0.300119
$900$	0.598279	−	1.03625i	0.0199426	−	0.0345416i
$901$	−0.0846564	+	0.0488764i	−0.00282031	+	0.00162831i
$902$		−	5.96260i		−	0.198533i
$903$	2.22667	+	1.28557i	0.0740989	+	0.0427810i
$904$	−1.03047	+	1.78483i	−0.0342730	+	0.0593625i
$905$	10.8567	+	6.26813i	0.360890	+	0.208360i
$906$	−20.9128	+	12.0740i	−0.694781	+	0.401132i
$907$	−9.21676	+	5.32130i	−0.306038	+	0.176691i	−0.645152	−	0.764054i	$-0.723206\pi$
$907$	−9.21676	+	5.32130i	−0.306038	+	0.176691i	0.339114	+	0.940745i	$0.389873\pi$
$908$	−9.72869	−	5.61686i	−0.322858	−	0.186402i
$909$	−2.39873	+	4.15473i	−0.0795609	+	0.137804i
$910$	−9.84715	−	5.68526i	−0.326430	−	0.188464i
$911$		−	5.59730i		−	0.185447i	−0.995692	−	0.0927234i	$-0.970443\pi$
$911$		−	5.59730i		−	0.185447i	0.995692	−	0.0927234i	$-0.0295572\pi$
$912$	2.44966	−	1.41431i	0.0811165	−	0.0468326i
$913$	2.65316	−	4.59540i	0.0878067	−	0.152086i
$914$	−22.2874			−0.737203
$915$	17.9117			0.592144
$916$	2.99531	−	5.18802i	0.0989677	−	0.171417i
$917$		−	14.1508i		−	0.467300i
$918$	−0.196373	−	0.340129i	−0.00648129	−	0.0112259i
$919$			32.0453i			1.05708i	0.848909	+	0.528539i	$0.177260\pi$
$919$			32.0453i			1.05708i	−0.848909	+	0.528539i	$0.822740\pi$
$920$	2.06829	−	1.19413i	0.0681893	−	0.0393691i
$921$	7.03172	+	12.1793i	0.231703	+	0.401321i
$922$	−15.5838	−	26.9919i	−0.513225	−	0.888932i
$923$	38.5845	+	22.2767i	1.27002	+	0.733248i
$924$	2.26729			0.0745882
$925$	0.294725	−	6.07562i	0.00969049	−	0.199765i
$926$	16.4897			0.541884
$927$	−18.5872	−	10.7313i	−0.610484	−	0.352463i
$928$	−0.585685	−	1.01444i	−0.0192261	−	0.0333005i
$929$	−9.23346	−	15.9928i	−0.302940	−	0.524707i	0.673861	−	0.738859i	$-0.264635\pi$
$929$	−9.23346	−	15.9928i	−0.302940	−	0.524707i	−0.976801	+	0.214151i	$0.931301\pi$
$930$	8.93431	−	5.15823i	0.292968	−	0.169145i
$931$			3.07866i			0.100899i
$932$	−12.1218	−	20.9955i	−0.397062	−	0.687731i
$933$		−	17.4133i		−	0.570086i
$934$	1.55981	−	2.70167i	0.0510385	−	0.0884012i
$935$	−0.0404480			−0.00132279
$936$	4.67721			0.152879
$937$	−3.11231	+	5.39068i	−0.101675	+	0.176106i	−0.912375	−	0.409356i	$-0.865753\pi$
$937$	−3.11231	+	5.39068i	−0.101675	+	0.176106i	0.810700	+	0.585462i	$0.199087\pi$
$938$	30.0971	−	17.3766i	0.982705	−	0.567365i
$939$			42.4160i			1.38419i
$940$	−3.80212	−	2.19515i	−0.124011	−	0.0715980i
$941$	−27.4162	+	47.4863i	−0.893743	+	1.54801i	−0.0583901	+	0.998294i	$0.518597\pi$
$941$	−27.4162	+	47.4863i	−0.893743	+	1.54801i	−0.835353	+	0.549714i	$0.814737\pi$
$942$	0.290261	+	0.167582i	0.00945721	+	0.00546013i
$943$	21.2480	−	12.2675i	0.691930	−	0.399486i
$944$	5.65114	−	3.26269i	0.183929	−	0.106191i
$945$	14.1972	+	8.19674i	0.461834	+	0.266640i
