LMFDB - Embedded newform 663.2.z.d.205.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [663,2,Mod(205,663)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(663, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("663.205");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 663 = 3 \cdot 13 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	663.z (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:	$5.29408165401$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} + 20x^{14} + 156x^{12} + 602x^{10} + 1212x^{8} + 1259x^{6} + 665x^{4} + 168x^{2} + 16 $ x^16 + 20x^14 + 156x^12 + 602x^10 + 1212x^8 + 1259x^6 + 665x^4 + 168*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			205.8
Root			$-2.45691i$ of defining polynomial
Character	$\chi$	$=$	663.205
Dual form			663.2.z.d.511.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.12774 - 1.22845i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(2.01819 - 3.49561i) q^{4} +0.284332i q^{5} +(-2.12774 - 1.22845i) q^{6} +(-4.07306 - 2.35158i) q^{7} -5.00321i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(2.12774 - 1.22845i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(2.01819 - 3.49561i) q^{4} +0.284332i q^{5} +(-2.12774 - 1.22845i) q^{6} +(-4.07306 - 2.35158i) q^{7} -5.00321i q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.349288 + 0.604985i) q^{10} +(0.407490 - 0.235264i) q^{11} -4.03639 q^{12} +(2.08559 - 2.94114i) q^{13} -11.5552 q^{14} +(0.246239 - 0.142166i) q^{15} +(-2.10982 - 3.65432i) q^{16} +(-0.500000 + 0.866025i) q^{17} +2.45691i q^{18} +(0.117827 + 0.0680272i) q^{19} +(0.993915 + 0.573837i) q^{20} +4.70317i q^{21} +(0.578023 - 1.00116i) q^{22} +(-4.31438 - 7.47273i) q^{23} +(-4.33291 + 2.50161i) q^{24} +4.91916 q^{25} +(0.824548 - 8.82004i) q^{26} +1.00000 q^{27} +(-16.4405 + 9.49190i) q^{28} +(3.26564 + 5.65626i) q^{29} +(0.349288 - 0.604985i) q^{30} +3.60080i q^{31} +(-0.312509 - 0.180427i) q^{32} +(-0.407490 - 0.235264i) q^{33} +2.45691i q^{34} +(0.668630 - 1.15810i) q^{35} +(2.01819 + 3.49561i) q^{36} +(5.09545 - 2.94186i) q^{37} +0.334273 q^{38} +(-3.58990 - 0.335604i) q^{39} +1.42257 q^{40} +(2.20323 - 1.27203i) q^{41} +(5.77762 + 10.0071i) q^{42} +(3.30027 - 5.71623i) q^{43} -1.89924i q^{44} +(-0.246239 - 0.142166i) q^{45} +(-18.3598 - 10.6000i) q^{46} +1.30120i q^{47} +(-2.10982 + 3.65432i) q^{48} +(7.55989 + 13.0941i) q^{49} +(10.4667 - 6.04295i) q^{50} +1.00000 q^{51} +(-6.07197 - 13.2262i) q^{52} -7.22455 q^{53} +(2.12774 - 1.22845i) q^{54} +(0.0668932 + 0.115862i) q^{55} +(-11.7655 + 20.3784i) q^{56} -0.136054i q^{57} +(13.8969 + 8.02337i) q^{58} +(1.81905 + 1.05023i) q^{59} -1.14767i q^{60} +(1.60773 - 2.78468i) q^{61} +(4.42341 + 7.66157i) q^{62} +(4.07306 - 2.35158i) q^{63} +7.55271 q^{64} +(0.836260 + 0.593000i) q^{65} -1.15605 q^{66} +(8.37426 - 4.83488i) q^{67} +(2.01819 + 3.49561i) q^{68} +(-4.31438 + 7.47273i) q^{69} -3.28552i q^{70} +(11.9378 + 6.89227i) q^{71} +(4.33291 + 2.50161i) q^{72} +0.728230i q^{73} +(7.22787 - 12.5190i) q^{74} +(-2.45958 - 4.26011i) q^{75} +(0.475594 - 0.274584i) q^{76} -2.21298 q^{77} +(-8.05065 + 3.69594i) q^{78} -15.1655 q^{79} +(1.03904 - 0.599890i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.12526 - 5.41312i) q^{82} +13.0056i q^{83} +(16.4405 + 9.49190i) q^{84} +(-0.246239 - 0.142166i) q^{85} -16.2169i q^{86} +(3.26564 - 5.65626i) q^{87} +(-1.17708 - 2.03876i) q^{88} +(3.80788 - 2.19848i) q^{89} -0.698577 q^{90} +(-15.4111 + 7.07501i) q^{91} -34.8290 q^{92} +(3.11838 - 1.80040i) q^{93} +(1.59846 + 2.76862i) q^{94} +(-0.0193423 + 0.0335019i) q^{95} +0.360854i q^{96} +(-10.5820 - 6.10952i) q^{97} +(32.1710 + 18.5739i) q^{98} +0.470529i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} + 4 q^{4} - 8 q^{9}+O(q^{10}) $ 16 * q - 8 * q^3 + 4 * q^4 - 8 * q^9	$ 16 q - 8 q^{3} + 4 q^{4} - 8 q^{9} + q^{10} + 3 q^{11} - 8 q^{12} - 2 q^{13} - 26 q^{14} - 3 q^{15} - 8 q^{17} + 27 q^{20} + q^{22} - 21 q^{23} + 14 q^{25} + 2 q^{26} + 16 q^{27} - 33 q^{28} + 29 q^{29} + q^{30} - 15 q^{32} - 3 q^{33} + 15 q^{35} + 4 q^{36} - 18 q^{37} + 62 q^{38} + q^{39} + 4 q^{40} + 12 q^{41} + 13 q^{42} - 3 q^{43} + 3 q^{45} - 9 q^{46} + 2 q^{49} - 36 q^{50} + 16 q^{51} - 8 q^{52} - 26 q^{53} + 9 q^{55} - 37 q^{56} + 30 q^{58} - 3 q^{59} + 29 q^{61} - 20 q^{62} + 36 q^{64} - 16 q^{65} - 2 q^{66} + 33 q^{67} + 4 q^{68} - 21 q^{69} + 27 q^{71} + 17 q^{74} - 7 q^{75} - 48 q^{76} - 8 q^{77} - q^{78} - 14 q^{79} - 39 q^{80} - 8 q^{81} - 3 q^{82} + 33 q^{84} + 3 q^{85} + 29 q^{87} - 5 q^{88} - 3 q^{89} - 2 q^{90} - 70 q^{91} - 64 q^{92} - 6 q^{93} - 25 q^{94} - 27 q^{95} + 6 q^{97} + 102 q^{98}+O(q^{100}) $ 16 * q - 8 * q^3 + 4 * q^4 - 8 * q^9 + q^10 + 3 * q^11 - 8 * q^12 - 2 * q^13 - 26 * q^14 - 3 * q^15 - 8 * q^17 + 27 * q^20 + q^22 - 21 * q^23 + 14 * q^25 + 2 * q^26 + 16 * q^27 - 33 * q^28 + 29 * q^29 + q^30 - 15 * q^32 - 3 * q^33 + 15 * q^35 + 4 * q^36 - 18 * q^37 + 62 * q^38 + q^39 + 4 * q^40 + 12 * q^41 + 13 * q^42 - 3 * q^43 + 3 * q^45 - 9 * q^46 + 2 * q^49 - 36 * q^50 + 16 * q^51 - 8 * q^52 - 26 * q^53 + 9 * q^55 - 37 * q^56 + 30 * q^58 - 3 * q^59 + 29 * q^61 - 20 * q^62 + 36 * q^64 - 16 * q^65 - 2 * q^66 + 33 * q^67 + 4 * q^68 - 21 * q^69 + 27 * q^71 + 17 * q^74 - 7 * q^75 - 48 * q^76 - 8 * q^77 - q^78 - 14 * q^79 - 39 * q^80 - 8 * q^81 - 3 * q^82 + 33 * q^84 + 3 * q^85 + 29 * q^87 - 5 * q^88 - 3 * q^89 - 2 * q^90 - 70 * q^91 - 64 * q^92 - 6 * q^93 - 25 * q^94 - 27 * q^95 + 6 * q^97 + 102 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/663\mathbb{Z}\right)^\times$.

