LMFDB - Embedded newform 1155.2.q.j.991.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(331,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1155.331");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.q (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:	$9.22272143346$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 13 x^{14} + 116 x^{12} + 545 x^{10} - 6 x^{9} + 1849 x^{8} + 78 x^{7} + 3192 x^{6} + 636 x^{5} + \cdots + 576 $ x^16 + 13x^14 + 116x^12 + 545x^10 - 6x^9 + 1849x^8 + 78x^7 + 3192x^6 + 636x^5 + 3912x^4 + 432x^3 + 1764x^2 - 144x + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			991.7
Root			$0.967294 - 1.67540i$ of defining polynomial
Character	$\chi$	$=$	1155.991
Dual form			1155.2.q.j.331.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.967294 + 1.67540i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.871314 + 1.50916i) q^{4} +(0.500000 + 0.866025i) q^{5} -1.93459 q^{6} +(2.59557 - 0.512871i) q^{7} +0.497910 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.967294 + 1.67540i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.871314 + 1.50916i) q^{4} +(0.500000 + 0.866025i) q^{5} -1.93459 q^{6} +(2.59557 - 0.512871i) q^{7} +0.497910 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.967294 + 1.67540i) q^{10} +(0.500000 - 0.866025i) q^{11} +(-0.871314 - 1.50916i) q^{12} -6.71159 q^{13} +(3.36994 + 3.85252i) q^{14} -1.00000 q^{15} +(2.22425 + 3.85252i) q^{16} +(-0.742627 + 1.28627i) q^{17} +(0.967294 - 1.67540i) q^{18} +(4.15259 + 7.19250i) q^{19} -1.74263 q^{20} +(-0.853623 + 2.50426i) q^{21} +1.93459 q^{22} +(2.04101 + 3.53513i) q^{23} +(-0.248955 + 0.431203i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-6.49208 - 11.2446i) q^{26} +1.00000 q^{27} +(-1.48755 + 4.36399i) q^{28} -3.69187 q^{29} +(-0.967294 - 1.67540i) q^{30} +(-1.10467 + 1.91334i) q^{31} +(-3.80510 + 6.59063i) q^{32} +(0.500000 + 0.866025i) q^{33} -2.87335 q^{34} +(1.74194 + 1.99139i) q^{35} +1.74263 q^{36} +(2.10505 + 3.64605i) q^{37} +(-8.03355 + 13.9145i) q^{38} +(3.35580 - 5.81241i) q^{39} +(0.248955 + 0.431203i) q^{40} -3.16689 q^{41} +(-5.02135 + 0.992194i) q^{42} +4.93147 q^{43} +(0.871314 + 1.50916i) q^{44} +(0.500000 - 0.866025i) q^{45} +(-3.94851 + 6.83903i) q^{46} +(1.92014 + 3.32578i) q^{47} -4.44850 q^{48} +(6.47393 - 2.66238i) q^{49} -1.93459 q^{50} +(-0.742627 - 1.28627i) q^{51} +(5.84790 - 10.1289i) q^{52} +(6.11167 - 10.5857i) q^{53} +(0.967294 + 1.67540i) q^{54} +1.00000 q^{55} +(1.29236 - 0.255364i) q^{56} -8.30518 q^{57} +(-3.57112 - 6.18536i) q^{58} +(-0.0703725 + 0.121889i) q^{59} +(0.871314 - 1.50916i) q^{60} +(-5.38486 - 9.32684i) q^{61} -4.27415 q^{62} +(-1.74194 - 1.99139i) q^{63} -5.82558 q^{64} +(-3.35580 - 5.81241i) q^{65} +(-0.967294 + 1.67540i) q^{66} +(5.23040 - 9.05932i) q^{67} +(-1.29412 - 2.24149i) q^{68} -4.08202 q^{69} +(-1.65141 + 4.84471i) q^{70} -14.9677 q^{71} +(-0.248955 - 0.431203i) q^{72} +(0.880191 - 1.52454i) q^{73} +(-4.07240 + 7.05361i) q^{74} +(-0.500000 - 0.866025i) q^{75} -14.4728 q^{76} +(0.853623 - 2.50426i) q^{77} +12.9842 q^{78} +(3.28402 + 5.68809i) q^{79} +(-2.22425 + 3.85252i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.06332 - 5.30582i) q^{82} +9.32844 q^{83} +(-3.03556 - 3.47025i) q^{84} -1.48525 q^{85} +(4.77018 + 8.26219i) q^{86} +(1.84593 - 3.19725i) q^{87} +(0.248955 - 0.431203i) q^{88} +(-1.59732 - 2.76664i) q^{89} +1.93459 q^{90} +(-17.4204 + 3.44218i) q^{91} -7.11344 q^{92} +(-1.10467 - 1.91334i) q^{93} +(-3.71468 + 6.43401i) q^{94} +(-4.15259 + 7.19250i) q^{95} +(-3.80510 - 6.59063i) q^{96} +10.3227 q^{97} +(10.7227 + 8.27112i) q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} - 10 q^{4} + 8 q^{5} - 8 q^{9}+O(q^{10}) $ 16 * q - 8 * q^3 - 10 * q^4 + 8 * q^5 - 8 * q^9	$ 16 q - 8 q^{3} - 10 q^{4} + 8 q^{5} - 8 q^{9} + 8 q^{11} - 10 q^{12} + 8 q^{13} + 6 q^{14} - 16 q^{15} - 2 q^{16} - 4 q^{17} - 9 q^{19} - 20 q^{20} + 3 q^{21} + 5 q^{23} - 8 q^{25} - 32 q^{26} + 16 q^{27} + 2 q^{28} - 10 q^{29} - 5 q^{31} + 8 q^{33} + 3 q^{35} + 20 q^{36} - 7 q^{37} + 8 q^{38} - 4 q^{39} + 18 q^{41} + 28 q^{43} + 10 q^{44} + 8 q^{45} - 18 q^{46} + 5 q^{47} + 4 q^{48} - 20 q^{49} - 4 q^{51} - 8 q^{52} + q^{53} + 16 q^{55} + 42 q^{56} + 18 q^{57} - 10 q^{58} - 16 q^{59} + 10 q^{60} - 26 q^{61} - 32 q^{62} - 3 q^{63} - 16 q^{64} + 4 q^{65} - 3 q^{67} - 88 q^{68} - 10 q^{69} + 6 q^{70} - 60 q^{71} - 15 q^{73} + 18 q^{74} - 8 q^{75} + 44 q^{76} - 3 q^{77} + 64 q^{78} - 11 q^{79} + 2 q^{80} - 8 q^{81} - 42 q^{82} + 24 q^{83} - 10 q^{84} - 8 q^{85} + 48 q^{86} + 5 q^{87} + 6 q^{91} + 56 q^{92} - 5 q^{93} - 24 q^{94} + 9 q^{95} + 88 q^{97} - 24 q^{98} - 16 q^{99}+O(q^{100}) $ 16 * q - 8 * q^3 - 10 * q^4 + 8 * q^5 - 8 * q^9 + 8 * q^11 - 10 * q^12 + 8 * q^13 + 6 * q^14 - 16 * q^15 - 2 * q^16 - 4 * q^17 - 9 * q^19 - 20 * q^20 + 3 * q^21 + 5 * q^23 - 8 * q^25 - 32 * q^26 + 16 * q^27 + 2 * q^28 - 10 * q^29 - 5 * q^31 + 8 * q^33 + 3 * q^35 + 20 * q^36 - 7 * q^37 + 8 * q^38 - 4 * q^39 + 18 * q^41 + 28 * q^43 + 10 * q^44 + 8 * q^45 - 18 * q^46 + 5 * q^47 + 4 * q^48 - 20 * q^49 - 4 * q^51 - 8 * q^52 + q^53 + 16 * q^55 + 42 * q^56 + 18 * q^57 - 10 * q^58 - 16 * q^59 + 10 * q^60 - 26 * q^61 - 32 * q^62 - 3 * q^63 - 16 * q^64 + 4 * q^65 - 3 * q^67 - 88 * q^68 - 10 * q^69 + 6 * q^70 - 60 * q^71 - 15 * q^73 + 18 * q^74 - 8 * q^75 + 44 * q^76 - 3 * q^77 + 64 * q^78 - 11 * q^79 + 2 * q^80 - 8 * q^81 - 42 * q^82 + 24 * q^83 - 10 * q^84 - 8 * q^85 + 48 * q^86 + 5 * q^87 + 6 * q^91 + 56 * q^92 - 5 * q^93 - 24 * q^94 + 9 * q^95 + 88 * q^97 - 24 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$386$	$661$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.967294	+	1.67540i	0.683980	+	1.18469i	0.973756	+	0.227593i	$0.0730857\pi$
$2$	0.967294	+	1.67540i	0.683980	+	1.18469i	−0.289776	+	0.957094i	$0.593581\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−0.871314	+	1.50916i	−0.435657	+	0.754580i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−1.93459			−0.789792
$7$	2.59557	−	0.512871i	0.981032	−	0.193847i
$7$	2.59557	−	0.512871i	0.981032	−	0.193847i
$8$	0.497910			0.176038
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−0.967294	+	1.67540i	−0.305885	+	0.529808i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$	−0.871314	−	1.50916i	−0.251527	−	0.435657i
$13$	−6.71159			−1.86146			−0.930731	−	0.365706i	$-0.880828\pi$
$13$	−6.71159			−1.86146			−0.930731	+	0.365706i	$0.880828\pi$
$14$	3.36994	+	3.85252i	0.900654	+	1.02963i
$15$	−1.00000			−0.258199
$16$	2.22425	+	3.85252i	0.556063	+	0.963130i
$17$	−0.742627	+	1.28627i	−0.180114	+	0.311966i	−0.941919	−	0.335840i	$-0.890980\pi$
$17$	−0.742627	+	1.28627i	−0.180114	+	0.311966i	0.761806	+	0.647806i	$0.224313\pi$
$18$	0.967294	−	1.67540i	0.227993	−	0.394896i
$19$	4.15259	+	7.19250i	0.952670	+	1.65007i	0.739612	+	0.673033i	$0.235009\pi$
$19$	4.15259	+	7.19250i	0.952670	+	1.65007i	0.213058	+	0.977040i	$0.431658\pi$
$20$	−1.74263			−0.389663
$21$	−0.853623	+	2.50426i	−0.186276	+	0.546475i
$22$	1.93459			0.412455
$23$	2.04101	+	3.53513i	0.425580	+	0.737126i	0.996474	−	0.0838971i	$-0.0267367\pi$
$23$	2.04101	+	3.53513i	0.425580	+	0.737126i	−0.570894	+	0.821024i	$0.693403\pi$
$24$	−0.248955	+	0.431203i	−0.0508177	+	0.0880189i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−6.49208	−	11.2446i	−1.27320	−	2.20525i
$27$	1.00000			0.192450
$28$	−1.48755	+	4.36399i	−0.281120	+	0.824717i
$29$	−3.69187			−0.685563			−0.342781	−	0.939415i	$-0.611369\pi$
$29$	−3.69187			−0.685563			−0.342781	+	0.939415i	$0.611369\pi$
$30$	−0.967294	−	1.67540i	−0.176603	−	0.305885i
$31$	−1.10467	+	1.91334i	−0.198404	+	0.343646i	−0.948011	−	0.318237i	$-0.896909\pi$
$31$	−1.10467	+	1.91334i	−0.198404	+	0.343646i	0.749607	+	0.661883i	$0.230243\pi$
$32$	−3.80510	+	6.59063i	−0.672653	+	1.16507i
$33$	0.500000	+	0.866025i	0.0870388	+	0.150756i
$34$	−2.87335			−0.492776
$35$	1.74194	+	1.99139i	0.294442	+	0.336606i
$36$	1.74263			0.290438
$37$	2.10505	+	3.64605i	0.346068	+	0.599407i	0.985547	−	0.169401i	$-0.0541833\pi$
$37$	2.10505	+	3.64605i	0.346068	+	0.599407i	−0.639479	+	0.768808i	$0.720850\pi$
$38$	−8.03355	+	13.9145i	−1.30321	+	2.25723i
$39$	3.35580	−	5.81241i	0.537358	−	0.930731i
$40$	0.248955	+	0.431203i	0.0393633	+	0.0681792i
$41$	−3.16689			−0.494586			−0.247293	−	0.968941i	$-0.579541\pi$
$41$	−3.16689			−0.494586			−0.247293	+	0.968941i	$0.579541\pi$
$42$	−5.02135	+	0.992194i	−0.774811	+	0.153099i
$43$	4.93147			0.752042			0.376021	−	0.926611i	$-0.377292\pi$
$43$	4.93147			0.752042			0.376021	+	0.926611i	$0.377292\pi$
$44$	0.871314	+	1.50916i	0.131355	+	0.227514i
$45$	0.500000	−	0.866025i	0.0745356	−	0.129099i
$46$	−3.94851	+	6.83903i	−0.582176	+	1.00836i
$47$	1.92014	+	3.32578i	0.280081	+	0.485115i	0.971404	−	0.237431i	$-0.0763053\pi$
$47$	1.92014	+	3.32578i	0.280081	+	0.485115i	−0.691323	+	0.722545i	$0.742972\pi$
$48$	−4.44850			−0.642086
$49$	6.47393	−	2.66238i	0.924847	−	0.380340i