$946$	−0.191005	+	0.330831i	−0.00621012	+	0.0107562i
$947$	46.3153	+	26.7402i	1.50505	+	0.868939i	0.999983	+	0.00585701i	$0.00186435\pi$
$947$	46.3153	+	26.7402i	1.50505	+	0.868939i	0.505064	+	0.863082i	$0.331469\pi$
$948$			3.17413i			0.103091i
$949$	−1.91869	+	1.10776i	−0.0622833	+	0.0359593i
$950$	1.05316	−	1.82413i	0.0341691	−	0.0591826i
$951$	15.0988			0.489613
$952$	0.202719			0.00657017
$953$	5.69292	−	9.86042i	0.184412	−	0.319410i	−0.758966	−	0.651130i	$-0.774295\pi$
$953$	5.69292	−	9.86042i	0.184412	−	0.319410i	0.943378	+	0.331719i	$0.107629\pi$
$954$			1.67840i			0.0543401i
$955$	2.35760	+	4.08348i	0.0762900	+	0.132138i
$956$		−	17.5003i		−	0.566001i
$957$	−0.790687	+	0.456503i	−0.0255593	+	0.0147566i
$958$	−12.7034	−	22.0029i	−0.410428	−	0.710883i
$959$	−18.1349	−	31.4106i	−0.585607	−	1.01430i
$960$	1.16301	+	0.671462i	0.0375358	+	0.0216713i
$961$	−28.0145			−0.903693
$962$	21.1432	−	10.8768i	0.681684	−	0.350681i
$963$	4.47038			0.144056
$964$	−13.8035	−	7.96945i	−0.444580	−	0.256679i
$965$	−10.1955	−	17.6592i	−0.328206	−	0.568470i
$966$	4.66474	+	8.07957i	0.150086	+	0.259956i
$967$	14.7914	−	8.53980i	0.475659	−	0.274622i	−0.242947	−	0.970040i	$-0.578114\pi$
$967$	14.7914	−	8.53980i	0.475659	−	0.274622i	0.718605	+	0.695418i	$0.244781\pi$
$968$		−	10.6631i		−	0.342726i
$969$	−0.0985631	−	0.170716i	−0.00316630	−	0.00548420i
$970$		−	0.619286i		−	0.0198841i
$971$	7.27135	−	12.5944i	0.233349	−	0.404172i	−0.725443	−	0.688283i	$-0.758365\pi$
$971$	7.27135	−	12.5944i	0.233349	−	0.404172i	0.958792	+	0.284111i	$0.0916983\pi$
$972$	−11.5640			−0.370917
$973$	−50.0528			−1.60462
$974$	0.858577	−	1.48710i	0.0275106	−	0.0476497i
$975$	−4.54606	+	2.62467i	−0.145590	+	0.0840566i
$976$		−	13.3379i		−	0.426935i
$977$	−8.78789	−	5.07369i	−0.281150	−	0.162322i	0.352794	−	0.935701i	$-0.385232\pi$
$977$	−8.78789	−	5.07369i	−0.281150	−	0.162322i	−0.633944	+	0.773379i	$0.718565\pi$
$978$	2.46694	−	4.27287i	0.0788841	−	0.136631i
$979$	−1.83480	−	1.05932i	−0.0586405	−	0.0338561i
$980$	−1.26581	+	0.730813i	−0.0404347	+	0.0233450i
$981$	13.1971	−	7.61933i	0.421350	−	0.243266i
$982$	35.7036	+	20.6135i	1.13935	+	0.657802i
$983$	27.0145	−	46.7905i	0.861630	−	1.49239i	−0.00872533	−	0.999962i	$-0.502777\pi$
$983$	27.0145	−	46.7905i	0.861630	−	1.49239i	0.870355	−	0.492425i	$-0.163889\pi$
$984$	11.9478	+	6.89809i	0.380883	+	0.219903i
$985$			9.90631i			0.315641i
$986$	−0.0706958	+	0.0408162i	−0.00225141	+	0.00129985i
$987$	8.57517	−	14.8526i	0.272951	−	0.472765i
$988$	8.23338			0.261939
$989$	−1.57191			−0.0499838
$990$	−0.347242	+	0.601440i	−0.0110361	+	0.0191150i
$991$			27.1605i			0.862782i	0.902165	+	0.431391i	$0.141977\pi$