$n$	$443$	$547$	$613$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	2.12774	−	1.22845i	1.50454	−	0.868647i	0.504555	−	0.863379i	$-0.331656\pi$
$2$	2.12774	−	1.22845i	1.50454	−	0.868647i	0.999986	−	0.00526816i	$-0.00167691\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	2.01819	−	3.49561i	1.00910	−	1.74781i
$5$			0.284332i			0.127157i	0.997977	+	0.0635786i	$0.0202513\pi$
$5$			0.284332i			0.127157i	−0.997977	+	0.0635786i	$0.979749\pi$
$6$	−2.12774	−	1.22845i	−0.868647	−	0.501514i
$7$	−4.07306	−	2.35158i	−1.53947	−	0.888815i	−0.998869	−	0.0475376i	$-0.984863\pi$
$7$	−4.07306	−	2.35158i	−1.53947	−	0.888815i	−0.540604	−	0.841277i	$-0.681804\pi$
$8$		−	5.00321i		−	1.76890i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.349288	+	0.604985i	0.110455	+	0.191313i
$11$	0.407490	−	0.235264i	0.122863	−	0.0709349i	−0.437309	−	0.899311i	$-0.644068\pi$
$11$	0.407490	−	0.235264i	0.122863	−	0.0709349i	0.560172	+	0.828376i	$0.310735\pi$
$12$	−4.03639			−1.16520
$13$	2.08559	−	2.94114i	0.578439	−	0.815726i
$13$	2.08559	−	2.94114i	0.578439	−	0.815726i
$14$	−11.5552			−3.08827
$15$	0.246239	−	0.142166i	0.0635786	−	0.0367071i
$16$	−2.10982	−	3.65432i	−0.527456	−	0.913581i
$17$	−0.500000	+	0.866025i	−0.121268	+	0.210042i
$17$	−0.500000	+	0.866025i	−0.121268	+	0.210042i
$18$			2.45691i			0.579098i
$19$	0.117827	+	0.0680272i	0.0270313	+	0.0156065i	0.513455	−	0.858117i	$-0.328365\pi$
$19$	0.117827	+	0.0680272i	0.0270313	+	0.0156065i	−0.486423	+	0.873723i	$0.661699\pi$
$20$	0.993915	+	0.573837i	0.222246	+	0.128314i
$21$			4.70317i			1.02632i
$22$	0.578023	−	1.00116i	0.123235	−	0.213449i
$23$	−4.31438	−	7.47273i	−0.899611	−	1.55817i	−0.827992	−	0.560740i	$-0.810517\pi$
$23$	−4.31438	−	7.47273i	−0.899611	−	1.55817i	−0.0716186	−	0.997432i	$-0.522816\pi$
$24$	−4.33291	+	2.50161i	−0.884451	+	0.510638i
$25$	4.91916			0.983831
$26$	0.824548	−	8.82004i	0.161707	−	1.72975i
$27$	1.00000			0.192450
$28$	−16.4405	+	9.49190i	−3.10695	+	1.79380i
$29$	3.26564	+	5.65626i	0.606414	+	1.05034i	0.991826	+	0.127596i	$0.0407260\pi$
$29$	3.26564	+	5.65626i	0.606414	+	1.05034i	−0.385412	+	0.922745i	$0.625941\pi$
$30$	0.349288	−	0.604985i	0.0637711	−	0.110455i
$31$			3.60080i			0.646723i	0.946276	+	0.323361i	$0.104813\pi$
$31$			3.60080i			0.646723i	−0.946276	+	0.323361i	$0.895187\pi$
$32$	−0.312509	−	0.180427i	−0.0552443	−	0.0318953i
$33$	−0.407490	−	0.235264i	−0.0709349	−	0.0409543i
$34$			2.45691i			0.421356i
$35$	0.668630	−	1.15810i	0.113019	−	0.195755i
$36$	2.01819	+	3.49561i	0.336366	+	0.582602i
$37$	5.09545	−	2.94186i	0.837686	−	0.483638i	−0.0187909	−	0.999823i	$-0.505982\pi$
$37$	5.09545	−	2.94186i	0.837686	−	0.483638i	0.856477	+	0.516185i	$0.172648\pi$
$38$	0.334273			0.0542262
$39$	−3.58990	−	0.335604i	−0.574844	−	0.0537397i
$40$	1.42257			0.224929
$41$	2.20323	−	1.27203i	0.344086	−	0.198658i	−0.317991	−	0.948094i	$-0.603008\pi$
$41$	2.20323	−	1.27203i	0.344086	−	0.198658i	0.662077	+	0.749435i	$0.269675\pi$
$42$	5.77762	+	10.0071i	0.891506	+	1.54413i
$43$	3.30027	−	5.71623i	0.503286	−	0.871717i	−0.496707	−	0.867918i	$-0.665458\pi$
$43$	3.30027	−	5.71623i	0.503286	−	0.871717i	0.999993	−	0.00379844i	$-0.00120908\pi$
$44$		−	1.89924i		−	0.286321i
$45$	−0.246239	−	0.142166i	−0.0367071	−	0.0211929i
$46$	−18.3598	−	10.6000i	−2.70700	−	1.56289i
$47$			1.30120i			0.189799i	0.995487	+	0.0948997i	$0.0302530\pi$
$47$			1.30120i			0.189799i	−0.995487	+	0.0948997i	$0.969747\pi$
$48$	−2.10982	+	3.65432i	−0.304527	+	0.527456i
$49$	7.55989	+	13.0941i	1.07998	+	1.87059i
$50$	10.4667	−	6.04295i	1.48021	−	0.854602i
$51$	1.00000			0.140028
$52$	−6.07197	−	13.2262i	−0.842030	−	1.83415i
$53$	−7.22455			−0.992369			−0.496184	−	0.868217i	$-0.665266\pi$
$53$	−7.22455			−0.992369			−0.496184	+	0.868217i	$0.665266\pi$
$54$	2.12774	−	1.22845i	0.289549	−	0.167171i
$55$	0.0668932	+	0.115862i	0.00901988	+	0.0156229i
$56$	−11.7655	+	20.3784i	−1.57223	+	2.72318i
$57$		−	0.136054i		−	0.0180208i