$50$	−1.93459			−0.273592
$51$	−0.742627	−	1.28627i	−0.103989	−	0.180114i
$52$	5.84790	−	10.1289i	0.810958	−	1.40462i
$53$	6.11167	−	10.5857i	0.839502	−	1.45406i	−0.0508100	−	0.998708i	$-0.516180\pi$
$53$	6.11167	−	10.5857i	0.839502	−	1.45406i	0.890312	−	0.455351i	$-0.150486\pi$
$54$	0.967294	+	1.67540i	0.131632	+	0.227993i
$55$	1.00000			0.134840
$56$	1.29236	−	0.255364i	0.172699	−	0.0341244i
$57$	−8.30518			−1.10005
$58$	−3.57112	−	6.18536i	−0.468911	−	0.812178i
$59$	−0.0703725	+	0.121889i	−0.00916171	+	0.0158686i	−0.870570	−	0.492045i	$-0.836250\pi$
$59$	−0.0703725	+	0.121889i	−0.00916171	+	0.0158686i	0.861408	+	0.507913i	$0.169583\pi$
$60$	0.871314	−	1.50916i	0.112486	−	0.194832i
$61$	−5.38486	−	9.32684i	−0.689460	−	1.19418i	−0.972013	−	0.234928i	$-0.924515\pi$
$61$	−5.38486	−	9.32684i	−0.689460	−	1.19418i	0.282553	−	0.959252i	$-0.408819\pi$
$62$	−4.27415			−0.542818
$63$	−1.74194	−	1.99139i	−0.219464	−	0.250892i
$64$	−5.82558			−0.728198
$65$	−3.35580	−	5.81241i	−0.416235	−	0.720941i
$66$	−0.967294	+	1.67540i	−0.119066	+	0.206228i
$67$	5.23040	−	9.05932i	0.638995	−	1.10677i	−0.346659	−	0.937991i	$-0.612684\pi$
$67$	5.23040	−	9.05932i	0.638995	−	1.10677i	0.985654	−	0.168781i	$-0.0539829\pi$
$68$	−1.29412	−	2.24149i	−0.156935	−	0.271820i
$69$	−4.08202			−0.491418
$70$	−1.65141	+	4.84471i	−0.197381	+	0.579054i
$71$	−14.9677			−1.77634			−0.888172	−	0.459511i	$-0.848025\pi$
$71$	−14.9677			−1.77634			−0.888172	+	0.459511i	$0.848025\pi$
$72$	−0.248955	−	0.431203i	−0.0293396	−	0.0508177i
$73$	0.880191	−	1.52454i	0.103019	−	0.178433i	−0.809908	−	0.586556i	$-0.800483\pi$
$73$	0.880191	−	1.52454i	0.103019	−	0.178433i	0.912927	+	0.408123i	$0.133817\pi$
$74$	−4.07240	+	7.05361i	−0.473407	+	0.819965i
$75$	−0.500000	−	0.866025i	−0.0577350	−	0.100000i
$76$	−14.4728			−1.66015
$77$	0.853623	−	2.50426i	0.0972794	−	0.285387i
$78$	12.9842			1.47017
$79$	3.28402	+	5.68809i	0.369481	+	0.639960i	0.989484	−	0.144639i	$-0.0462021\pi$
$79$	3.28402	+	5.68809i	0.369481	+	0.639960i	−0.620003	+	0.784599i	$0.712869\pi$
$80$	−2.22425	+	3.85252i	−0.248679	+	0.430725i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−3.06332	−	5.30582i	−0.338287	−	0.585930i
$83$	9.32844			1.02393			0.511964	−	0.859007i	$-0.328918\pi$
$83$	9.32844			1.02393			0.511964	+	0.859007i	$0.328918\pi$
$84$	−3.03556	−	3.47025i	−0.331206	−	0.378635i
$85$	−1.48525			−0.161098
$86$	4.77018	+	8.26219i	0.514382	+	0.890935i
$87$	1.84593	−	3.19725i	0.197905	−	0.342781i
$88$	0.248955	−	0.431203i	0.0265387	−	0.0459664i
$89$	−1.59732	−	2.76664i	−0.169316	−	0.293263i	0.768864	−	0.639413i	$-0.220822\pi$
$89$	−1.59732	−	2.76664i	−0.169316	−	0.293263i	−0.938179	+	0.346149i	$0.887489\pi$
$90$	1.93459			0.203923
$91$	−17.4204	+	3.44218i	−1.82615	+	0.360839i
$92$	−7.11344			−0.741628
$93$	−1.10467	−	1.91334i	−0.114549	−	0.198404i
$94$	−3.71468	+	6.43401i	−0.383140	+	0.663617i
$95$	−4.15259	+	7.19250i	−0.426047	+	0.737935i
$96$	−3.80510	−	6.59063i	−0.388356	−	0.672653i
$97$	10.3227			1.04811			0.524057	−	0.851683i	$-0.324418\pi$
$97$	10.3227			1.04811			0.524057	+	0.851683i	$0.324418\pi$
$98$	10.7227	+	8.27112i	1.08316	+	0.835509i
$99$	−1.00000			−0.100504
$100$	−0.871314	−	1.50916i	−0.0871314	−	0.150916i
$101$	−4.28525	+	7.42228i	−0.426399	+	0.738544i	−0.996550	−	0.0829956i	$-0.973551\pi$
$101$	−4.28525	+	7.42228i	−0.426399	+	0.738544i	0.570151	+	0.821540i	$0.306885\pi$
$102$	1.43668	−	2.48840i	0.142252	−	0.246388i
$103$	−2.62205	−	4.54152i	−0.258358	−	0.447490i	0.707444	−	0.706769i	$-0.249848\pi$
$103$	−2.62205	−	4.54152i	−0.258358	−	0.447490i	−0.965802	+	0.259280i	$0.916515\pi$
$104$	−3.34177			−0.327688
$105$	−2.59557	+	0.512871i	−0.253301	+	0.0500511i
$106$	23.6471			2.29681
$107$	−8.77618	−	15.2008i	−0.848425	−	1.46952i	−0.882613	−	0.470100i	$-0.844218\pi$
$107$	−8.77618	−	15.2008i	−0.848425	−	1.46952i	0.0341878	−	0.999415i	$-0.489116\pi$
$108$	−0.871314	+	1.50916i	−0.0838422	+	0.145219i
$109$	−1.15644	+	2.00301i	−0.110767	+	0.191853i	−0.916080	−	0.400997i	$-0.868664\pi$
$109$	−1.15644	+	2.00301i	−0.110767	+	0.191853i	0.805313	+	0.592850i	$0.201997\pi$
$110$	0.967294	+	1.67540i	0.0922278	+	0.159743i
$111$	−4.21010			−0.399605
$112$	7.74904	+	8.85871i	0.732215	+	0.837069i
$113$	−1.08495			−0.102064			−0.0510319	−	0.998697i	$-0.516251\pi$
$113$	−1.08495			−0.102064			−0.0510319	+	0.998697i	$0.516251\pi$
$114$	−8.03355	−	13.9145i	−0.752411	−	1.30321i
$115$	−2.04101	+	3.53513i	−0.190325	+	0.329653i
$116$	3.21678	−	5.57162i	0.298670	−	0.517312i
$117$	3.35580	+	5.81241i	0.310244	+	0.537358i
$118$	−0.272283			−0.0250657
$119$	−1.26785	+	3.71947i	−0.116223	+	0.340963i
$120$	−0.497910			−0.0454528
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	10.4175	−	18.0436i	0.943154	−	1.63359i
$123$	1.58345	−	2.74261i	0.142775	−	0.247293i
$124$	−1.92503	−	3.33424i	−0.172872	−	0.299424i
$125$	−1.00000			−0.0894427
$126$	1.65141	−	4.84471i	0.147119	−	0.431601i
$127$	19.8630			1.76255			0.881277	−	0.472600i	$-0.156684\pi$
$127$	19.8630			1.76255			0.881277	+	0.472600i	$0.156684\pi$
$128$	1.97515	+	3.42106i	0.174580	+	0.302382i
$129$	−2.46574	+	4.27078i	−0.217096	+	0.376021i
$130$	6.49208	−	11.2446i	0.569393	−	0.986218i
$131$	−6.00156	−	10.3950i	−0.524359	−	0.908216i	−0.999598	−	0.0283592i	$-0.990972\pi$
$131$	−6.00156	−	10.3950i	−0.524359	−	0.908216i	0.475239	−	0.879857i	$-0.342362\pi$
$132$	−1.74263			−0.151676
$133$	14.4672	+	16.5389i	1.25446	+	1.43410i
$134$	20.2373			1.74824
$135$	0.500000	+	0.866025i	0.0430331	+	0.0745356i
$136$	−0.369762	+	0.640446i	−0.0317068	+	0.0549178i
$137$	7.75768	−	13.4367i	0.662783	−	1.14797i	−0.317098	−	0.948393i	$-0.602708\pi$
$137$	7.75768	−	13.4367i	0.662783	−	1.14797i	0.979881	−	0.199581i	$-0.0639583\pi$
$138$	−3.94851	−	6.83903i	−0.336120	−	0.582176i
$139$	22.8224			1.93577			0.967887	−	0.251386i	$-0.0808863\pi$
$139$	22.8224			1.93577			0.967887	+	0.251386i	$0.0808863\pi$
$140$	−4.52310	+	0.893743i	−0.382272	+	0.0755351i
$141$	−3.84028			−0.323410
$142$	−14.4782	−	25.0770i	−1.21498	−	2.10441i
$143$	−3.35580	+	5.81241i	−0.280626	+	0.486058i
$144$	2.22425	−	3.85252i	0.185354	−	0.321043i
$145$	−1.84593	−	3.19725i	−0.153297	−	0.265517i
$146$	3.40561			0.281850
$147$	−0.931272	+	6.93778i	−0.0768100	+	0.572218i
$148$	−7.33663			−0.603068
$149$	−4.09472	−	7.09227i	−0.335453	−	0.581021i	0.648119	−	0.761539i	$-0.275556\pi$
$149$	−4.09472	−	7.09227i	−0.335453	−	0.581021i	−0.983572	+	0.180518i	$0.942223\pi$
$150$	0.967294	−	1.67540i	0.0789792	−	0.136796i
$151$	6.00050	−	10.3932i	0.488314	−	0.845784i	−0.511596	−	0.859226i	$-0.670945\pi$
$151$	6.00050	−	10.3932i	0.488314	−	0.845784i	0.999910	+	0.0134418i	$0.00427878\pi$
$152$	2.06762	+	3.58122i	0.167706	+	0.290475i
$153$	1.48525			0.120076
$154$	5.02135	−	0.992194i	0.404632	−	0.0799533i
$155$	−2.20934			−0.177458
$156$	5.84790	+	10.1289i	0.468207	+	0.810958i
$157$	−6.10013	+	10.5657i	−0.486843	+	0.843237i	−0.999886	−	0.0151262i	$-0.995185\pi$
$157$	−6.10013	+	10.5657i	−0.486843	+	0.843237i	0.513042	+	0.858363i	$0.328518\pi$
$158$	−6.35322	+	11.0041i	−0.505435	+	0.875439i
$159$	6.11167	+	10.5857i	0.484687	+	0.839502i
$160$	−7.61020			−0.601639
$161$	7.11065	+	8.12890i	0.560397	+	0.640647i
$162$	−1.93459			−0.151996
$163$	−8.03365	−	13.9147i	−0.629244	−	1.08988i	−0.987704	−	0.156338i	$-0.950031\pi$
$163$	−8.03365	−	13.9147i	−0.629244	−	1.08988i	0.358460	−	0.933545i	$-0.383302\pi$
$164$	2.75936	−	4.77935i	0.215470	−	0.373204i
$165$	−0.500000	+	0.866025i	−0.0389249	+	0.0674200i
$166$	9.02334	+	15.6289i	0.700347	+	1.21304i
$167$	−9.14403			−0.707586			−0.353793	−	0.935324i	$-0.615108\pi$
$167$	−9.14403			−0.707586			−0.353793	+	0.935324i	$0.615108\pi$
$168$	−0.425028	+	1.24690i	−0.0327916	+	0.0962002i
$169$	32.0455			2.46504
$170$	−1.43668	−	2.48840i	−0.110188	−	0.190851i
$171$	4.15259	−	7.19250i	0.317557	−	0.550024i
$172$	−4.29686	+	7.44238i	−0.327632	+	0.567476i
$173$	3.23075	+	5.59582i	0.245629	+	0.425443i	0.962308	−	0.271961i	$-0.0876720\pi$
$173$	3.23075	+	5.59582i	0.245629	+	0.425443i	−0.716679	+	0.697403i	$0.754339\pi$
$174$	7.14224			0.541452
$175$	−0.853623	+	2.50426i	−0.0645279	+	0.189304i
$176$	4.44850			0.335319
$177$	−0.0703725	−	0.121889i	−0.00528952	−	0.00916171i
$178$	3.09016	−	5.35231i	0.231617	−	0.401173i
$179$	3.95950	−	6.85805i	0.295947	−	0.512595i	−0.679258	−	0.733900i	$-0.737698\pi$
$179$	3.95950	−	6.85805i	0.295947	−	0.512595i	0.975205	+	0.221305i	$0.0710315\pi$
$180$	0.871314	+	1.50916i	0.0649439	+	0.112486i
$181$	−3.53233			−0.262556			−0.131278	−	0.991346i	$-0.541908\pi$
$181$	−3.53233			−0.262556			−0.131278	+	0.991346i	$0.541908\pi$
$182$	−22.6177	−	25.8565i	−1.67653	−	1.91661i
$183$	10.7697			0.796120
$184$	1.01624	+	1.76018i	0.0749182	+	0.129762i
$185$	−2.10505	+	3.64605i	−0.154766	+	0.268063i
$186$	2.13708	−	3.70153i	0.156698	−	0.271409i
$187$	0.742627	+	1.28627i	0.0543063	+	0.0940612i
$188$	−6.69217			−0.488077
$189$	2.59557	−	0.512871i	0.188800	−	0.0373059i