$991$			27.1605i			0.862782i	−0.902165	+	0.431391i	$0.858023\pi$
$992$	−3.84104	−	6.65288i	−0.121953	−	0.211229i
$993$			4.99111i			0.158388i
$994$	28.7135	−	16.5777i	0.910737	−	0.525814i
$995$	−5.06775	−	8.77760i	−0.160659	−	0.278269i
$996$	6.13884	+	10.6328i	0.194516	+	0.336912i
$997$	39.9950	+	23.0911i	1.26665	+	0.731303i	0.974353	−	0.225024i	$-0.0722460\pi$
$997$	39.9950	+	23.0911i	1.26665	+	0.731303i	0.292300	+	0.956327i	$0.405579\pi$
$998$	−10.1386			−0.320931
$999$	−30.4833	+	15.6816i	−0.964448	+	0.496144i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.l.c.101.4	yes	12
37.11	even	6	inner	370.2.l.c.11.4	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.l.c.11.4	✓	12	37.11	even	6	inner
370.2.l.c.101.4	yes	12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.671462 - 1.16301i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} -1.34292i q^{6} +(-1.45444 - 2.51917i) q^{7} +1.00000i q^{8} +(0.598279 - 1.03625i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.671462 - 1.16301i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} -1.34292i q^{6} +(-1.45444 - 2.51917i) q^{7} +1.00000i q^{8} +(0.598279 - 1.03625i) q^{9} +1.00000 q^{10} -0.580401 q^{11} +(0.671462 - 1.16301i) q^{12} +(3.38520 - 1.95444i) q^{13} -2.90889i q^{14} +(-1.16301 - 0.671462i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.0603530 + 0.0348448i) q^{17} +(1.03625 - 0.598279i) q^{18} +(1.82413 - 1.05316i) q^{19} +(0.866025 + 0.500000i) q^{20} +(-1.95321 + 3.38305i) q^{21} +(-0.502642 - 0.290201i) q^{22} -2.38825i q^{23} +(1.16301 - 0.671462i) q^{24} +(0.500000 - 0.866025i) q^{25} +3.90889 q^{26} -5.63565 q^{27} +(1.45444 - 2.51917i) q^{28} +1.17137i q^{29} +(-0.671462 - 1.16301i) q^{30} +7.68209i q^{31} +(-0.866025 + 0.500000i) q^{32} +(0.389717 + 0.675010i) q^{33} +(0.0348448 + 0.0603530i) q^{34} +(-2.51917 - 1.45444i) q^{35} +1.19656 q^{36} +(5.40900 - 2.78257i) q^{37} +2.10632 q^{38} +(-4.54606 - 2.62467i) q^{39} +(0.500000 + 0.866025i) q^{40} +(5.13662 + 8.89689i) q^{41} +(-3.38305 + 1.95321i) q^{42} -0.658184i q^{43} +(-0.290201 - 0.502642i) q^{44} -1.19656i q^{45} +(1.19413 - 2.06829i) q^{46} -4.39031 q^{47} +1.34292 q^{48} +(-0.730813 + 1.26581i) q^{49} +(0.866025 - 0.500000i) q^{50} -0.0935879i q^{51} +(3.38520 + 1.95444i) q^{52} +(-0.701343 + 1.21476i) q^{53} +(-4.88062 - 2.81783i) q^{54} +(-0.502642 + 0.290201i) q^{55} +(2.51917 - 1.45444i) q^{56} +(-2.44966 - 1.41431i) q^{57} +(-0.585685 + 1.01444i) q^{58} +(-5.65114 - 3.26269i) q^{59} -1.34292i q^{60} +(-11.5509 + 6.66893i) q^{61} +(-3.84104 + 6.65288i) q^{62} -3.48065 q^{63} -1.00000 q^{64} +(1.95444 - 3.38520i) q^{65} +0.779434i q^{66} +(5.97361 + 10.3466i) q^{67} +0.0696897i