$58$	13.8969	+	8.02337i	1.82475	+	1.05352i
$59$	1.81905	+	1.05023i	0.236820	+	0.136728i	0.613715	−	0.789528i	$-0.289675\pi$
$59$	1.81905	+	1.05023i	0.236820	+	0.136728i	−0.376894	+	0.926256i	$0.623008\pi$
$60$		−	1.14767i		−	0.148164i
$61$	1.60773	−	2.78468i	0.205849	−	0.356541i	−0.744554	−	0.667562i	$-0.767338\pi$
$61$	1.60773	−	2.78468i	0.205849	−	0.356541i	0.950403	+	0.311021i	$0.100671\pi$
$62$	4.42341	+	7.66157i	0.561774	+	0.973021i
$63$	4.07306	−	2.35158i	0.513158	−	0.296272i
$64$	7.55271			0.944089
$65$	0.836260	+	0.593000i	0.103725	+	0.0735526i
$66$	−1.15605			−0.142299
$67$	8.37426	−	4.83488i	1.02308	−	0.590675i	0.108084	−	0.994142i	$-0.465528\pi$
$67$	8.37426	−	4.83488i	1.02308	−	0.590675i	0.914994	+	0.403467i	$0.132195\pi$
$68$	2.01819	+	3.49561i	0.244742	+	0.423905i
$69$	−4.31438	+	7.47273i	−0.519391	+	0.899611i
$70$		−	3.28552i		−	0.392695i
$71$	11.9378	+	6.89227i	1.41675	+	0.817962i	0.996012	−	0.0892187i	$-0.0284370\pi$
$71$	11.9378	+	6.89227i	1.41675	+	0.817962i	0.420740	+	0.907181i	$0.361770\pi$
$72$	4.33291	+	2.50161i	0.510638	+	0.294817i
$73$			0.728230i			0.0852329i	0.999092	+	0.0426165i	$0.0135693\pi$
$73$			0.728230i			0.0852329i	−0.999092	+	0.0426165i	$0.986431\pi$
$74$	7.22787	−	12.5190i	0.840222	−	1.45531i
$75$	−2.45958	−	4.26011i	−0.284008	−	0.491916i
$76$	0.475594	−	0.274584i	0.0545543	−	0.0314970i
$77$	−2.21298			−0.252192
$78$	−8.05065	+	3.69594i	−0.911557	+	0.418483i
$79$	−15.1655			−1.70625			−0.853127	−	0.521704i	$-0.825297\pi$
$79$	−15.1655			−1.70625			−0.853127	+	0.521704i	$0.825297\pi$
$80$	1.03904	−	0.599890i	0.116168	−	0.0670698i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	3.12526	−	5.41312i	0.345128	−	0.597779i
$83$			13.0056i			1.42755i	0.700377	+	0.713773i	$0.253015\pi$
$83$			13.0056i			1.42755i	−0.700377	+	0.713773i	$0.746985\pi$
$84$	16.4405	+	9.49190i	1.79380	+	1.03565i
$85$	−0.246239	−	0.142166i	−0.0267083	−	0.0154201i
$86$		−	16.2169i		−	1.74871i
$87$	3.26564	−	5.65626i	0.350113	−	0.606414i
$88$	−1.17708	−	2.03876i	−0.125477	−	0.217332i
$89$	3.80788	−	2.19848i	0.403635	−	0.233039i	−0.284416	−	0.958701i	$-0.591800\pi$
$89$	3.80788	−	2.19848i	0.403635	−	0.233039i	0.688051	+	0.725662i	$0.258467\pi$
$90$	−0.698577			−0.0736365
$91$	−15.4111	+	7.07501i	−1.61552	+	0.741663i
$92$	−34.8290			−3.63118
$93$	3.11838	−	1.80040i	0.323361	−	0.186693i
$94$	1.59846	+	2.76862i	0.164869	+	0.285561i
$95$	−0.0193423	+	0.0335019i	−0.00198448	+	0.00343722i
$96$			0.360854i			0.0368295i
$97$	−10.5820	−	6.10952i	−1.07444	−	0.620327i	−0.145048	−	0.989425i	$-0.546334\pi$
$97$	−10.5820	−	6.10952i	−1.07444	−	0.620327i	−0.929391	+	0.369097i	$0.879667\pi$
$98$	32.1710	+	18.5739i	3.24976	+	1.87625i
$99$			0.470529i			0.0472899i
$100$	9.92781	−	17.1955i	0.992781	−	1.71955i
$101$	1.58069	+	2.73783i	0.157284	+	0.272425i	0.933889	−	0.357564i	$-0.116393\pi$
$101$	1.58069	+	2.73783i	0.157284	+	0.272425i	−0.776604	+	0.629989i	$0.783059\pi$
$102$	2.12774	−	1.22845i	0.210678	−	0.121635i
$103$	−17.7088			−1.74490			−0.872448	−	0.488706i	$-0.837469\pi$
$103$	−17.7088			−1.74490			−0.872448	+	0.488706i	$0.837469\pi$
$104$	−14.7152	−	10.4347i	−1.44294	−	1.02320i
$105$	−1.33726			−0.130503
$106$	−15.3720	+	8.87502i	−1.49306	+	0.862019i
$107$	1.50519	+	2.60706i	0.145512	+	0.252034i	0.929564	−	0.368661i	$-0.120184\pi$
$107$	1.50519	+	2.60706i	0.145512	+	0.252034i	−0.784052	+	0.620695i	$0.786850\pi$
$108$	2.01819	−	3.49561i	0.194201	−	0.336366i
$109$			6.53766i			0.626194i	0.949721	+	0.313097i	$0.101367\pi$
$109$			6.53766i			0.626194i	−0.949721	+	0.313097i	$0.898633\pi$
$110$	0.284663	+	0.164350i	0.0271416	+	0.0156702i
$111$	−5.09545	−	2.94186i	−0.483638	−	0.279229i
$112$			19.8457i			1.87524i
$113$	6.28350	−	10.8833i	0.591102	−	1.02382i	−0.402983	−	0.915208i	$-0.632026\pi$
$113$	6.28350	−	10.8833i	0.591102	−	1.02382i	0.994084	−	0.108611i	$-0.0346402\pi$
$114$	−0.167136	−	0.289489i	−0.0156538	−	0.0271131i
$115$	2.12474	−	1.22672i	0.198133	−	0.114392i