$190$	−16.0671			−1.16563
$191$	11.3178	+	19.6031i	0.818930	+	1.41843i	0.906471	+	0.422267i	$0.138766\pi$
$191$	11.3178	+	19.6031i	0.818930	+	1.41843i	−0.0875417	+	0.996161i	$0.527901\pi$
$192$	2.91279	−	5.04510i	0.210213	−	0.364099i
$193$	−0.824670	+	1.42837i	−0.0593610	+	0.102816i	−0.894179	−	0.447710i	$-0.852240\pi$
$193$	−0.824670	+	1.42837i	−0.0593610	+	0.102816i	0.834818	+	0.550526i	$0.185573\pi$
$194$	9.98510	+	17.2947i	0.716888	+	1.24169i
$195$	6.71159			0.480627
$196$	−1.62286	+	12.0900i	−0.115919	+	0.863568i
$197$	11.3222			0.806674			0.403337	−	0.915052i	$-0.367850\pi$
$197$	11.3222			0.806674			0.403337	+	0.915052i	$0.367850\pi$
$198$	−0.967294	−	1.67540i	−0.0687426	−	0.119066i
$199$	−2.72939	+	4.72744i	−0.193481	+	0.335119i	−0.946402	−	0.322992i	$-0.895311\pi$
$199$	−2.72939	+	4.72744i	−0.193481	+	0.335119i	0.752920	+	0.658112i	$0.228645\pi$
$200$	−0.248955	+	0.431203i	−0.0176038	+	0.0304906i
$201$	5.23040	+	9.05932i	0.368924	+	0.638995i
$202$	−16.5804			−1.16659
$203$	−9.58249	+	1.89345i	−0.672559	+	0.132894i
$204$	2.58824			0.181213
$205$	−1.58345	−	2.74261i	−0.110593	−	0.191552i
$206$	5.07258	−	8.78597i	0.353424	−	0.612148i
$207$	2.04101	−	3.53513i	0.141860	−	0.245709i
$208$	−14.9283	−	25.8565i	−1.03509	−	1.79283i
$209$	8.30518			0.574482
$210$	−3.36994	−	3.85252i	−0.232548	−	0.265849i
$211$	−15.3620			−1.05756			−0.528781	−	0.848758i	$-0.677351\pi$
$211$	−15.3620			−1.05756			−0.528781	+	0.848758i	$0.677351\pi$
$212$	10.6504	+	18.4470i	0.731469	+	1.26694i
$213$	7.48387	−	12.9624i	0.512786	−	0.888172i
$214$	16.9783	−	29.4072i	1.16061	−	2.01024i
$215$	2.46574	+	4.27078i	0.168162	+	0.291265i
$216$	0.497910			0.0338785
$217$	−1.88594	+	5.53276i	−0.128026	+	0.375588i
$218$	−4.47446			−0.303049
$219$	0.880191	+	1.52454i	0.0594778	+	0.103019i
$220$	−0.871314	+	1.50916i	−0.0587439	+	0.101748i
$221$	4.98421	−	8.63291i	0.335274	−	0.580712i
$222$	−4.07240	−	7.05361i	−0.273322	−	0.473407i
$223$	17.4320			1.16733			0.583665	−	0.811994i	$-0.301618\pi$
$223$	17.4320			1.16733			0.583665	+	0.811994i	$0.301618\pi$
$224$	−6.49625	+	19.0579i	−0.434049	+	1.27336i
$225$	1.00000			0.0666667
$226$	−1.04947	−	1.81773i	−0.0698096	−	0.120914i
$227$	−8.51562	+	14.7495i	−0.565202	+	0.978958i	0.431829	+	0.901955i	$0.357868\pi$
$227$	−8.51562	+	14.7495i	−0.565202	+	0.978958i	−0.997031	+	0.0770026i	$0.975465\pi$
$228$	7.23642	−	12.5338i	0.479244	−	0.830074i
$229$	0.0543697	+	0.0941710i	0.00359285	+	0.00622300i	0.867816	−	0.496885i	$-0.165523\pi$
$229$	0.0543697	+	0.0941710i	0.00359285	+	0.00622300i	−0.864223	+	0.503108i	$0.832190\pi$
$230$	−7.89703			−0.520714
$231$	1.74194	+	1.99139i	0.114611	+	0.131024i
$232$	−1.83822			−0.120685
$233$	9.84305	+	17.0487i	0.644840	+	1.11690i	0.984338	+	0.176289i	$0.0564093\pi$
$233$	9.84305	+	17.0487i	0.644840	+	1.11690i	−0.339499	+	0.940607i	$0.610257\pi$
$234$	−6.49208	+	11.2446i	−0.424401	+	0.735083i
$235$	−1.92014	+	3.32578i	−0.125256	+	0.216950i
$236$	−0.122633	−	0.212407i	−0.00798273	−	0.0138265i
$237$	−6.56804			−0.426640
$238$	−7.45798	+	1.47366i	−0.483429	+	0.0955232i
$239$	−15.2615			−0.987187			−0.493593	−	0.869693i	$-0.664317\pi$
$239$	−15.2615			−0.987187			−0.493593	+	0.869693i	$0.664317\pi$
$240$	−2.22425	−	3.85252i	−0.143575	−	0.248679i
$241$	4.53668	−	7.85775i	0.292233	−	0.506162i	−0.682104	−	0.731255i	$-0.738935\pi$
$241$	4.53668	−	7.85775i	0.292233	−	0.506162i	0.974337	+	0.225092i	$0.0722684\pi$
$242$	0.967294	−	1.67540i	0.0621800	−	0.107699i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	18.7676			1.20147
$245$	5.54265	+	4.27539i	0.354107	+	0.273145i
$246$	6.12663			0.390620
$247$	−27.8705	−	48.2731i	−1.77336	−	3.07155i
$248$	−0.550026	+	0.952672i	−0.0349267	+	0.0604948i
$249$	−4.66422	+	8.07866i	−0.295583	+	0.511964i
$250$	−0.967294	−	1.67540i	−0.0611770	−	0.105962i
$251$	−19.4642			−1.22857			−0.614286	−	0.789084i	$-0.710556\pi$
$251$	−19.4642			−1.22857			−0.614286	+	0.789084i	$0.710556\pi$
$252$	4.52310	−	0.893743i	0.284929	−	0.0563005i
$253$	4.08202			0.256634
$254$	19.2133	+	33.2785i	1.20555	+	2.08808i
$255$	0.742627	−	1.28627i	0.0465051	−	0.0805492i
$256$	−9.64668	+	16.7085i	−0.602918	+	1.04428i
$257$	−1.80559	−	3.12737i	−0.112630	−	0.195080i	0.804200	−	0.594359i	$-0.202594\pi$
$257$	−1.80559	−	3.12737i	−0.112630	−	0.195080i	−0.916830	+	0.399279i	$0.869261\pi$
$258$	−9.54036			−0.593957
$259$	7.33375	+	8.38395i	0.455697	+	0.520953i
$260$	11.6958			0.725343
$261$	1.84593	+	3.19725i	0.114260	+	0.197905i
$262$	11.6105	−	20.1100i	0.717302	−	1.24240i
$263$	5.98090	−	10.3592i	0.368798	−	0.638777i	−0.620580	−	0.784143i	$-0.713103\pi$
$263$	5.98090	−	10.3592i	0.368798	−	0.638777i	0.989378	+	0.145366i	$0.0464361\pi$
$264$	0.248955	+	0.431203i	0.0153221	+	0.0265387i
$265$	12.2233			0.750873
$266$	−13.7153	+	40.2362i	−0.840936	+	2.46704i
$267$	3.19464			0.195509
$268$	9.11464	+	15.7870i	0.556765	+	0.964345i
$269$	−1.16155	+	2.01187i	−0.0708211	+	0.122666i	−0.899261	−	0.437412i	$-0.855895\pi$
$269$	−1.16155	+	2.01187i	−0.0708211	+	0.122666i	0.828440	+	0.560077i	$0.189229\pi$
$270$	−0.967294	+	1.67540i	−0.0588676	+	0.101962i
$271$	−7.52808	−	13.0390i	−0.457298	−	0.792063i	0.541519	−	0.840688i	$-0.317849\pi$
$271$	−7.52808	−	13.0390i	−0.457298	−	0.792063i	−0.998817	+	0.0486250i	$0.984516\pi$
$272$	−6.60716			−0.400618
$273$	5.72917	−	16.8076i	0.346745	−	1.01724i
$274$	30.0158			1.81332
$275$	0.500000	+	0.866025i	0.0301511	+	0.0522233i
$276$	3.55672	−	6.16042i	0.214089	−	0.370814i
$277$	−2.04530	+	3.54256i	−0.122890	+	0.212852i	−0.920906	−	0.389784i	$-0.872550\pi$
$277$	−2.04530	+	3.54256i	−0.122890	+	0.212852i	0.798016	+	0.602636i	$0.205883\pi$
$278$	22.0760	+	38.2367i	1.32403	+	2.29329i
$279$	2.20934			0.132270
$280$	0.867331	+	0.991534i	0.0518329	+	0.0592555i
$281$	6.87097			0.409888			0.204944	−	0.978774i	$-0.434299\pi$
$281$	6.87097			0.409888			0.204944	+	0.978774i	$0.434299\pi$
$282$	−3.71468	−	6.43401i	−0.221206	−	0.383140i
$283$	11.3049	−	19.5806i	0.672005	−	1.16395i	−0.305330	−	0.952247i	$-0.598767\pi$
$283$	11.3049	−	19.5806i	0.672005	−	1.16395i	0.977335	−	0.211700i	$-0.0679000\pi$
$284$	13.0416	−	22.5887i	0.773877	−	1.34039i
$285$	−4.15259	−	7.19250i	−0.245978	−	0.426047i
$286$	−12.9842			−0.767770
$287$	−8.21988	+	1.62421i	−0.485204	+	0.0958740i
$288$	7.61020			0.448435
$289$	7.39701	+	12.8120i	0.435118	+	0.753647i
$290$	3.57112	−	6.18536i	0.209703	−	0.363217i
$291$	−5.16136	+	8.93974i	−0.302564	+	0.524057i
$292$	1.53384	+	2.65670i	0.0897615	+	0.155471i
$293$	−26.2364			−1.53275			−0.766374	−	0.642395i	$-0.777941\pi$
$293$	−26.2364			−1.53275			−0.766374	+	0.642395i	$0.777941\pi$
$294$	−12.5244	+	5.15061i	−0.730436	+	0.300390i
$295$	−0.140745			−0.00819449
$296$	1.04813	+	1.81541i	0.0609211	+	0.105518i
$297$	0.500000	−	0.866025i	0.0290129	−	0.0502519i
$298$	7.92160	−	13.7206i	0.458886	−	0.794813i
$299$	−13.6984	−	23.7264i	−0.792201	−	1.37213i
$300$	1.74263			0.100611
$301$	12.8000	−	2.52921i	0.737777	−	0.145781i
$302$	23.2170			1.33599
$303$	−4.28525	−	7.42228i	−0.246181	−	0.426399i
$304$	−18.4728	+	31.9959i	−1.05949	+	1.83509i
$305$	5.38486	−	9.32684i	0.308336	−	0.534053i
$306$	1.43668	+	2.48840i	0.0821293	+	0.142252i
$307$	−14.4580			−0.825160			−0.412580	−	0.910921i	$-0.635372\pi$
$307$	−14.4580			−0.825160			−0.412580	+	0.910921i	$0.635372\pi$
$308$	3.03556	+	3.47025i	0.172967	+	0.197736i
$309$	5.24410			0.298326
$310$	−2.13708	−	3.70153i	−0.121378	−	0.210233i
$311$	5.37022	−	9.30149i	0.304517	−	0.527439i	−0.672637	−	0.739973i	$-0.734838\pi$
$311$	5.37022	−	9.30149i	0.304517	−	0.527439i	0.977154	+	0.212534i	$0.0681716\pi$
$312$	1.67089	−	2.89406i	0.0945953	−	0.163844i
$313$	−4.57696	−	7.92752i	−0.258705	−	0.448090i	0.707190	−	0.707023i	$-0.249962\pi$
$313$	−4.57696	−	7.92752i	−0.258705	−	0.448090i	−0.965895	+	0.258933i	$0.916629\pi$
$314$	−23.6025			−1.33196
$315$	0.853623	−	2.50426i	0.0480962	−	0.141099i
$316$	−11.4456			−0.643868
$317$	−4.90213	−	8.49073i	−0.275331	−	0.476887i	0.694888	−	0.719118i	$-0.255454\pi$
$317$	−4.90213	−	8.49073i	−0.275331	−	0.476887i	−0.970219	+	0.242231i	$0.922121\pi$
$318$	−11.8235	+	20.4790i	−0.663032	+	1.14840i
$319$	−1.84593	+	3.19725i	−0.103352	+	0.179012i
$320$	−2.91279	−	5.04510i	−0.162830	−	0.282030i
$321$	17.5524			0.979677
$322$	−6.74109	+	19.7762i	−0.375666	+	1.10209i
$323$	−12.3353			−0.686355
$324$	−0.871314	−	1.50916i	−0.0484063	−	0.0838422i
$325$	3.35580	−	5.81241i	0.186146	−	0.322415i
$326$	15.5418	−	26.9192i	0.860781	−	1.49092i
$327$	−1.15644	−	2.00301i	−0.0639511	−	0.110767i
$328$	−1.57683			−0.0870658
$329$	6.68954	+	7.64749i	0.368806	+	0.421620i
$330$	−1.93459			−0.106496
$331$	−2.25380	−	3.90369i	−0.123880	−	0.214566i	0.797415	−	0.603432i	$-0.206200\pi$
$331$	−2.25380	−	3.90369i	−0.123880	−	0.214566i	−0.921295	+	0.388866i	$0.872867\pi$
$332$	−8.12799	+	14.0781i	−0.446082	+	0.772636i
$333$	2.10505	−	3.64605i	0.115356	−	0.199802i