q^{68} +(-2.77755 + 1.60362i) q^{69} +(-1.45444 - 2.51917i) q^{70} +(5.69900 + 9.87096i) q^{71} +(1.03625 + 0.598279i) q^{72} -0.566789 q^{73} +(6.07562 + 0.294725i) q^{74} -1.34292 q^{75} +(1.82413 + 1.05316i) q^{76} +(0.844161 + 1.46213i) q^{77} +(-2.62467 - 4.54606i) q^{78} +(-2.04694 + 1.18180i) q^{79} +1.00000i q^{80} +(1.98929 + 3.44555i) q^{81} +10.2732i q^{82} +(-4.57125 + 7.91763i) q^{83} -3.90641 q^{84} +0.0696897 q^{85} +(0.329092 - 0.570004i) q^{86} +(1.36231 - 0.786530i) q^{87} -0.580401i q^{88} +(3.16126 + 1.82516i) q^{89} +(0.598279 - 1.03625i) q^{90} +(-9.84715 - 5.68526i) q^{91} +(2.06829 - 1.19413i) q^{92} +(8.93431 - 5.15823i) q^{93} +(-3.80212 - 2.19515i) q^{94} +(1.05316 - 1.82413i) q^{95} +(1.16301 + 0.671462i) q^{96} -0.619286i q^{97} +(-1.26581 + 0.730813i) q^{98} +(-0.347242 + 0.601440i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{3} + 6 q^{4} + 2 q^{7} - 2 q^{9}+O(q^{10}) \) 12 * q + 4 * q^3 + 6 * q^4 + 2 * q^7 - 2 * q^9	\( 12 q + 4 q^{3} + 6 q^{4} + 2 q^{7} - 2 q^{9} + 12 q^{10} - 16 q^{11} - 4 q^{12} + 6 q^{13} - 6 q^{16} - 6 q^{17} + 18 q^{19} - 14 q^{21} + 6 q^{22} + 6 q^{25} + 8 q^{26} - 32 q^{27} - 2 q^{28} + 4 q^{30} - 10 q^{33} - 10 q^{34} - 6 q^{35} - 4 q^{36} - 26 q^{37} + 8 q^{38} + 18 q^{39} + 6 q^{40} + 4 q^{41} + 18 q^{42} - 8 q^{44} - 4 q^{46} - 20 q^{47} - 8 q^{48} + 2 q^{49} + 6 q^{52} - 2 q^{53} + 6 q^{55} + 6 q^{56} + 36 q^{57} + 8 q^{58} + 12 q^{59} + 24 q^{61} + 10 q^{62} - 16 q^{63} - 12 q^{64} + 4 q^{65} + 28 q^{67} - 6 q^{69} + 2 q^{70} - 40 q^{71} - 12 q^{73} + 14 q^{74} + 8 q^{75} + 18 q^{76} - 24 q^{77} - 10 q^{78} + 24 q^{79} - 6 q^{81} - 16 q^{83} - 28 q^{84} - 20 q^{85} - 16 q^{86} - 24 q^{87} + 6 q^{89} - 2 q^{90} - 18 q^{91} + 6 q^{92} + 78 q^{93} + 4 q^{95} - 12 q^{98} + 22 q^{99}+O(q^{100}) \) 12 * q + 4 * q^3 + 6 * q^4 + 2 * q^7 - 2 * q^9 + 12 * q^10 - 16 * q^11 - 4 * q^12 + 6 * q^13 - 6 * q^16 - 6 * q^17 + 18 * q^19 - 14 * q^21 + 6 * q^22 + 6 * q^25 + 8 * q^26 - 32 * q^27 - 2 * q^28 + 4 * q^30 - 10 * q^33 - 10 * q^34 - 6 * q^35 - 4 * q^36 - 26 * q^37 + 8 * q^38 + 18 * q^39 + 6 * q^40 + 4 * q^41 + 18 * q^42 - 8 * q^44 - 4 * q^46 - 20 * q^47 - 8 * q^48 + 2 * q^49 + 6 * q^52 - 2 * q^53 + 6 * q^55 + 6 * q^56 + 36 * q^57 + 8 * q^58 + 12 * q^59 + 24 * q^61 + 10 * q^62 - 16 * q^63 - 12 * q^64 + 4 * q^65 + 28 * q^67 - 6 * q^69 + 2 * q^70 - 40 * q^71 - 12 * q^73 + 14 * q^74 + 8 * q^75 + 18 * q^76 - 24 * q^77 - 10 * q^78 + 24 * q^79 - 6 * q^81 - 16 * q^83 - 28 * q^84 - 20 * q^85 - 16 * q^86 - 24 * q^87 + 6 * q^89 - 2 * q^90 - 18 * q^91 + 6 * q^92 + 78 * q^93 + 4 * q^95 - 12 * q^98 + 22 * q^99

Introduction

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