$116$	26.3628			2.44772
$117$	1.50431	+	3.27675i	0.139073	+	0.302935i
$118$	5.16063			0.475075
$119$	4.07306	−	2.35158i	0.373377	−	0.215569i
$120$	−0.711287	−	1.23198i	−0.0649313	−	0.112464i
$121$	−5.38930	+	9.33454i	−0.489936	+	0.848595i
$122$		−	7.90010i		−	0.715241i
$123$	−2.20323	−	1.27203i	−0.198658	−	0.114695i
$124$	12.5870	+	7.26711i	1.13035	+	0.652606i
$125$			2.82033i			0.252258i
$126$	5.77762	−	10.0071i	0.514711	−	0.891506i
$127$	−7.80205	−	13.5135i	−0.692320	−	1.19913i	−0.971076	−	0.238771i	$-0.923255\pi$
$127$	−7.80205	−	13.5135i	−0.692320	−	1.19913i	0.278756	−	0.960362i	$-0.410078\pi$
$128$	16.6952	−	9.63901i	1.47567	−	0.851976i
$129$	−6.60053			−0.581145
$130$	2.50782	+	0.234445i	0.219950	+	0.0205622i
$131$	8.88619			0.776390			0.388195	−	0.921577i	$-0.373099\pi$
$131$	8.88619			0.776390			0.388195	+	0.921577i	$0.373099\pi$
$132$	−1.64479	+	0.949619i	−0.143160	+	0.0826537i
$133$	−0.319943	−	0.554158i	−0.0277426	−	0.0480516i
$134$	11.8788	−	20.5748i	1.02618	−	1.77739i
$135$			0.284332i			0.0244714i
$136$	4.33291	+	2.50161i	0.371544	+	0.214511i
$137$	6.06107	+	3.49936i	0.517832	+	0.298971i	0.736047	−	0.676930i	$-0.236690\pi$
$137$	6.06107	+	3.49936i	0.517832	+	0.298971i	−0.218215	+	0.975901i	$0.570023\pi$
$138$			21.2001i			1.80467i
$139$	2.12001	−	3.67196i	0.179817	−	0.311452i	−0.762001	−	0.647576i	$-0.775783\pi$
$139$	2.12001	−	3.67196i	0.179817	−	0.311452i	0.941818	+	0.336124i	$0.109116\pi$
$140$	−2.69885	−	4.67455i	−0.228095	−	0.395071i
$141$	1.12687	−	0.650599i	0.0948997	−	0.0547904i
$142$	33.8673			2.84208
$143$	0.157911	−	1.68915i	0.0132052	−	0.141254i
$144$	4.21965			0.351637
$145$	−1.60825	+	0.928526i	−0.133558	+	0.0771099i
$146$	0.894597	+	1.54949i	0.0740374	+	0.128236i
$147$	7.55989	−	13.0941i	0.623529	−	1.07998i
$148$		−	23.7489i		−	1.95215i
$149$	9.63703	+	5.56394i	0.789497	+	0.455816i	0.839785	−	0.542919i	$-0.182681\pi$
$149$	9.63703	+	5.56394i	0.789497	+	0.455816i	−0.0502887	+	0.998735i	$0.516014\pi$
$150$	−10.4667	−	6.04295i	−0.854602	−	0.493405i
$151$			7.59663i			0.618205i	0.951029	+	0.309102i	$0.100029\pi$
$151$			7.59663i			0.618205i	−0.951029	+	0.309102i	$0.899971\pi$
$152$	0.340355	−	0.589511i	0.0276064	−	0.0478157i
$153$	−0.500000	−	0.866025i	−0.0404226	−	0.0700140i
$154$	−4.70865	+	2.71854i	−0.379433	+	0.219066i
$155$	−1.02382			−0.0822354
$156$	−8.41825	+	11.8716i	−0.674000	+	0.950487i
$157$	14.2471			1.13705			0.568523	−	0.822668i	$-0.307515\pi$
$157$	14.2471			1.13705			0.568523	+	0.822668i	$0.307515\pi$
$158$	−32.2683	+	18.6301i	−2.56713	+	1.48213i
$159$	3.61228	+	6.25665i	0.286472	+	0.496184i
$160$	0.0513012	−	0.0888563i	0.00405572	−	0.00702471i
$161$			40.5825i			3.19835i
$162$	−2.12774	−	1.22845i	−0.167171	−	0.0965164i
$163$	14.3517	+	8.28594i	1.12411	+	0.649005i	0.942447	−	0.334356i	$-0.108519\pi$
$163$	14.3517	+	8.28594i	1.12411	+	0.649005i	0.181663	+	0.983361i	$0.441852\pi$
$164$		−	10.2688i		−	0.801861i
$165$	0.0668932	−	0.115862i	0.00520763	−	0.00901988i
$166$	15.9767	+	27.6725i	1.24003	+	2.14780i
$167$	−6.49824	+	3.75176i	−0.502849	+	0.290320i	−0.729889	−	0.683565i	$-0.760428\pi$
$167$	−6.49824	+	3.75176i	−0.502849	+	0.290320i	0.227040	+	0.973885i	$0.427095\pi$
$168$	23.5309			1.81545
$169$	−4.30062	−	12.2680i	−0.330817	−	0.943695i
$170$	−0.698577			−0.0535784
$171$	−0.117827	+	0.0680272i	−0.00901042	+	0.00520217i
$172$	−13.3212	−	23.0729i	−1.01573	−	1.75929i
$173$	−12.8314	+	22.2247i	−0.975555	+	1.68971i	−0.297463	+	0.954733i	$0.596141\pi$
$173$	−12.8314	+	22.2247i	−0.975555	+	1.68971i	−0.678092	+	0.734977i	$0.737193\pi$
$174$		−	16.0467i		−	1.21650i
$175$	−20.0360	−	11.5678i	−1.51458	−	0.874444i
$176$	−1.71946	−	0.992733i	−0.129610	−	0.0748301i
$177$		−	2.10046i		−	0.157880i
$178$	5.40146	−	9.35561i	0.404857	−	0.701232i
$179$	−7.12667	−	12.3437i	−0.532672	−	0.922615i	−0.999272	−	0.0381467i	$-0.987855\pi$
$179$	−7.12667	−	12.3437i	−0.532672	−	0.922615i	0.466600	−	0.884468i	$-0.345479\pi$