$334$	−8.84496	−	15.3199i	−0.483975	−	0.838269i
$335$	10.4608			0.571535
$336$	−11.5464	+	2.28151i	−0.629907	+	0.124467i
$337$	32.0610			1.74647			0.873236	−	0.487297i	$-0.162017\pi$
$337$	32.0610			1.74647			0.873236	+	0.487297i	$0.162017\pi$
$338$	30.9974	+	53.6891i	1.68604	+	2.92030i
$339$	0.542476	−	0.939597i	0.0294633	−	0.0510319i
$340$	1.29412	−	2.24149i	0.0701836	−	0.121562i
$341$	1.10467	+	1.91334i	0.0598211	+	0.103613i
$342$	16.0671			0.868809
$343$	15.4380	−	10.2307i	0.833576	−	0.552405i
$344$	2.45543			0.132388
$345$	−2.04101	−	3.53513i	−0.109884	−	0.190325i
$346$	−6.25017	+	10.8256i	−0.336011	+	0.581988i
$347$	−10.4269	+	18.0599i	−0.559743	+	0.969504i	0.437774	+	0.899085i	$0.355767\pi$
$347$	−10.4269	+	18.0599i	−0.559743	+	0.969504i	−0.997518	+	0.0704190i	$0.977566\pi$
$348$	3.21678	+	5.57162i	0.172437	+	0.298670i
$349$	−33.6499			−1.80124			−0.900618	−	0.434612i	$-0.856885\pi$
$349$	−33.6499			−1.80124			−0.900618	+	0.434612i	$0.856885\pi$
$350$	−5.02135	+	0.992194i	−0.268402	+	0.0530350i
$351$	−6.71159			−0.358238
$352$	3.80510	+	6.59063i	0.202813	+	0.351282i
$353$	8.93173	−	15.4702i	0.475388	−	0.823396i	−0.524215	−	0.851586i	$-0.675641\pi$
$353$	8.93173	−	15.4702i	0.475388	−	0.823396i	0.999603	+	0.0281903i	$0.00897444\pi$
$354$	0.136142	−	0.235804i	0.00723585	−	0.0125329i
$355$	−7.48387	−	12.9624i	−0.397203	−	0.687975i
$356$	5.56707			0.295054
$357$	−2.58723	−	2.95772i	−0.136931	−	0.156539i
$358$	15.3200			0.809687
$359$	2.31980	+	4.01801i	0.122434	+	0.212062i	0.920727	−	0.390207i	$-0.127597\pi$
$359$	2.31980	+	4.01801i	0.122434	+	0.212062i	−0.798293	+	0.602269i	$0.794263\pi$
$360$	0.248955	−	0.431203i	0.0131211	−	0.0227264i
$361$	−24.9880	+	43.2806i	−1.31516	+	2.27792i
$362$	−3.41680	−	5.91807i	−0.179583	−	0.311047i
$363$	1.00000			0.0524864
$364$	9.98381	−	29.2894i	0.523294	−	1.53518i
$365$	1.76038			0.0921426
$366$	10.4175	+	18.0436i	0.544530	+	0.943154i
$367$	−0.629346	+	1.09006i	−0.0328516	+	0.0569006i	−0.881984	−	0.471280i	$-0.843792\pi$
$367$	−0.629346	+	1.09006i	−0.0328516	+	0.0569006i	0.849132	+	0.528180i	$0.177126\pi$
$368$	−9.07945	+	15.7261i	−0.473299	+	0.819778i
$369$	1.58345	+	2.74261i	0.0824309	+	0.142775i
$370$	−8.14480			−0.423428
$371$	10.4341	−	30.6104i	0.541713	−	1.58921i
$372$	3.85005			0.199616
$373$	−12.1628	−	21.0666i	−0.629766	−	1.09079i	−0.987599	−	0.157001i	$-0.949818\pi$
$373$	−12.1628	−	21.0666i	−0.629766	−	1.09079i	0.357833	−	0.933786i	$-0.383516\pi$
$374$	−1.43668	+	2.48840i	−0.0742888	+	0.128672i
$375$	0.500000	−	0.866025i	0.0258199	−	0.0447214i
$376$	0.956057	+	1.65594i	0.0493049	+	0.0853985i
$377$	24.7783			1.27615
$378$	3.36994	+	3.85252i	0.173331	+	0.198152i
$379$	−9.27384			−0.476365			−0.238182	−	0.971220i	$-0.576552\pi$
$379$	−9.27384			−0.476365			−0.238182	+	0.971220i	$0.576552\pi$
$380$	−7.23642	−	12.5338i	−0.371221	−	0.642973i
$381$	−9.93149	+	17.2018i	−0.508806	+	0.881277i
$382$	−21.8953	+	37.9238i	−1.12026	+	1.94035i
$383$	0.943946	+	1.63496i	0.0482334	+	0.0835427i	0.889134	−	0.457647i	$-0.151308\pi$
$383$	0.943946	+	1.63496i	0.0482334	+	0.0835427i	−0.840901	+	0.541189i	$0.817974\pi$
$384$	−3.95030			−0.201588
$385$	2.59557	−	0.512871i	0.132282	−	0.0261383i
$386$	−3.19079			−0.162407
$387$	−2.46574	−	4.27078i	−0.125340	−	0.217096i
$388$	−8.99433	+	15.5786i	−0.456618	+	0.790885i
$389$	0.341938	−	0.592253i	0.0173369	−	0.0300284i	−0.857227	−	0.514939i	$-0.827815\pi$
$389$	0.341938	−	0.592253i	0.0173369	−	0.0300284i	0.874564	+	0.484911i	$0.161148\pi$
$390$	6.49208	+	11.2446i	0.328739	+	0.569393i
$391$	−6.06284			−0.306611
$392$	3.22343	−	1.32563i	0.162808	−	0.0669543i
$393$	12.0031			0.605477
$394$	10.9519	+	18.9692i	0.551748	+	0.955656i
$395$	−3.28402	+	5.68809i	−0.165237	+	0.286199i
$396$	0.871314	−	1.50916i	0.0437852	−	0.0758381i
$397$	5.89210	+	10.2054i	0.295716	+	0.512195i	0.975151	−	0.221540i	$-0.0711084\pi$
$397$	5.89210	+	10.2054i	0.295716	+	0.512195i	−0.679435	+	0.733736i	$0.737775\pi$
$398$	−10.5605			−0.529349
$399$	−21.5567	+	4.25949i	−1.07918	+	0.213241i
$400$	−4.44850			−0.222425
$401$	−6.90540	−	11.9605i	−0.344839	−	0.597279i	0.640485	−	0.767970i	$-0.278733\pi$
$401$	−6.90540	−	11.9605i	−0.344839	−	0.597279i	−0.985325	+	0.170692i	$0.945400\pi$
$402$	−10.1187	+	17.5260i	−0.504673	+	0.874120i
$403$	7.41409	−	12.8416i	0.369322	−	0.639684i
$404$	−7.46760	−	12.9343i	−0.371527	−	0.643504i
$405$	−1.00000			−0.0496904
$406$	−12.4414	−	14.2230i	−0.617455	−	0.705875i
$407$	4.21010			0.208687
$408$	−0.369762	−	0.640446i	−0.0183059	−	0.0317068i
$409$	−3.58345	+	6.20672i	−0.177190	+	0.306903i	−0.940917	−	0.338637i	$-0.890034\pi$
$409$	−3.58345	+	6.20672i	−0.177190	+	0.306903i	0.763727	+	0.645540i	$0.223367\pi$
$410$	3.06332	−	5.30582i	0.151286	−	0.262036i
$411$	7.75768	+	13.4367i	0.382658	+	0.662783i
$412$	9.13851			0.450222
$413$	−0.120143	+	0.352462i	−0.00591186	+	0.0173435i
$414$	7.89703			0.388118
$415$	4.66422	+	8.07866i	0.228957	+	0.396566i
$416$	25.5383	−	44.2336i	1.25212	−	2.16873i
$417$	−11.4112	+	19.7648i	−0.558810	+	0.967887i
$418$	8.03355	+	13.9145i	0.392934	+	0.680581i
$419$	30.6409			1.49691			0.748453	−	0.663188i	$-0.230797\pi$
$419$	30.6409			1.49691			0.748453	+	0.663188i	$0.230797\pi$
$420$	1.48755	−	4.36399i	0.0725849	−	0.212941i
$421$	4.81097			0.234472			0.117236	−	0.993104i	$-0.462597\pi$
$421$	4.81097			0.234472			0.117236	+	0.993104i	$0.462597\pi$
$422$	−14.8596	−	25.7375i	−0.723352	−	1.25288i
$423$	1.92014	−	3.32578i	0.0933604	−	0.161705i
$424$	3.04306	−	5.27074i	0.147784	−	0.255970i
$425$	−0.742627	−	1.28627i	−0.0360227	−	0.0623932i
$426$	28.9564			1.40294
$427$	−18.7602	−	21.4467i	−0.907871	−	1.03788i
$428$	30.5872			1.47849
$429$	−3.35580	−	5.81241i	−0.162019	−	0.280626i
$430$	−4.77018	+	8.26219i	−0.230038	+	0.398438i
$431$	5.84307	−	10.1205i	0.281451	−	0.487487i	−0.690292	−	0.723531i	$-0.742518\pi$
$431$	5.84307	−	10.1205i	0.281451	−	0.487487i	0.971742	+	0.236045i	$0.0758511\pi$
$432$	2.22425	+	3.85252i	0.107014	+	0.185354i
$433$	−16.2375			−0.780327			−0.390163	−	0.920746i	$-0.627581\pi$
$433$	−16.2375			−0.780327			−0.390163	+	0.920746i	$0.627581\pi$
$434$	−11.0938	+	2.19209i	−0.532522	+	0.105224i
$435$	3.69187			0.177012
$436$	−2.01524	−	3.49050i	−0.0965125	−	0.167164i
$437$	−16.9510	+	29.3599i	−0.810875	+	1.40448i
$438$	−1.70281	+	2.94935i	−0.0813632	+	0.140925i
$439$	5.39211	+	9.33941i	0.257351	+	0.445746i	0.965532	−	0.260286i	$-0.0838169\pi$
$439$	5.39211	+	9.33941i	0.257351	+	0.445746i	−0.708180	+	0.706032i	$0.750484\pi$
$440$	0.497910			0.0237369
$441$	−5.54265	−	4.27539i	−0.263936	−	0.203590i
$442$	19.2848			0.917284
$443$	−12.5604	−	21.7552i	−0.596761	−	1.03362i	−0.993296	−	0.115600i	$-0.963121\pi$
$443$	−12.5604	−	21.7552i	−0.596761	−	1.03362i	0.396535	−	0.918020i	$-0.370213\pi$
$444$	3.66832	−	6.35371i	0.174091	−	0.301534i
$445$	1.59732	−	2.76664i	0.0757203	−	0.131151i
$446$	16.8618	+	29.2055i	0.798430	+	1.38292i
$447$	8.18944			0.387347
$448$	−15.1207	+	2.98777i	−0.714385	+	0.141159i
$449$	−25.0533			−1.18234			−0.591168	−	0.806548i	$-0.701333\pi$
$449$	−25.0533			−1.18234			−0.591168	+	0.806548i	$0.701333\pi$
$450$	0.967294	+	1.67540i	0.0455987	+	0.0789792i
$451$	−1.58345	+	2.74261i	−0.0745616	+	0.129144i
$452$	0.945334	−	1.63737i	0.0444648	−	0.0770152i
$453$	6.00050	+	10.3932i	0.281928	+	0.488314i
$454$	−32.9484			−1.54635
$455$	−11.6912	−	13.3654i	−0.548092	−	0.626580i
$456$	−4.13524			−0.193650
$457$	9.76322	+	16.9104i	0.456704	+	0.791035i	0.998784	−	0.0492919i	$-0.0156964\pi$
$457$	9.76322	+	16.9104i	0.456704	+	0.791035i	−0.542080	+	0.840327i	$0.682363\pi$
$458$	−0.105183	+	0.182182i	−0.00491487	+	0.00851281i
$459$	−0.742627	+	1.28627i	−0.0346629	+	0.0600378i
$460$	−3.55672	−	6.16042i	−0.165833	−	0.287231i
$461$	24.0868			1.12183			0.560916	−	0.827873i	$-0.310449\pi$
$461$	24.0868			1.12183			0.560916	+	0.827873i	$0.310449\pi$
$462$	−1.65141	+	4.84471i	−0.0768305	+	0.225396i
$463$	36.8049			1.71047			0.855234	−	0.518242i	$-0.173413\pi$
$463$	36.8049			1.71047			0.855234	+	0.518242i	$0.173413\pi$
$464$	−8.21165	−	14.2230i	−0.381216	−	0.660286i
$465$	1.10467	−	1.91334i	0.0512278	−	0.0887291i
$466$	−19.0422	+	32.9821i	−0.882115	+	1.52787i
$467$	−20.6222	−	35.7187i	−0.954282	−	1.65286i	−0.736004	−	0.676978i	$-0.763289\pi$
$467$	−20.6222	−	35.7187i	−0.954282	−	1.65286i	−0.218278	−	0.975887i	$-0.570044\pi$
$468$	−11.6958			−0.540639
$469$	8.92959	−	26.1966i	0.412330	−	1.20965i
$470$	−7.42935			−0.342690
$471$	−6.10013	−	10.5657i	−0.281079	−	0.486843i
$472$	−0.0350392	+	0.0606896i	−0.00161281	+	0.00279347i
$473$	2.46574	−	4.27078i	0.113375	−	0.196371i
$474$	−6.35322	−	11.0041i	−0.291813	−	0.505435i
$475$	−8.30518			−0.381068
$476$	−4.50857	−	5.15421i	−0.206650	−	0.236243i
$477$	−12.2233			−0.559668
$478$	−14.7624	−	25.5692i	−0.675216	−	1.16951i
$479$	−16.7904	+	29.0818i	−0.767173	+	1.32878i	0.171917	+	0.985111i	$0.445004\pi$
$479$	−16.7904	+	29.0818i	−0.767173	+	1.32878i	−0.939090	+	0.343671i	$0.888329\pi$