$180$	−0.993915	+	0.573837i	−0.0740820	+	0.0427713i
$181$	−3.84190			−0.285566			−0.142783	−	0.989754i	$-0.545605\pi$
$181$	−3.84190			−0.285566			−0.142783	+	0.989754i	$0.545605\pi$
$182$	−24.0995	+	33.9856i	−1.78637	+	2.51918i
$183$	−3.21547			−0.237694
$184$	−37.3876	+	21.5858i	−2.75625	+	1.59132i
$185$	0.836464	+	1.44880i	0.0614981	+	0.106518i
$186$	4.42341	−	7.66157i	0.324340	−	0.561774i
$187$			0.470529i			0.0344085i
$188$	4.54849	+	2.62607i	0.331733	+	0.191526i
$189$	−4.07306	−	2.35158i	−0.296272	−	0.171053i
$190$			0.0950445i			0.00689525i
$191$	3.72595	−	6.45353i	0.269600	−	0.466961i	−0.699159	−	0.714967i	$-0.746442\pi$
$191$	3.72595	−	6.45353i	0.269600	−	0.466961i	0.968759	+	0.248006i	$0.0797752\pi$
$192$	−3.77636	−	6.54084i	−0.272535	−	0.472044i
$193$	−2.89705	+	1.67261i	−0.208534	+	0.120397i	−0.600630	−	0.799527i	$-0.705083\pi$
$193$	−2.89705	+	1.67261i	−0.208534	+	0.120397i	0.392096	+	0.919924i	$0.371750\pi$
$194$	−30.0210			−2.15538
$195$	0.0954230	−	1.02072i	0.00683338	−	0.0730955i
$196$	61.0293			4.35924
$197$	11.9020	−	6.87162i	0.847982	−	0.489583i	−0.0119875	−	0.999928i	$-0.503816\pi$
$197$	11.9020	−	6.87162i	0.847982	−	0.489583i	0.859969	+	0.510346i	$0.170482\pi$
$198$	0.578023	+	1.00116i	0.0410783	+	0.0711497i
$199$	−4.06661	+	7.04358i	−0.288275	+	0.499306i	−0.973398	−	0.229121i	$-0.926415\pi$
$199$	−4.06661	+	7.04358i	−0.288275	+	0.499306i	0.685123	+	0.728427i	$0.259748\pi$
$200$		−	24.6116i		−	1.74030i
$201$	−8.37426	−	4.83488i	−0.590675	−	0.341026i
$202$	6.72660	+	3.88361i	0.473282	+	0.273250i
$203$		−	30.7177i		−	2.15596i
$204$	2.01819	−	3.49561i	0.141302	−	0.244742i
$205$	0.361680	+	0.626447i	0.0252608	+	0.0437530i
$206$	−37.6797	+	21.7544i	−2.62527	+	1.51570i
$207$	8.62876			0.599741
$208$	−15.1481	−	1.41613i	−1.05033	−	0.0981910i
$209$	0.0640175			0.00442819
$210$	−2.84535	+	1.64276i	−0.196348	+	0.113361i
$211$	−7.96336	−	13.7929i	−0.548220	−	0.949545i	−0.998397	−	0.0566056i	$-0.981972\pi$
$211$	−7.96336	−	13.7929i	−0.548220	−	0.949545i	0.450176	−	0.892940i	$-0.351361\pi$
$212$	−14.5805	+	25.2543i	−1.00140	+	1.73447i
$213$		−	13.7845i		−	0.944502i
$214$	6.40530	+	3.69810i	0.437857	+	0.252797i
$215$	1.62531	+	0.938371i	0.110845	+	0.0639964i
$216$		−	5.00321i		−	0.340425i
$217$	8.46758	−	14.6663i	0.574817	−	0.995612i
$218$	8.03121	+	13.9105i	0.543942	+	0.942135i
$219$	0.630666	−	0.364115i	0.0426165	−	0.0246046i
$220$	0.540014			0.0364077
$221$	1.50431	+	3.27675i	0.101191	+	0.220418i
$222$	−14.4557			−0.970205
$223$	−24.5066	+	14.1489i	−1.64108	+	0.947479i	−0.660632	+	0.750710i	$0.729712\pi$
$223$	−24.5066	+	14.1489i	−1.64108	+	0.947479i	−0.980450	+	0.196769i	$0.936955\pi$
$224$	0.848579	+	1.46978i	0.0566981	+	0.0982039i
$225$	−2.45958	+	4.26011i	−0.163972	+	0.284008i
$226$		−	30.8759i		−	2.05384i
$227$	7.34691	+	4.24174i	0.487632	+	0.281534i	0.723591	−	0.690229i	$-0.242490\pi$
$227$	7.34691	+	4.24174i	0.487632	+	0.281534i	−0.235960	+	0.971763i	$0.575823\pi$
$228$	−0.475594	−	0.274584i	−0.0314970	−	0.0181848i
$229$		−	22.6533i		−	1.49697i	−0.663150	−	0.748486i	$-0.730781\pi$
$229$		−	22.6533i		−	1.49697i	0.663150	−	0.748486i	$-0.269219\pi$
$230$	3.01393	−	5.22028i	0.198733	−	0.344215i
$231$	1.10649	+	1.91649i	0.0728016	+	0.126096i
$232$	28.2994	−	16.3387i	1.85795	−	1.07269i
$233$	−17.6416			−1.15574			−0.577870	−	0.816129i	$-0.696116\pi$
$233$	−17.6416			−1.15574			−0.577870	+	0.816129i	$0.696116\pi$
$234$	7.22611	+	5.12410i	0.472385	+	0.334973i
$235$	−0.369972			−0.0241343
$236$	7.34240	−	4.23914i	0.477950	−	0.275944i
$237$	7.58276	+	13.1337i	0.492553	+	0.853127i
$238$	5.77762	−	10.0071i	0.374508	−	0.648666i
$239$			13.7518i			0.889529i	0.895647	+	0.444765i	$0.146713\pi$
$239$			13.7518i			0.889529i	−0.895647	+	0.444765i	$0.853287\pi$
$240$	−1.03904	−	0.599890i	−0.0670698	−	0.0387228i
$241$	1.13817	+	0.657123i	0.0733160	+	0.0423290i	0.536210	−	0.844085i	$-0.319856\pi$
$241$	1.13817	+	0.657123i	0.0733160	+	0.0423290i	−0.462894	+	0.886414i	$0.653189\pi$
$242$			26.4820i			1.70233i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−6.48943	−	11.2400i	−0.415443	−	0.719569i
$245$	−3.72308	+	2.14952i	−0.237859	+	0.137328i
$246$	−6.25053			−0.398519
$247$	0.445816	−	0.204668i	0.0283666	−	0.0130227i
$248$	18.0156			1.14399
$249$	11.2631	−	6.50278i	0.713773	−	0.412097i
$250$	3.46465	+	6.00094i	0.219124	+	0.379533i
$251$	−6.96257	+	12.0595i	−0.439473	+	0.761190i	−0.997649	−	0.0685329i	$-0.978168\pi$
$251$	−6.96257	+	12.0595i	−0.439473	+	0.761190i	0.558176	+	0.829723i	$0.311502\pi$
$252$		−	18.9838i		−	1.19587i
$253$	−3.51614	−	2.03004i	−0.221058	−	0.127628i
$254$	−33.2015	−	19.1689i	−2.08325	−	1.20276i
$255$			0.284332i			0.0178056i
$256$	16.1294	−	27.9370i	1.00809	−	1.74606i
$257$	11.5475	+	20.0009i	0.720315	+	1.24762i	0.960873	+	0.276988i	$0.0893363\pi$
$257$	11.5475	+	20.0009i	0.720315	+	1.24762i	−0.240558	+	0.970635i	$0.577330\pi$
$258$	−14.0442	+	8.10845i	−0.874356	+	0.504810i
$259$	−27.6721			−1.71946
$260$	3.76064	−	1.72645i	0.233225	−	0.107070i
$261$	−6.53128			−0.404276
$262$	18.9075	−	10.9163i	1.16811	−	0.674409i
$263$	3.28739	+	5.69392i	0.202709	+	0.351102i	0.949400	−	0.314068i	$-0.101692\pi$
$263$	3.28739	+	5.69392i	0.202709	+	0.351102i	−0.746691	+	0.665171i	$0.768359\pi$
$264$	−1.17708	+	2.03876i	−0.0724442	+	0.125477i
$265$		−	2.05417i		−	0.126187i
$266$	−1.36151	−	0.786071i	−0.0834798	−	0.0481971i
$267$	−3.80788	−	2.19848i	−0.233039	−	0.134545i
$268$		−	39.0309i		−	2.38419i
$269$	−4.95420	+	8.58093i	−0.302063	+	0.523189i	−0.976603	−	0.215050i	$-0.931009\pi$
$269$	−4.95420	+	8.58093i	−0.302063	+	0.523189i	0.674540	+	0.738238i	$0.264342\pi$
$270$	0.349288	+	0.604985i	0.0212570	+	0.0368182i
$271$	5.21903	−	3.01321i	0.317034	−	0.183039i	−0.333036	−	0.942914i	$-0.608073\pi$
$271$	5.21903	−	3.01321i	0.317034	−	0.183039i	0.650070	+	0.759875i	$0.274740\pi$
$272$	4.21965			0.255854
$273$	13.8327	+	9.80888i	0.837192	+	0.593661i
$274$	17.1952			1.03880
$275$	2.00451	−	1.15730i	0.120876	−	0.0697880i
$276$	17.4145	+	30.1628i	1.04823	+	1.81559i
$277$	1.86136	−	3.22396i	0.111838	−	0.193709i	−0.804673	−	0.593718i	$-0.797660\pi$
$277$	1.86136	−	3.22396i	0.111838	−	0.193709i	0.916511	+	0.400009i	$0.130993\pi$
$278$		−	10.4173i		−	0.624789i
$279$	−3.11838	−	1.80040i	−0.186693	−	0.107787i
$280$	−5.79423	−	3.34530i	−0.346271	−	0.199920i
$281$			1.41750i			0.0845611i	0.999106	+	0.0422806i	$0.0134623\pi$
$281$			1.41750i			0.0845611i	−0.999106	+	0.0422806i	$0.986538\pi$
$282$	1.59846	−	2.76862i	0.0951870	−	0.164869i
$283$	10.2793	+	17.8044i	0.611044	+	1.05836i	0.991065	+	0.133381i	$0.0425834\pi$
$283$	10.2793	+	17.8044i	0.611044	+	1.05836i	−0.380021	+	0.924978i	$0.624083\pi$
$284$	48.1855	−	27.8199i	2.85928	−	1.65081i
$285$	0.0386846			0.00229148
$286$	−1.73905	−	3.78807i	−0.102832	−	0.223993i
$287$	−11.9652			−0.706281
$288$	0.312509	−	0.180427i	0.0184148	−	0.0106318i
$289$	−0.500000	−	0.866025i	−0.0294118	−	0.0509427i
$290$	−2.28130	+	3.95133i	−0.133963	+	0.232030i
$291$			12.2190i			0.716292i
$292$	2.54561	+	1.46971i	0.148971	+	0.0860083i
$293$	−22.9891	−	13.2727i	−1.34304	−	0.775402i	−0.355784	−	0.934568i	$-0.615786\pi$
$293$	−22.9891	−	13.2727i	−1.34304	−	0.775402i	−0.987252	+	0.159166i	$0.949119\pi$
$294$		−	37.1479i		−	2.16651i
$295$	−0.298614	+	0.517215i	−0.0173860	+	0.0301134i
$296$	−14.7187	−	25.4936i	−0.855509	−	1.48179i
$297$	0.407490	−	0.235264i	0.0236450	−	0.0136514i
$298$	27.3402			1.58377
$299$	−30.9764	−	2.89585i	−1.79141	−	0.167471i
$300$	−19.8556			−1.14636
$301$	−26.8844	+	15.5217i	−1.54959	+	0.894656i
$302$	9.33210	+	16.1637i	0.537002	+	0.930115i
$303$	1.58069	−	2.73783i	0.0908082	−	0.157284i
$304$		−	0.574102i		−	0.0329270i
$305$	0.791772	+	0.457130i	0.0453367	+	0.0261752i
$306$	−2.12774	−	1.22845i	−0.121635	−	0.0702260i
$307$			13.5305i			0.772225i	0.922452	+	0.386113i	$0.126182\pi$
$307$			13.5305i			0.772225i	−0.922452	+	0.386113i	$0.873818\pi$