$480$	3.80510	−	6.59063i	0.173678	−	0.300820i
$481$	−14.1282	−	24.4708i	−0.644192	−	1.11577i
$482$	17.5532			0.799526
$483$	−10.5952	+	2.09355i	−0.482096	+	0.0952599i
$484$	1.74263			0.0792103
$485$	5.16136	+	8.93974i	0.234365	+	0.405933i
$486$	0.967294	−	1.67540i	0.0438773	−	0.0759978i
$487$	15.6253	−	27.0638i	0.708051	−	1.22638i	−0.257529	−	0.966271i	$-0.582908\pi$
$487$	15.6253	−	27.0638i	0.708051	−	1.22638i	0.965579	−	0.260109i	$-0.0837584\pi$
$488$	−2.68117	−	4.64393i	−0.121371	−	0.210221i
$489$	16.0673			0.726588
$490$	−1.80163	+	13.4217i	−0.0813892	+	0.606332i
$491$	−10.8532			−0.489800			−0.244900	−	0.969548i	$-0.578755\pi$
$491$	−10.8532			−0.489800			−0.244900	+	0.969548i	$0.578755\pi$
$492$	2.75936	+	4.77935i	0.124401	+	0.215470i
$493$	2.74168	−	4.74873i	0.123479	−	0.213872i
$494$	53.9179	−	93.3886i	2.42588	−	4.20175i
$495$	−0.500000	−	0.866025i	−0.0224733	−	0.0389249i
$496$	−9.82825			−0.441301
$497$	−38.8498	+	7.67653i	−1.74265	+	0.344339i
$498$	−18.0467			−0.808691
$499$	11.4004	+	19.7461i	0.510354	+	0.883958i	0.999928	+	0.0119969i	$0.00381883\pi$
$499$	11.4004	+	19.7461i	0.510354	+	0.883958i	−0.489574	+	0.871962i	$0.662848\pi$
$500$	0.871314	−	1.50916i	0.0389663	−	0.0674917i
$501$	4.57202	−	7.91896i	0.204263	−	0.353793i
$502$	−18.8276	−	32.6104i	−0.840318	−	1.45547i
$503$	−10.1945			−0.454551			−0.227275	−	0.973831i	$-0.572982\pi$
$503$	−10.1945			−0.454551			−0.227275	+	0.973831i	$0.572982\pi$
$504$	−0.867331	−	0.991534i	−0.0386340	−	0.0441664i
$505$	−8.57051			−0.381383
$506$	3.94851	+	6.83903i	0.175533	+	0.304032i
$507$	−16.0227	+	27.7522i	−0.711595	+	1.23252i
$508$	−17.3069	+	29.9764i	−0.767869	+	1.32999i
$509$	15.2426	+	26.4010i	0.675619	+	1.17021i	0.976288	+	0.216477i	$0.0694567\pi$
$509$	15.2426	+	26.4010i	0.675619	+	1.17021i	−0.300669	+	0.953729i	$0.597210\pi$
$510$	2.87335			0.127234
$511$	1.50270	−	4.40846i	0.0664757	−	0.195019i
$512$	−29.4241			−1.30037
$513$	4.15259	+	7.19250i	0.183341	+	0.317557i
$514$	3.49307	−	6.05017i	0.154073	−	0.266862i
$515$	2.62205	−	4.54152i	0.115541	−	0.200123i
$516$	−4.29686	−	7.44238i	−0.189159	−	0.327632i
$517$	3.84028			0.168895
$518$	−6.95260	+	20.3967i	−0.305480	+	0.896180i
$519$	−6.46150			−0.283628
$520$	−1.67089	−	2.89406i	−0.0732732	−	0.126913i
$521$	6.01884	−	10.4249i	0.263690	−	0.456725i	−0.703529	−	0.710666i	$-0.748394\pi$
$521$	6.01884	−	10.4249i	0.263690	−	0.456725i	0.967220	+	0.253941i	$0.0817269\pi$
$522$	−3.57112	+	6.18536i	−0.156304	+	0.270726i
$523$	−7.07186	−	12.2488i	−0.309231	−	0.535604i	0.668963	−	0.743295i	$-0.266738\pi$
$523$	−7.07186	−	12.2488i	−0.309231	−	0.535604i	−0.978194	+	0.207692i	$0.933405\pi$
$524$	20.9170			0.913762
$525$	−1.74194	−	1.99139i	−0.0760246	−	0.0869114i
$526$	23.1411			1.00900
$527$	−1.64071	−	2.84180i	−0.0714706	−	0.123791i
$528$	−2.22425	+	3.85252i	−0.0967982	+	0.167659i
$529$	3.16855	−	5.48809i	0.137763	−	0.238613i
$530$	11.8235	+	20.4790i	0.513582	+	0.889550i
$531$	0.140745			0.00610781
$532$	−37.5652	+	7.42270i	−1.62866	+	0.321815i
$533$	21.2549			0.920652
$534$	3.09016	+	5.35231i	0.133724	+	0.231617i
$535$	8.77618	−	15.2008i	0.379427	−	0.657187i
$536$	2.60427	−	4.51073i	0.112487	−	0.194834i
$537$	3.95950	+	6.85805i	0.170865	+	0.295947i
$538$	−4.49425			−0.193761
$539$	0.931272	−	6.93778i	0.0401127	−	0.298831i
$540$	−1.74263			−0.0749907
$541$	10.5683	+	18.3048i	0.454366	+	0.786986i	0.998652	−	0.0519146i	$-0.0165324\pi$
$541$	10.5683	+	18.3048i	0.454366	+	0.786986i	−0.544285	+	0.838900i	$0.683199\pi$
$542$	14.5637	−	25.2251i	0.625565	−	1.08351i
$543$	1.76616	−	3.05909i	0.0757934	−	0.131278i
$544$	−5.65154	−	9.78876i	−0.242308	−	0.419689i
$545$	−2.31288			−0.0990727
$546$	33.7013	−	6.65920i	1.44228	−	0.284988i
$547$	0.0576853			0.00246644			0.00123322	−	0.999999i	$-0.499607\pi$
$547$	0.0576853			0.00246644			0.00123322	+	0.999999i	$0.499607\pi$
$548$	13.5187	+	23.4151i	0.577492	+	1.00025i
$549$	−5.38486	+	9.32684i	−0.229820	+	0.398060i
$550$	−0.967294	+	1.67540i	−0.0412455	+	0.0714394i
$551$	−15.3308	−	26.5538i	−0.653115	−	1.13123i
$552$	−2.03248			−0.0865081
$553$	11.4411	+	13.0795i	0.486527	+	0.556198i
$554$	−7.91362			−0.336217
$555$	−2.10505	−	3.64605i	−0.0893544	−	0.154766i
$556$	−19.8855	+	34.4427i	−0.843333	+	1.46070i
$557$	−19.6919	+	34.1073i	−0.834371	+	1.44517i	0.0601712	+	0.998188i	$0.480835\pi$
$557$	−19.6919	+	34.1073i	−0.834371	+	1.44517i	−0.894542	+	0.446984i	$0.852498\pi$
$558$	2.13708	+	3.70153i	0.0904697	+	0.156698i
$559$	−33.0980			−1.39990
$560$	−3.79735	+	11.1402i	−0.160467	+	0.470760i
$561$	−1.48525			−0.0627075
$562$	6.64625	+	11.5116i	0.280355	+	0.485589i
$563$	−6.69418	+	11.5947i	−0.282126	+	0.488656i	−0.971908	−	0.235360i	$-0.924373\pi$
$563$	−6.69418	+	11.5947i	−0.282126	+	0.488656i	0.689782	+	0.724017i	$0.257706\pi$
$564$	3.34609	−	5.79559i	0.140896	−	0.244038i
$565$	−0.542476	−	0.939597i	−0.0228222	−	0.0395291i
$566$	43.7405			1.83855
$567$	−0.853623	+	2.50426i	−0.0358488	+	0.105169i
$568$	−7.45259			−0.312704
$569$	1.68655	+	2.92119i	0.0707037	+	0.122462i	0.899210	−	0.437517i	$-0.144142\pi$
$569$	1.68655	+	2.92119i	0.0707037	+	0.122462i	−0.828506	+	0.559980i	$0.810809\pi$
$570$	8.03355	−	13.9145i	0.336488	−	0.582815i
$571$	−3.00409	+	5.20324i	−0.125717	+	0.217749i	−0.922013	−	0.387159i	$-0.873457\pi$
$571$	−3.00409	+	5.20324i	−0.125717	+	0.217749i	0.796296	+	0.604908i	$0.206790\pi$
$572$	−5.84790	−	10.1289i	−0.244513	−	0.423509i
$573$	−22.6357			−0.945619
$574$	−10.6722	−	12.2005i	−0.445451	−	0.509240i
$575$	−4.08202			−0.170232
$576$	2.91279	+	5.04510i	0.121366	+	0.210213i
$577$	7.34196	−	12.7166i	0.305650	−	0.529401i	−0.671756	−	0.740772i	$-0.734460\pi$
$577$	7.34196	−	12.7166i	0.305650	−	0.529401i	0.977406	+	0.211372i	$0.0677931\pi$
$578$	−14.3102	+	24.7859i	−0.595224	+	1.03096i
$579$	−0.824670	−	1.42837i	−0.0342721	−	0.0593610i
$580$	6.43355			0.267139
$581$	24.2126	−	4.78429i	1.00451	−	0.198486i
$582$	−19.9702			−0.827791
$583$	−6.11167	−	10.5857i	−0.253119	−	0.438416i
$584$	0.438256	−	0.759082i	0.0181352	−	0.0314110i
$585$	−3.35580	+	5.81241i	−0.138745	+	0.240314i
$586$	−25.3783	−	43.9565i	−1.04837	−	1.81583i
$587$	47.2416			1.94987			0.974934	−	0.222495i	$-0.0714201\pi$
$587$	47.2416			1.94987			0.974934	+	0.222495i	$0.0714201\pi$
$588$	−9.65878	−	7.45042i	−0.398321	−	0.307250i
$589$	−18.3489			−0.756055
$590$	−0.136142	−	0.235804i	−0.00560486	−	0.00970791i
$591$	−5.66110	+	9.80532i	−0.232867	+	0.403337i
$592$	−9.36432	+	16.2195i	−0.384871	+	0.666617i
$593$	−9.59850	−	16.6251i	−0.394163	−	0.682711i	0.598831	−	0.800876i	$-0.295632\pi$
$593$	−9.59850	−	16.6251i	−0.394163	−	0.682711i	−0.992994	+	0.118165i	$0.962299\pi$
$594$	1.93459			0.0793771
$595$	−3.85508	+	0.761744i	−0.158043	+	0.0312285i
$596$	14.2711			0.584569
$597$	−2.72939	−	4.72744i	−0.111706	−	0.193481i
$598$	26.5008	−	45.9008i	1.08370	−	1.87702i
$599$	−2.53108	+	4.38396i	−0.103417	+	0.179124i	−0.913090	−	0.407757i	$-0.866311\pi$
$599$	−2.53108	+	4.38396i	−0.103417	+	0.179124i	0.809673	+	0.586881i	$0.199644\pi$
$600$	−0.248955	−	0.431203i	−0.0101635	−	0.0176038i
$601$	23.9745			0.977940			0.488970	−	0.872301i	$-0.337373\pi$
$601$	23.9745			0.977940			0.488970	+	0.872301i	$0.337373\pi$
$602$	16.6188	+	18.9986i	0.677330	+	0.774324i
$603$	−10.4608			−0.425997
$604$	10.4566	+	18.1114i	0.425475	+	0.736944i
$605$	0.500000	−	0.866025i	0.0203279	−	0.0352089i
$606$	8.29020	−	14.3590i	0.336766	−	0.583296i
$607$	−9.42181	−	16.3191i	−0.382419	−	0.662370i	0.608988	−	0.793179i	$-0.291576\pi$
$607$	−9.42181	−	16.3191i	−0.382419	−	0.662370i	−0.991408	+	0.130809i	$0.958242\pi$
$608$	−63.2041			−2.56327
$609$	3.15147	−	9.24541i	0.127704	−	0.374643i
$610$	20.8349			0.843582
$611$	−12.8872	−	22.3213i	−0.521360	−	0.903022i
$612$	−1.29412	+	2.24149i	−0.0523118	+	0.0906067i
$613$	−12.6399	+	21.8930i	−0.510521	+	0.884248i	0.489405	+	0.872057i	$0.337214\pi$
$613$	−12.6399	+	21.8930i	−0.510521	+	0.884248i	−0.999926	+	0.0121916i	$0.996119\pi$
$614$	−13.9851	−	24.2229i	−0.564393	−	0.977557i
$615$	3.16689			0.127701
$616$	0.425028	−	1.24690i	0.0171249	−	0.0502389i
$617$	10.7730			0.433703			0.216852	−	0.976205i	$-0.430421\pi$
$617$	10.7730			0.433703			0.216852	+	0.976205i	$0.430421\pi$
$618$	5.07258	+	8.78597i	0.204049	+	0.353424i
$619$	−7.30219	+	12.6478i	−0.293500	+	0.508356i	−0.974635	−	0.223801i	$-0.928153\pi$
$619$	−7.30219	+	12.6478i	−0.293500	+	0.508356i	0.681135	+	0.732158i	$0.261487\pi$
$620$	1.92503	−	3.33424i	0.0773109	−	0.133906i
$621$	2.04101	+	3.53513i	0.0819029	+	0.141860i
$622$	20.7783			0.833134
$623$	−5.56488	−	6.36178i	−0.222952	−	0.254879i
$624$	29.8566			1.19522
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	8.85452	−	15.3365i	0.353898	−	0.612969i
$627$	−4.15259	+	7.19250i	−0.165839	+	0.287241i
$628$	−10.6302	−	18.4121i	−0.424193	−	0.734724i
$629$	−6.25307			−0.249326
$630$	5.02135	−	0.992194i	0.200055	−	0.0395300i
$631$	−3.29278			−0.131083			−0.0655417	−	0.997850i	$-0.520878\pi$