$308$	−4.46622	+	7.73571i	−0.254486	+	0.440783i
$309$	8.85438	+	15.3362i	0.503708	+	0.872448i
$310$	−2.17843	+	1.25772i	−0.123727	+	0.0714336i
$311$	−2.88225			−0.163437			−0.0817187	−	0.996655i	$-0.526041\pi$
$311$	−2.88225			−0.163437			−0.0817187	+	0.996655i	$0.526041\pi$
$312$	−1.67910	+	17.9610i	−0.0950602	+	1.01684i
$313$	−24.4829			−1.38385			−0.691927	−	0.721967i	$-0.743238\pi$
$313$	−24.4829			−1.38385			−0.691927	+	0.721967i	$0.743238\pi$
$314$	30.3143	−	17.5019i	1.71073	−	0.987692i
$315$	0.668630	+	1.15810i	0.0376731	+	0.0652517i
$316$	−30.6069	+	53.0128i	−1.72178	+	2.98220i
$317$			30.7367i			1.72634i	0.504911	+	0.863172i	$0.331525\pi$
$317$			30.7367i			1.72634i	−0.504911	+	0.863172i	$0.668475\pi$
$318$	15.3720	+	8.87502i	0.862019	+	0.497687i
$319$	2.66143	+	1.53658i	0.149012	+	0.0860319i
$320$			2.14748i			0.120048i
$321$	1.50519	−	2.60706i	0.0840114	−	0.145512i
$322$	49.8537	+	86.3492i	2.77824	+	4.81205i
$323$	−0.117827	+	0.0680272i	−0.00655605	+	0.00378514i
$324$	−4.03639			−0.224244
$325$	10.2593	−	14.4679i	0.569086	−	0.802536i
$326$	40.7156			2.25503
$327$	5.66178	−	3.26883i	0.313097	−	0.180767i
$328$	−6.36425	−	11.0232i	−0.351407	−	0.608655i
$329$	3.05988	−	5.29986i	0.168697	−	0.292191i
$330$		−	0.328701i		−	0.0180944i
$331$	6.73745	+	3.88987i	0.370324	+	0.213806i	0.673600	−	0.739096i	$-0.264747\pi$
$331$	6.73745	+	3.88987i	0.370324	+	0.213806i	−0.303276	+	0.952903i	$0.598080\pi$
$332$	45.4624	+	26.2477i	2.49507	+	1.44053i
$333$			5.88371i			0.322426i
$334$	−9.21772	+	15.9656i	−0.504371	+	0.873597i
$335$	1.37471	+	2.38107i	0.0751085	+	0.130092i
$336$	17.1869	−	9.92286i	0.937622	−	0.541336i
$337$	20.1777			1.09915			0.549574	−	0.835445i	$-0.314790\pi$
$337$	20.1777			1.09915			0.549574	+	0.835445i	$0.314790\pi$
$338$	−24.2213	−	20.8201i	−1.31747	−	1.13246i
$339$	−12.5670			−0.682546
$340$	−0.993915	+	0.573837i	−0.0539026	+	0.0311207i
$341$	0.847140	+	1.46729i	0.0458752	+	0.0794582i
$342$	−0.167136	+	0.289489i	−0.00903770	+	0.0156538i
$343$		−	38.1887i		−	2.06200i
$344$	−28.5995	−	16.5119i	−1.54198	−	0.890264i
$345$	−2.12474	−	1.22672i	−0.114392	−	0.0660442i
$346$			63.0512i			3.38965i
$347$	13.3254	−	23.0802i	0.715344	−	1.23901i	−0.247483	−	0.968892i	$-0.579603\pi$
$347$	13.3254	−	23.0802i	0.715344	−	1.23901i	0.962827	−	0.270120i	$-0.0870633\pi$
$348$	−13.1814	−	22.8308i	−0.706597	−	1.22386i
$349$	−21.2517	+	12.2697i	−1.13758	+	0.656780i	−0.945829	−	0.324664i	$-0.894749\pi$
$349$	−21.2517	+	12.2697i	−1.13758	+	0.656780i	−0.191748	+	0.981444i	$0.561416\pi$
$350$	−56.8420			−3.03833
$351$	2.08559	−	2.94114i	0.111321	−	0.156986i
$352$	−0.169792			−0.00904996
$353$	−18.3903	+	10.6177i	−0.978818	+	0.565121i	−0.901913	−	0.431917i	$-0.857837\pi$
$353$	−18.3903	+	10.6177i	−0.978818	+	0.565121i	−0.0769053	+	0.997038i	$0.524504\pi$
$354$	−2.58032	−	4.46924i	−0.137142	−	0.237537i
$355$	−1.95969	+	3.39429i	−0.104010	+	0.180150i
$356$		−	17.7478i		−	0.940634i
$357$	−4.07306	−	2.35158i	−0.215569	−	0.124459i
$358$	−30.3274	−	17.5096i	−1.60285	−	0.925409i
$359$		−	30.7675i		−	1.62385i	−0.583764	−	0.811923i	$-0.698421\pi$
$359$		−	30.7675i		−	1.62385i	0.583764	−	0.811923i	$-0.301579\pi$
$360$	−0.711287	+	1.23198i	−0.0374881	+	0.0649313i
$361$	−9.49074	−	16.4385i	−0.499513	−	0.865182i
$362$	−8.17458	+	4.71959i	−0.429646	+	0.248056i
$363$	10.7786			0.565730
$364$	−6.37104	+	68.1499i	−0.333933	+	3.57203i
$365$	−0.207059			−0.0108380
$366$	−6.84169	+	3.95005i	−0.357621	+	0.206472i
$367$	16.8821	+	29.2407i	0.881240	+	1.52635i	0.849963	+	0.526842i	$0.176624\pi$
$367$	16.8821	+	29.2407i	0.881240	+	1.52635i	0.0312770	+	0.999511i	$0.490043\pi$
$368$	−18.2052	+	31.5323i	−0.949010	+	1.64373i
$369$			2.54407i			0.132439i
$370$	3.55956	+	2.05511i	0.185053	+	0.106840i
$371$	29.4261	+	16.9891i	1.52772	+	0.882032i
$372$		−	14.5342i		−	0.753564i
$373$	3.56477	−	6.17437i	0.184577	−	0.319697i	−0.758857	−	0.651257i	$-0.774242\pi$