$631$	−3.29278			−0.131083			−0.0655417	+	0.997850i	$0.520878\pi$
$632$	1.63515	+	2.83216i	0.0650426	+	0.112657i
$633$	7.68099	−	13.3039i	0.305292	−	0.528781i
$634$	9.48359	−	16.4261i	0.376641	−	0.652362i
$635$	9.93149	+	17.2018i	0.394119	+	0.682634i
$636$	−21.3007			−0.844628
$637$	−43.4504	+	17.8688i	−1.72157	+	0.707989i
$638$	−7.14224			−0.282764
$639$	7.48387	+	12.9624i	0.296057	+	0.512786i
$640$	−1.97515	+	3.42106i	−0.0780747	+	0.135229i
$641$	10.3185	−	17.8722i	0.407556	−	0.705908i	−0.587059	−	0.809544i	$-0.699714\pi$
$641$	10.3185	−	17.8722i	0.407556	−	0.705908i	0.994615	+	0.103636i	$0.0330477\pi$
$642$	16.9783	+	29.4072i	0.670079	+	1.16061i
$643$	16.8602			0.664901			0.332451	−	0.943121i	$-0.392124\pi$
$643$	16.8602			0.664901			0.332451	+	0.943121i	$0.392124\pi$
$644$	−18.4634	+	3.64828i	−0.727560	+	0.143762i
$645$	−4.93147			−0.194176
$646$	−11.9319	−	20.6666i	−0.469453	−	0.813116i
$647$	23.7704	−	41.1715i	0.934510	−	1.61862i	0.159005	−	0.987278i	$-0.449171\pi$
$647$	23.7704	−	41.1715i	0.934510	−	1.61862i	0.775505	−	0.631341i	$-0.217495\pi$
$648$	−0.248955	+	0.431203i	−0.00977988	+	0.0169392i
$649$	0.0703725	+	0.121889i	0.00276236	+	0.00478455i
$650$	12.9842			0.509281
$651$	−3.84854	−	4.39965i	−0.150836	−	0.172436i
$652$	27.9993			1.09654
$653$	12.5898	+	21.8062i	0.492678	+	0.853343i	0.999964	−	0.00843470i	$-0.00268488\pi$
$653$	12.5898	+	21.8062i	0.492678	+	0.853343i	−0.507287	+	0.861777i	$0.669352\pi$
$654$	2.23723	−	3.87499i	0.0874826	−	0.151524i
$655$	6.00156	−	10.3950i	0.234500	−	0.406167i
$656$	−7.04397	−	12.2005i	−0.275021	−	0.476350i
$657$	−1.76038			−0.0686790
$658$	−6.34187	+	18.6050i	−0.247232	+	0.725300i
$659$	−45.8239			−1.78504			−0.892522	−	0.451004i	$-0.851066\pi$
$659$	−45.8239			−1.78504			−0.892522	+	0.451004i	$0.851066\pi$
$660$	−0.871314	−	1.50916i	−0.0339158	−	0.0587439i
$661$	15.4574	−	26.7729i	0.601222	−	1.04135i	−0.391414	−	0.920214i	$-0.628014\pi$
$661$	15.4574	−	26.7729i	0.601222	−	1.04135i	0.992636	−	0.121132i	$-0.0386525\pi$
$662$	4.36016	−	7.55203i	0.169463	−	0.293518i
$663$	4.98421	+	8.63291i	0.193571	+	0.335274i
$664$	4.64472			0.180250
$665$	−7.08950	+	20.7984i	−0.274919	+	0.806526i
$666$	8.14480			0.315605
$667$	−7.53514	−	13.0513i	−0.291762	−	0.505346i
$668$	7.96732	−	13.7998i	0.308265	−	0.533930i
$669$	−8.71598	+	15.0965i	−0.336979	+	0.583665i
$670$	10.1187	+	17.5260i	0.390918	+	0.677090i
$671$	−10.7697			−0.415760
$672$	−13.2565	−	15.1549i	−0.511382	−	0.584612i
$673$	6.08146			0.234423			0.117212	−	0.993107i	$-0.462604\pi$
$673$	6.08146			0.234423			0.117212	+	0.993107i	$0.462604\pi$
$674$	31.0124	+	53.7150i	1.19455	+	2.06902i
$675$	−0.500000	+	0.866025i	−0.0192450	+	0.0333333i
$676$	−27.9217	+	48.3618i	−1.07391	+	1.86007i
$677$	−10.3255	−	17.8842i	−0.396840	−	0.687346i	0.596495	−	0.802617i	$-0.296560\pi$
$677$	−10.3255	−	17.8842i	−0.396840	−	0.687346i	−0.993334	+	0.115271i	$0.963226\pi$
$678$	2.09894			0.0806091
$679$	26.7933	−	5.29423i	1.02823	−	0.203174i
$680$	−0.739523			−0.0283594
$681$	−8.51562	−	14.7495i	−0.326319	−	0.565202i
$682$	−2.13708	+	3.70153i	−0.0818329	+	0.141739i
$683$	23.5436	−	40.7787i	0.900871	−	1.56035i	0.0745051	−	0.997221i	$-0.476262\pi$
$683$	23.5436	−	40.7787i	0.900871	−	1.56035i	0.826366	−	0.563134i	$-0.190404\pi$
$684$	7.23642	+	12.5338i	0.276691	+	0.479244i
$685$	15.5154			0.592811
$686$	32.0736	+	15.9689i	1.22458	+	0.609694i
$687$	−0.108739			−0.00414867
$688$	10.9688	+	18.9986i	0.418183	+	0.724314i
$689$	−41.0190	+	71.0470i	−1.56270	+	2.70668i
$690$	3.94851	−	6.83903i	0.150317	−	0.260357i
$691$	16.5909	+	28.7362i	0.631146	+	1.09318i	0.987318	+	0.158756i	$0.0507484\pi$
$691$	16.5909	+	28.7362i	0.631146	+	1.09318i	−0.356172	+	0.934420i	$0.615918\pi$
$692$	−11.2600			−0.428040
$693$	−2.59557	+	0.512871i	−0.0985974	+	0.0194824i
$694$	−40.3434			−1.53141
$695$	11.4112	+	19.7648i	0.432852	+	0.749722i
$696$	0.919110	−	1.59194i	0.0348388	−	0.0603425i
$697$	2.35182	−	4.07347i	0.0890816	−	0.154294i
$698$	−32.5493	−	56.3770i	−1.23201	−	2.13390i
$699$	−19.6861			−0.744597
$700$	−3.03556	−	3.47025i	−0.114733	−	0.131163i
$701$	−29.0289			−1.09641			−0.548203	−	0.836345i	$-0.684688\pi$
$701$	−29.0289			−1.09641			−0.548203	+	0.836345i	$0.684688\pi$
$702$	−6.49208	−	11.2446i	−0.245028	−	0.424401i
$703$	−17.4828	+	30.2811i	−0.659377	+	1.14207i
$704$	−2.91279	+	5.04510i	−0.109780	+	0.190145i
$705$	−1.92014	−	3.32578i	−0.0723166	−	0.125256i
$706$	34.5584			1.30062
$707$	−7.31599	+	21.4628i	−0.275146	+	0.807191i
$708$	0.245266			0.00921766
$709$	−14.1229	−	24.4616i	−0.530397	−	0.918675i	−0.999371	−	0.0354631i	$-0.988709\pi$
$709$	−14.1229	−	24.4616i	−0.530397	−	0.918675i	0.468974	−	0.883212i	$-0.344624\pi$
$710$	14.4782	−	25.0770i	0.543357	−	0.941122i
$711$	3.28402	−	5.68809i	0.123160	−	0.213320i
$712$	−0.795323	−	1.37754i	−0.0298060	−	0.0516255i
$713$	−9.01856			−0.337748
$714$	2.45276	−	7.19563i	0.0917923	−	0.269290i
$715$	−6.71159			−0.250999
$716$	6.89993	+	11.9510i	0.257862	+	0.446631i
$717$	7.63077	−	13.2169i	0.284976	−	0.493593i
$718$	−4.48785	+	7.77318i	−0.167485	+	0.290093i
$719$	2.49725	+	4.32537i	0.0931317	+	0.161309i	0.908827	−	0.417172i	$-0.136979\pi$
$719$	2.49725	+	4.32537i	0.0931317	+	0.161309i	−0.815696	+	0.578481i	$0.803646\pi$
$720$	4.44850			0.165786
$721$	−9.13492	−	10.4431i	−0.340202	−	0.388920i
$722$	−96.6831			−3.59817
$723$	4.53668	+	7.85775i	0.168721	+	0.292233i
$724$	3.07777	−	5.33085i	0.114384	−	0.198119i
$725$	1.84593	−	3.19725i	0.0685563	−	0.118743i
$726$	0.967294	+	1.67540i	0.0358996	+	0.0621800i
$727$	−19.7282			−0.731679			−0.365840	−	0.930678i	$-0.619218\pi$
$727$	−19.7282			−0.731679			−0.365840	+	0.930678i	$0.619218\pi$
$728$	−8.67379	+	1.71390i	−0.321472	+	0.0635213i
$729$	1.00000			0.0370370
$730$	1.70281	+	2.94935i	0.0630237	+	0.109160i
$731$	−3.66224	+	6.34319i	−0.135453	+	0.234611i
$732$	−9.38380	+	16.2532i	−0.346835	+	0.600736i
$733$	2.72573	+	4.72110i	0.100677	+	0.174378i	0.911964	−	0.410271i	$-0.134566\pi$
$733$	2.72573	+	4.72110i	0.100677	+	0.174378i	−0.811287	+	0.584649i	$0.801232\pi$
$734$	−2.43505			−0.0898793
$735$	−6.47393	+	2.66238i	−0.238794	+	0.0982035i
$736$	−31.0650			−1.14507
$737$	−5.23040	−	9.05932i	−0.192664	−	0.333704i
$738$	−3.06332	+	5.30582i	−0.112762	+	0.195310i
$739$	−22.3038	+	38.6313i	−0.820458	+	1.42107i	0.0848840	+	0.996391i	$0.472948\pi$
$739$	−22.3038	+	38.6313i	−0.820458	+	1.42107i	−0.905342	+	0.424684i	$0.860385\pi$
$740$	−3.66832	−	6.35371i	−0.134850	−	0.233567i
$741$	55.7410			2.04770
$742$	61.3776	−	12.1279i	2.25324	−	0.445230i
$743$	−44.4200			−1.62961			−0.814805	−	0.579735i	$-0.803156\pi$
$743$	−44.4200			−1.62961			−0.814805	+	0.579735i	$0.803156\pi$
$744$	−0.550026	−	0.952672i	−0.0201649	−	0.0349267i
$745$	4.09472	−	7.09227i	0.150019	−	0.259841i
$746$	23.5300	−	40.7551i	0.861494	−	1.49215i
$747$	−4.66422	−	8.07866i	−0.170655	−	0.295583i
$748$	−2.58824			−0.0946356
$749$	−30.5752	−	34.9536i	−1.11719	−	1.27718i
$750$	1.93459			0.0706411
$751$	18.9230	+	32.7755i	0.690509	+	1.19600i	0.971671	+	0.236336i	$0.0759467\pi$
$751$	18.9230	+	32.7755i	0.690509	+	1.19600i	−0.281163	+	0.959660i	$0.590720\pi$
$752$	−8.54175	+	14.7947i	−0.311486	+	0.539509i
$753$	9.73211	−	16.8565i	0.354658	−	0.614286i
$754$	23.9679	+	41.5136i	0.872860	+	1.51184i
$755$	12.0010			0.436761
$756$	−1.48755	+	4.36399i	−0.0541016	+	0.158717i
$757$	35.1022			1.27581			0.637905	−	0.770115i	$-0.279801\pi$
$757$	35.1022			1.27581			0.637905	+	0.770115i	$0.279801\pi$
$758$	−8.97052	−	15.5374i	−0.325824	−	0.564344i
$759$	−2.04101	+	3.53513i	−0.0740840	+	0.128317i
$760$	−2.06762	+	3.58122i	−0.0750004	+	0.129904i
$761$	−16.2649	−	28.1715i	−0.589600	−	1.02122i	−0.994285	−	0.106761i	$-0.965952\pi$
$761$	−16.2649	−	28.1715i	−0.589600	−	1.02122i	0.404684	−	0.914456i	$-0.367381\pi$
$762$	−38.4267			−1.39205
$763$	−1.97432	+	5.79204i	−0.0714753	+	0.209686i
$764$	−39.4455			−1.42709
$765$	0.742627	+	1.28627i	0.0268497	+	0.0465051i
$766$	−1.82615	+	3.16298i	−0.0659813	+	0.114283i
$767$	0.472311	−	0.818067i	0.0170542	−	0.0295387i
$768$	−9.64668	−	16.7085i	−0.348095	−	0.602918i
$769$	15.7130			0.566626			0.283313	−	0.959027i	$-0.408566\pi$
$769$	15.7130			0.566626			0.283313	+	0.959027i	$0.408566\pi$
$770$	3.36994	+	3.85252i	0.121444	+	0.138835i
$771$	3.61118			0.130053
$772$	−1.43709	−	2.48912i	−0.0517221	−	0.0895852i
$773$	3.73624	−	6.47136i	0.134383	−	0.232758i	−0.790978	−	0.611844i	$-0.790428\pi$
$773$	3.73624	−	6.47136i	0.134383	−	0.232758i	0.925362	+	0.379085i	$0.123761\pi$
$774$	4.77018	−	8.26219i	0.171461	−	0.296978i
$775$	−1.10467	−	1.91334i	−0.0396809	−	0.0687293i
$776$	5.13979			0.184508
$777$	−10.9276	+	2.15924i	−0.392025	+	0.0774623i
$778$	1.32302			0.0474324
$779$	−13.1508	−	22.7779i	−0.471177	−	0.816102i
$780$	−5.84790	+	10.1289i	−0.209389	+	0.362672i
$781$	−7.48387	+	12.9624i	−0.267794	+	0.463833i
$782$	−5.86455	−	10.1577i	−0.209716	−	0.363238i
$783$	−3.69187			−0.131937
$784$	24.6565	+	19.0191i	0.880590	+	0.679254i
$785$	−12.2003			−0.435446
$786$	11.6105	+	20.1100i	0.414134	+	0.717302i
$787$	−23.2515	+	40.2727i	−0.828825	+	1.43557i	0.0701348	+	0.997538i	$0.477657\pi$
$787$	−23.2515	+	40.2727i	−0.828825	+	1.43557i	−0.898960	+	0.438030i	$0.855676\pi$
$788$	−9.86519	+	17.0870i	−0.351433	+	0.608700i
$789$	5.98090	+	10.3592i	0.212926	+	0.368798i
$790$	−12.7064			−0.452075
$791$	−2.81607	+	0.556441i	−0.100128	+	0.0197848i
$792$	−0.497910			−0.0176925
$793$	36.1410	+	62.5980i	1.28340	+	2.22292i
$794$	−11.3988	+	19.7433i	−0.404528	+	0.700663i
$795$	−6.11167	+	10.5857i	−0.216758	+	0.375437i
$796$	−4.75631	−	8.23816i	−0.168583	−	0.291994i
$797$	16.4790			0.583717			0.291859	−	0.956461i	$-0.405726\pi$
$797$	16.4790			0.583717			0.291859	+	0.956461i	$0.405726\pi$
$798$	−27.9880	−	31.9959i	−0.990763	−	1.13264i
$799$	−5.70379			−0.201786
$800$	−3.80510	−	6.59063i	−0.134531	−	0.233014i
$801$	−1.59732	+	2.76664i	−0.0564386	+	0.0977545i
$802$	13.3591	−	23.1386i	0.471726	−	0.817053i
$803$	−0.880191	−	1.52454i	−0.0310613	−	0.0537997i
$804$	−18.2293			−0.642897
$805$	−3.48451	+	10.2225i	−0.122813	+	0.360294i
$806$	28.6864			1.01043
$807$	−1.16155	−	2.01187i	−0.0408886	−	0.0708211i
$808$	−2.13367	+	3.69563i	−0.0750623	+	0.130012i
$809$	−2.99358	+	5.18502i	−0.105249	+	0.182296i	−0.913840	−	0.406075i	$-0.866897\pi$
$809$	−2.99358	+	5.18502i	−0.105249	+	0.182296i	0.808591	+	0.588371i	$0.200230\pi$
$810$	−0.967294	−	1.67540i	−0.0339872	−	0.0588676i
$811$	13.7351			0.482304			0.241152	−	0.970487i	$-0.422475\pi$
$811$	13.7351			0.482304			0.241152	+	0.970487i	$0.422475\pi$
$812$	5.49183	−	16.1113i	0.192725	−	0.565396i
$813$	15.0562			0.528042
$814$	4.07240	+	7.05361i	0.142738	+	0.247229i
$815$	8.03365	−	13.9147i	0.281407	−	0.487410i
$816$	3.30358	−	5.72197i	0.115648	−	0.200309i
$817$	20.4784	+	35.4696i	0.716448	+	1.24092i
$818$	−13.8650			−0.484778
$819$	11.6912	+	13.3654i	0.408524	+	0.467025i
$820$	5.51871			0.192722
$821$	−22.5723	−	39.0963i	−0.787777	−	1.36447i	−0.927326	−	0.374255i	$-0.877898\pi$
$821$	−22.5723	−	39.0963i	−0.787777	−	1.36447i	0.139549	−	0.990215i	$-0.455435\pi$
$822$	−15.0079	+	25.9945i	−0.523461	+	0.906661i
$823$	−23.0776	+	39.9717i	−0.804436	+	1.39332i	0.112235	+	0.993682i	$0.464199\pi$
$823$	−23.0776	+	39.9717i	−0.804436	+	1.39332i	−0.916671	+	0.399642i	$0.869134\pi$
$824$	−1.30555	−	2.26127i	−0.0454808	−	0.0787751i
$825$	−1.00000			−0.0348155
$826$	−0.706729	+	0.139646i	−0.0245903	+	0.00485892i
$827$	−35.3533			−1.22936			−0.614678	−	0.788778i	$-0.710714\pi$
$827$	−35.3533			−1.22936			−0.614678	+	0.788778i	$0.710714\pi$
$828$	3.55672	+	6.16042i	0.123605	+	0.214089i
$829$	−7.46328	+	12.9268i	−0.259210	+	0.448965i	−0.966031	−	0.258428i	$-0.916796\pi$
$829$	−7.46328	+	12.9268i	−0.259210	+	0.448965i	0.706820	+	0.707393i	$0.250129\pi$
$830$	−9.02334	+	15.6289i	−0.313205	+	0.542486i
$831$	−2.04530	−	3.54256i	−0.0709506	−	0.122890i
$832$	39.0990			1.35551
$833$	−1.38318	+	10.3044i	−0.0479242	+	0.357025i
$834$	−44.1520			−1.52886
$835$	−4.57202	−	7.91896i	−0.158221	−	0.274047i
$836$	−7.23642	+	12.5338i	−0.250277	+	0.433492i
$837$	−1.10467	+	1.91334i	−0.0381829	+	0.0661348i
$838$	29.6388	+	51.3358i	1.02385	+	1.77337i
$839$	47.9378			1.65500			0.827499	−	0.561468i	$-0.189763\pi$
$839$	47.9378			1.65500			0.827499	+	0.561468i	$0.189763\pi$
$840$	−1.29236	+	0.255364i	−0.0445906	+	0.00881089i
$841$	−15.3701			−0.530004
$842$	4.65362	+	8.06031i	0.160374	+	0.277777i
$843$	−3.43549	+	5.95044i	−0.118324	+	0.204944i
$844$	13.3851	−	23.1837i	0.460734	−	0.798015i
$845$	16.0227	+	27.7522i	0.551199	+	0.954705i
$846$	7.42935			0.255426
$847$	−1.74194	−	1.99139i	−0.0598539	−	0.0684250i
$848$	54.3755			1.86726
$849$	11.3049	+	19.5806i	0.387982	+	0.672005i
$850$	1.43668	−	2.48840i	0.0492776	−	0.0853513i
$851$	−8.59286	+	14.8833i	−0.294559	+	0.510192i
$852$	13.0416	+	22.5887i	0.446798	+	0.773877i
$853$	39.3719			1.34807			0.674035	−	0.738700i	$-0.264560\pi$
$853$	39.3719			1.34807			0.674035	+	0.738700i	$0.264560\pi$
$854$	17.7852	−	52.1762i	0.608597	−	1.78543i
$855$	8.30518			0.284031
$856$	−4.36975	−	7.56863i	−0.149355	−	0.258690i
$857$	−20.1062	+	34.8250i	−0.686816	+	1.18960i	0.286046	+	0.958216i	$0.407659\pi$
$857$	−20.1062	+	34.8250i	−0.686816	+	1.18960i	−0.972862	+	0.231385i	$0.925674\pi$
$858$	6.49208	−	11.2446i	0.221636	−	0.383885i
$859$	−24.8187	−	42.9872i	−0.846802	−	1.46670i	−0.884047	−	0.467397i	$-0.845192\pi$
$859$	−24.8187	−	42.9872i	−0.846802	−	1.46670i	0.0372455	−	0.999306i	$-0.488142\pi$
$860$	−8.59371			−0.293043
$861$	2.70333	−	7.93073i	0.0921294	−	0.270279i
$862$	22.6078			0.770026
$863$	10.0476	+	17.4029i	0.342024	+	0.592402i	0.984808	−	0.173645i	$-0.0555544\pi$
$863$	10.0476	+	17.4029i	0.342024	+	0.592402i	−0.642785	+	0.766047i	$0.722221\pi$
$864$	−3.80510	+	6.59063i	−0.129452	+	0.224218i
$865$	−3.23075	+	5.59582i	−0.109849	+	0.190264i
$866$	−15.7065	−	27.2044i	−0.533728	−	0.924444i
$867$	−14.7940			−0.502431
$868$	−6.70657	−	7.66695i	−0.227636	−	0.260233i
$869$	6.56804			0.222805
$870$	3.57112	+	6.18536i	0.121072	+	0.209703i
$871$	−35.1043	+	60.8025i	−1.18946	+	2.06021i
$872$	−0.575802	+	0.997318i	−0.0194991	+	0.0337735i
$873$	−5.16136	−	8.93974i	−0.174686	−	0.302564i
$874$	−65.5863			−2.21849
$875$	−2.59557	+	0.512871i	−0.0877461	+	0.0173382i
$876$	−3.06769			−0.103648
$877$	−4.68691	−	8.11796i	−0.158266	−	0.274124i	0.775978	−	0.630760i	$-0.217257\pi$
$877$	−4.68691	−	8.11796i	−0.158266	−	0.274124i	−0.934243	+	0.356636i	$0.883924\pi$
$878$	−10.4315	+	18.0679i	−0.352046	+	0.609762i
$879$	13.1182	−	22.7214i	0.442466	−	0.766374i
$880$	2.22425	+	3.85252i	0.0749795	+	0.129868i
$881$	−29.5052			−0.994057			−0.497028	−	0.867734i	$-0.665576\pi$
$881$	−29.5052			−0.994057			−0.497028	+	0.867734i	$0.665576\pi$
$882$	1.80163	−	13.4217i	0.0606639	−	0.451933i
$883$	−35.2052			−1.18475			−0.592374	−	0.805663i	$-0.701809\pi$
$883$	−35.2052			−1.18475			−0.592374	+	0.805663i	$0.701809\pi$
$884$	8.68562	+	15.0439i	0.292129	+	0.505982i
$885$	0.0703725	−	0.121889i	0.00236554	−	0.00409724i
$886$	24.2991	−	42.0873i	0.816345	−	1.41395i
$887$	18.9201	+	32.7706i	0.635276	+	1.10033i	0.986457	+	0.164023i	$0.0524470\pi$
$887$	18.9201	+	32.7706i	0.635276	+	1.10033i	−0.351181	+	0.936308i	$0.614220\pi$
$888$	−2.09625			−0.0703456
$889$	51.5557	−	10.1872i	1.72912	−	0.341666i
$890$	6.18031			0.207165
$891$	0.500000	+	0.866025i	0.0167506	+	0.0290129i
$892$	−15.1887	+	26.3076i	−0.508555	+	0.880844i
$893$	−15.9471	+	27.6212i	−0.533650	+	0.924308i
$894$	7.92160	+	13.7206i	0.264938	+	0.458886i
$895$	7.91900			0.264703
$896$	6.88120	+	7.86659i	0.229885	+	0.262804i
$897$	27.3969			0.914755
$898$	−24.2339	−	41.9743i	−0.808695	−	1.40070i
$899$	4.07829	−	7.06381i	0.136019	−	0.235591i
$900$	−0.871314	+	1.50916i	−0.0290438	+	0.0503053i
$901$	9.07738	+	15.7225i	0.302411	+	0.523792i
$902$	−6.12663			−0.203994
$903$	−4.20962	+	12.3497i	−0.140087	+	0.410972i
$904$	−0.540209			−0.0179671
$905$	−1.76616	−	3.05909i	−0.0587093	−	0.101687i
$906$	−11.6085	+	20.1065i	−0.385666	+	0.667994i
$907$	1.88107	−	3.25810i	0.0624598	−	0.108184i	−0.833105	−	0.553116i	$-0.813439\pi$
$907$	1.88107	−	3.25810i	0.0624598	−	0.108184i	0.895564	+	0.444932i	$0.146772\pi$
$908$	−14.8396	−	25.7029i	−0.492468	−	0.852979i
$909$	8.57051			0.284266
$910$	11.0836	−	32.5157i	0.367417	−	1.07789i
$911$	22.8513			0.757097			0.378548	−	0.925582i	$-0.376423\pi$
$911$	22.8513			0.757097			0.378548	+	0.925582i	$0.376423\pi$
$912$	−18.4728	−	31.9959i	−0.611696	−	1.05949i
$913$	4.66422	−	8.07866i	0.154363	−	0.267365i
$914$	−18.8878	+	32.7146i	−0.624753	+	1.08210i
$915$	5.38486	+	9.32684i	0.178018	+	0.308336i
$916$	−0.189492			−0.00626100
$917$	−20.9087	−	23.9029i	−0.690468	−	0.789343i
$918$	−2.87335			−0.0948348
$919$	−4.63134	−	8.02171i	−0.152774	−	0.264612i	0.779472	−	0.626437i	$-0.215487\pi$
$919$	−4.63134	−	8.02171i	−0.152774	−	0.264612i	−0.932246	+	0.361825i	$0.882154\pi$
$920$	−1.01624	+	1.76018i	−0.0335044	+	0.0580314i
$921$	7.22898	−	12.5210i	0.238203	−	0.412580i
$922$	23.2990	+	40.3550i	0.767310	+	1.32902i
$923$	100.457			3.30660
$924$	−4.52310	+	0.893743i	−0.148799	+	0.0294020i
$925$	−4.21010			−0.138427
$926$	35.6011	+	61.6630i	1.16993	+	2.02637i
$927$	−2.62205	+	4.54152i	−0.0861194	+	0.149163i
$928$	14.0479	−	24.3317i	0.461146	−	0.798728i
$929$	7.67671	+	13.2965i	0.251865	+	0.436242i	0.964039	−	0.265760i	$-0.0856229\pi$
$929$	7.67671	+	13.2965i	0.251865	+	0.436242i	−0.712175	+	0.702002i	$0.752290\pi$
$930$	4.27415			0.140155
$931$	46.0328	+	35.5079i	1.50866	+	1.16373i
$932$	−34.3055			−1.12372
$933$	5.37022	+	9.30149i	0.175813	+	0.304517i
$934$	39.8954	−	69.1009i	1.30542	−	2.26105i
$935$	−0.742627	+	1.28627i	−0.0242865	+	0.0420655i
$936$	1.67089	+	2.89406i	0.0546146	+	0.0945953i
$937$	21.0242			0.686831			0.343416	−	0.939184i	$-0.388416\pi$
$937$	21.0242			0.686831			0.343416	+	0.939184i	$0.388416\pi$
$938$	52.5273	−	10.3791i	1.71508	−	0.338891i
$939$	9.15391			0.298727
$940$	−3.34609	−	5.79559i	−0.109137	−	0.189031i
$941$	9.22868	−	15.9845i	0.300846	−	0.521081i	−0.675482	−	0.737377i	$-0.736064\pi$
$941$	9.22868	−	15.9845i	0.300846	−	0.521081i	0.976328	+	0.216296i	$0.0693976\pi$
$942$	11.8012	−	20.4403i	0.384505	−	0.665982i
$943$	−6.46366	−	11.1954i	−0.210486	−	0.364572i
$944$	−0.626104			−0.0203780
$945$	1.74194	+	1.99139i	0.0566654	+	0.0647799i
$946$	9.54036			0.310184
$947$	−23.9167	−	41.4249i	−0.777188	−	1.34613i	−0.933557	−	0.358430i	$-0.883312\pi$
$947$	−23.9167	−	41.4249i	−0.777188	−	1.34613i	0.156369	−	0.987699i	$-0.450021\pi$
$948$	5.72282	−	9.91222i	0.185869	−	0.321934i
$949$	−5.90748	+	10.2321i	−0.191765	+	0.332147i
$950$	−8.03355	−	13.9145i	−0.260643	−	0.451447i
$951$	9.80425			0.317925
$952$	−0.631274	+	1.85196i	−0.0204597	+	0.0600224i
$953$	−15.1716			−0.491456			−0.245728	−	0.969339i	$-0.579027\pi$
$953$	−15.1716			−0.491456			−0.245728	+	0.969339i	$0.579027\pi$
$954$	−11.8235	−	20.4790i	−0.382802	−	0.663032i
$955$	−11.3178	+	19.6031i	−0.366237	+	0.634340i
$956$	13.2976	−	23.0321i	0.430075	−	0.744911i
$957$	−1.84593	−	3.19725i	−0.0596706	−	0.103352i
$958$	−64.9650			−2.09892
$959$	13.2443	−	38.8545i	0.427680	−	1.25468i
$960$	5.82558			0.188020
$961$	13.0594	+	22.6196i	0.421271	+	0.729664i
$962$	27.3323	−	47.3409i	0.881229	−	1.52633i
$963$	−8.77618	+	15.2008i	−0.282808	+	0.489839i
$964$	7.90573	+	13.6931i	0.254627	+	0.441026i
$965$	−1.64934			−0.0530941
$966$	−13.7562	−	15.7261i	−0.442597	−	0.505978i
$967$	33.0832			1.06388			0.531942	−	0.846781i	$-0.321463\pi$
$967$	33.0832			1.06388			0.531942	+	0.846781i	$0.321463\pi$
$968$	−0.248955	−	0.431203i	−0.00800172	−	0.0138594i
$969$	6.16766	−	10.6827i	0.198134	−	0.343178i
$970$	−9.98510	+	17.2947i	−0.320602	+	0.555299i
$971$	−10.6467	−	18.4406i	−0.341669	−	0.591788i	0.643074	−	0.765804i	$-0.277659\pi$
$971$	−10.6467	−	18.4406i	−0.341669	−	0.591788i	−0.984743	+	0.174016i	$0.944325\pi$
$972$	1.74263			0.0558948
$973$	59.2371	−	11.7050i	1.89906	−	0.375244i
$974$	60.4571			1.93717
$975$	3.35580	+	5.81241i	0.107472	+	0.186146i
$976$	23.9546	−	41.4905i	0.766767	−	1.32808i
$977$	−24.2717	+	42.0398i	−0.776521	+	1.34497i	0.157415	+	0.987533i	$0.449684\pi$
$977$	−24.2717	+	42.0398i	−0.776521	+	1.34497i	−0.933936	+	0.357441i	$0.883649\pi$
$978$	15.5418	+	26.9192i	0.496972	+	0.860781i
$979$	−3.19464			−0.102101
$980$	−11.2816	+	4.63954i	−0.360379	+	0.148205i
$981$	2.31288			0.0738444
$982$	−10.4983	−	18.1835i	−0.335013	−	0.580260i
$983$	6.00012	−	10.3925i	0.191374	−	0.331470i	−0.754332	−	0.656493i	$-0.772039\pi$
$983$	6.00012	−	10.3925i	0.191374	−	0.331470i	0.945706	+	0.325024i	$0.105372\pi$
$984$	0.788414	−	1.36557i	0.0251337	−	0.0435329i
$985$	5.66110	+	9.80532i	0.180378	+	0.312423i
$986$	10.6080			0.337829
$987$	−9.96770	+	1.96957i	−0.317275	+	0.0626921i
$988$	97.1358			3.09030
$989$	10.0652	+	17.4334i	0.320054	+	0.554350i
$990$	0.967294	−	1.67540i	0.0307426	−	0.0532478i
$991$	−1.91385	+	3.31489i	−0.0607955	+	0.105301i	−0.894821	−	0.446425i	$-0.852697\pi$
$991$	−1.91385	+	3.31489i	−0.0607955	+	0.105301i	0.834026	+	0.551726i	$0.186030\pi$
$992$	−8.40675	−	14.5609i	−0.266914	−	0.462309i
$993$	4.50759			0.143044
$994$	−50.4404	−	57.6635i	−1.59987	−	1.82898i
$995$	−5.45878			−0.173055
$996$	−8.12799	−	14.0781i	−0.257545	−	0.446082i
$997$	−11.3296	+	19.6234i	−0.358811	+	0.621478i	−0.987762	−	0.155966i	$-0.950151\pi$
$997$	−11.3296	+	19.6234i	−0.358811	+	0.621478i	0.628952	+	0.777444i	$0.283484\pi$
$998$	−22.0551	+	38.2006i	−0.698143	+	1.20922i
$999$	2.10505	+	3.64605i	0.0666008	+	0.115356i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.q.j.991.7	yes	16
7.2	even	3	inner	1155.2.q.j.331.7	✓	16
7.3	odd	6		8085.2.a.ce.1.2		8
7.4	even	3		8085.2.a.cf.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.q.j.331.7	✓	16	7.2	even	3	inner
1155.2.q.j.991.7	yes	16	1.1	even	1	trivial
8085.2.a.ce.1.2		8	7.3	odd	6
8085.2.a.cf.1.2		8	7.4	even	3

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:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.967294 + 1.67540i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.871314 + 1.50916i) q^{4} +(0.500000 + 0.866025i) q^{5} -1.93459 q^{6} +(2.59557 - 0.512871i) q^{7} +0.497910 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.967294 + 1.67540i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.871314 + 1.50916i) q^{4} +(0.500000 + 0.866025i) q^{5} -1.93459 q^{6} +(2.59557 - 0.512871i) q^{7} +0.497910 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.967294 + 1.67540i) q^{10} +(0.500000 - 0.866025i) q^{11} +(-0.871314 - 1.50916i) q^{12} -6.71159 q^{13} +(3.36994 + 3.85252i) q^{14} -1.00000 q^{15} +(2.22425 + 3.85252i) q^{16} +(-0.742627 + 1.28627i) q^{17} +(0.967294 - 1.67540i) q^{18} +(4.15259 + 7.19250i) q^{19} -1.74263 q^{20} +(-0.853623 + 2.50426i) q^{21} +1.93459 q^{22} +(2.04101 + 3.53513i) q^{23} +(-0.248955 + 0.431203i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-6.49208 - 11.2446i) q^{26} +1.00000 q^{27} +(-1.48755 + 4.36399i) q^{28} -3.69187 q^{29} +(-0.967294 - 1.67540i) q^{30} +(-1.10467 + 1.91334i) q^{31} +(-3.80510 + 6.59063i) q^{32} +(0.500000 + 0.866025i) q^{33} -2.87335 q^{34} +(1.74194 + 1.99139i) q^{35} +1.74263 q^{36} +(2.10505 + 3.64605i) q^{37} +(-8.03355 + 13.9145i) q^{38} +(3.35580 - 5.81241i) q^{39} +(0.248955 + 0.431203i) q^{40} -3.16689 q^{41} +(-5.02135 + 0.992194i) q^{42} +4.93147 q^{43} +(0.871314 + 1.50916i) q^{44} +(0.500000 - 0.866025i) q^{45} +(-3.94851 + 6.83903i) q^{46} +(1.92014 + 3.32578i) q^{47} -4.44850 q^{48} +(6.47393 - 2.66238i) q^{49} -1.93459 q^{50} +(-0.742627 - 1.28627i) q^{51} +(5.84790 - 10.1289i) q^{52} +(6.11167 - 10.5857i) q^{53} +(0.967294 + 1.67540i) q^{54} +1.00000 q^{55} +(1.29236 - 0.255364i) q^{56} -8.30518 q^{57} +(-3.57112 - 6.18536i) q^{58} +(-0.0703725 + 0.121889i) q^{59} +(0.871314 - 1.50916i) q^{60} +(-5.38486 - 9.32684i) q^{61} -4.27415 q^{62} +(-1.74194 - 1.99139i) q^{63} -5.82558 q^{64} +(-3.35580 - 5.81241i) q^{65} +(-0.967294 + 1.67540i) q^{66} +(5.23040 - 9.05932i) q^{67} +(-1.29412 - 2.24149i) q^{68} -4.08202 q^{69} +(-1.65141 + 4.84471i) q^{70} -14.9677 q^{71} +(-0.248955 - 0.431203i) q^{72} +(0.880191 - 1.52454i) q^{73} +(-4.07240 + 7.05361i) q^{74} +(-0.500000 - 0.866025i) q^{75} -14.4728 q^{76} +(0.853623 - 2.50426i) q^{77} +12.9842 q^{78} +(3.28402 + 5.68809i) q^{79} +(-2.22425 + 3.85252i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.06332 - 5.30582i) q^{82} +9.32844 q^{83} +(-3.03556 - 3.47025i) q^{84} -1.48525 q^{85} +(4.77018 + 8.26219i) q^{86} +(1.84593 - 3.19725i) q^{87} +(0.248955 - 0.431203i) q^{88} +(-1.59732 - 2.76664i) q^{89} +1.93459 q^{90} +(-17.4204 + 3.44218i) q^{91} -7.11344 q^{92} +(-1.10467 - 1.91334i) q^{93} +(-3.71468 + 6.43401i) q^{94} +(-4.15259 + 7.19250i) q^{95} +(-3.80510 - 6.59063i) q^{96} +10.3227 q^{97} +(10.7227 + 8.27112i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} - 10 q^{4} + 8 q^{5} - 8 q^{9}+O(q^{10}) \) 16 * q - 8 * q^3 - 10 * q^4 + 8 * q^5 - 8 * q^9	\( 16 q - 8 q^{3} - 10 q^{4} + 8 q^{5} - 8 q^{9} + 8 q^{11} - 10 q^{12} + 8 q^{13} + 6 q^{14} - 16 q^{15} - 2 q^{16} - 4 q^{17} - 9 q^{19} - 20 q^{20} + 3 q^{21} + 5 q^{23} - 8 q^{25} - 32 q^{26} + 16 q^{27} + 2 q^{28} - 10 q^{29} - 5 q^{31} + 8 q^{33} + 3 q^{35} + 20 q^{36} - 7 q^{37} + 8 q^{38} - 4 q^{39} + 18 q^{41} + 28 q^{43} + 10 q^{44} + 8 q^{45} - 18 q^{46} + 5 q^{47} + 4 q^{48} - 20 q^{49} - 4 q^{51} - 8 q^{52} + q^{53} + 16 q^{55} + 42 q^{56} + 18 q^{57} - 10 q^{58} - 16 q^{59} + 10 q^{60} - 26 q^{61} - 32 q^{62} - 3 q^{63} - 16 q^{64} + 4 q^{65} - 3 q^{67} - 88 q^{68} - 10 q^{69} + 6 q^{70} - 60 q^{71} - 15 q^{73} + 18 q^{74} - 8 q^{75} + 44 q^{76} - 3 q^{77} + 64 q^{78} - 11 q^{79} + 2 q^{80} - 8 q^{81} - 42 q^{82} + 24 q^{83} - 10 q^{84} - 8 q^{85} + 48 q^{86} + 5 q^{87} + 6 q^{91} + 56 q^{92} - 5 q^{93} - 24 q^{94} + 9 q^{95} + 88 q^{97} - 24 q^{98} - 16 q^{99}+O(q^{100}) \) 16 * q - 8 * q^3 - 10 * q^4 + 8 * q^5 - 8 * q^9 + 8 * q^11 - 10 * q^12 + 8 * q^13 + 6 * q^14 - 16 * q^15 - 2 * q^16 - 4 * q^17 - 9 * q^19 - 20 * q^20 + 3 * q^21 + 5 * q^23 - 8 * q^25 - 32 * q^26 + 16 * q^27 + 2 * q^28 - 10 * q^29 - 5 * q^31 + 8 * q^33 + 3 * q^35 + 20 * q^36 - 7 * q^37 + 8 * q^38 - 4 * q^39 + 18 * q^41 + 28 * q^43 + 10 * q^44 + 8 * q^45 - 18 * q^46 + 5 * q^47 + 4 * q^48 - 20 * q^49 - 4 * q^51 - 8 * q^52 + q^53 + 16 * q^55 + 42 * q^56 + 18 * q^57 - 10 * q^58 - 16 * q^59 + 10 * q^60 - 26 * q^61 - 32 * q^62 - 3 * q^63 - 16 * q^64 + 4 * q^65 - 3 * q^67 - 88 * q^68 - 10 * q^69 + 6 * q^70 - 60 * q^71 - 15 * q^73 + 18 * q^74 - 8 * q^75 + 44 * q^76 - 3 * q^77 + 64 * q^78 - 11 * q^79 + 2 * q^80 - 8 * q^81 - 42 * q^82 + 24 * q^83 - 10 * q^84 - 8 * q^85 + 48 * q^86 + 5 * q^87 + 6 * q^91 + 56 * q^92 - 5 * q^93 - 24 * q^94 + 9 * q^95 + 88 * q^97 - 24 * q^98 - 16 * q^99

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