$373$	3.56477	−	6.17437i	0.184577	−	0.319697i	0.943434	+	0.331561i	$0.107575\pi$
$374$	0.578023	+	1.00116i	0.0298888	+	0.0517690i
$375$	2.44248	−	1.41017i	0.126129	−	0.0728207i
$376$	6.51017			0.335737
$377$	23.4466	+	2.19192i	1.20756	+	0.112890i
$378$	−11.5552			−0.594337
$379$	2.92977	−	1.69150i	0.150492	−	0.0868866i	−0.422863	−	0.906194i	$-0.638975\pi$
$379$	2.92977	−	1.69150i	0.150492	−	0.0868866i	0.573355	+	0.819307i	$0.305642\pi$
$380$	0.0780731	+	0.135227i	0.00400506	+	0.00693697i
$381$	−7.80205	+	13.5135i	−0.399711	+	0.692320i
$382$		−	18.3086i		−	0.936749i
$383$	10.2415	+	5.91294i	0.523317	+	0.302137i	0.738291	−	0.674483i	$-0.235633\pi$
$383$	10.2415	+	5.91294i	0.523317	+	0.302137i	−0.214974	+	0.976620i	$0.568967\pi$
$384$	−16.6952	−	9.63901i	−0.851976	−	0.491888i
$385$		−	0.629220i		−	0.0320680i
$386$	−4.10945	+	7.11777i	−0.209165	+	0.362285i
$387$	3.30027	+	5.71623i	0.167762	+	0.290572i
$388$	−42.7130	+	24.6604i	−2.16843	+	1.25194i
$389$	−2.26895			−0.115040			−0.0575201	−	0.998344i	$-0.518319\pi$
$389$	−2.26895			−0.115040			−0.0575201	+	0.998344i	$0.518319\pi$
$390$	−1.05087	−	2.28906i	−0.0532131	−	0.115911i
$391$	8.62876			0.436375
$392$	65.5127	−	37.8237i	3.30889	−	1.91039i
$393$	−4.44310	−	7.69567i	−0.224125	−	0.388195i
$394$	16.8829	−	29.2421i	0.850549	−	1.47319i
$395$		−	4.31204i		−	0.216962i
$396$	1.64479	+	0.949619i	0.0826537	+	0.0477201i
$397$	−20.2999	−	11.7202i	−1.01882	−	0.588218i	−0.105060	−	0.994466i	$-0.533503\pi$
$397$	−20.2999	−	11.7202i	−1.01882	−	0.588218i	−0.913763	+	0.406248i	$0.866837\pi$
$398$			19.9826i			1.00164i
$399$	−0.319943	+	0.554158i	−0.0160172	+	0.0277426i
$400$	−10.3786	−	17.9762i	−0.518928	−	0.898809i
$401$	7.57309	−	4.37232i	0.378182	−	0.218343i	−0.298845	−	0.954302i	$-0.596601\pi$
$401$	7.57309	−	4.37232i	0.378182	−	0.218343i	0.677027	+	0.735958i	$0.263268\pi$
$402$	−23.7577			−1.18493
$403$	10.5905	+	7.50979i	0.527548	+	0.374089i
$404$	12.7605			0.634861
$405$	0.246239	−	0.142166i	0.0122357	−	0.00706428i
$406$	−37.7353	−	65.3594i	−1.87277	−	3.24373i
$407$	1.38423	−	2.39755i	0.0686137	−	0.118842i
$408$		−	5.00321i		−	0.247696i
$409$	27.0853	+	15.6377i	1.33928	+	0.773235i	0.986701	−	0.162546i	$-0.0519706\pi$
$409$	27.0853	+	15.6377i	1.33928	+	0.773235i	0.352581	+	0.935781i	$0.385304\pi$
$410$	1.53912	+	0.888613i	0.0760118	+	0.0438855i
$411$		−	6.99873i		−	0.345222i
$412$	−35.7397	+	61.9030i	−1.76077	+	3.04974i
$413$	−4.93941	−	8.55531i	−0.243052	−	0.420979i
$414$	18.3598	−	10.6000i	0.902335	−	0.520963i
$415$	−3.69790			−0.181523
$416$	−1.18243	+	0.542836i	−0.0579733	+	0.0266147i
$417$	−4.24002			−0.207634
$418$	0.136213	−	0.0786425i	0.00666239	−	0.00384653i
$419$	−8.58631	−	14.8719i	−0.419469	−	0.726541i	0.576417	−	0.817155i	$-0.304450\pi$
$419$	−8.58631	−	14.8719i	−0.419469	−	0.726541i	−0.995886	+	0.0906145i	$0.971117\pi$
$420$	−2.69885	+	4.67455i	−0.131690	+	0.228095i
$421$		−	13.2245i		−	0.644522i	−0.946651	−	0.322261i	$-0.895557\pi$
$421$		−	13.2245i		−	0.644522i	0.946651	−	0.322261i	$-0.104443\pi$
$422$	−33.8880	−	19.5652i	−1.64964	−	0.952420i
$423$	−1.12687	−	0.650599i	−0.0547904	−	0.0316332i
$424$			36.1460i			1.75540i
$425$	−2.45958	+	4.26011i	−0.119307	+	0.206646i
$426$	−16.9337	−	29.3300i	−0.820439	−	1.42104i
$427$	−13.0968	+	7.56144i	−0.633798	+	0.365924i
$428$	12.1510			0.587343
$429$	−1.54180	+	0.707820i	−0.0744390	+	0.0341739i
$430$	4.61098			0.222361
$431$	15.4902	−	8.94328i	0.746137	−	0.430783i	−0.0781592	−	0.996941i	$-0.524904\pi$
$431$	15.4902	−	8.94328i	0.746137	−	0.430783i	0.824297	+	0.566158i	$0.191571\pi$
$432$	−2.10982	−	3.65432i	−0.101509	−	0.175819i
$433$	10.7482	−	18.6164i	0.516526	−	0.894649i	−0.483290	−	0.875460i	$-0.660558\pi$
$433$	10.7482	−	18.6164i	0.516526	−	0.894649i	0.999816	−	0.0191886i	$-0.00610830\pi$
$434$		−	41.6081i		−	1.99725i
$435$	1.60825	+	0.928526i	0.0771099	+	0.0445194i
$436$	22.8531	+	13.1943i	1.09447	+	0.631890i
$437$		−	1.17398i		−	0.0561591i
$438$	0.894597	−	1.54949i	0.0427455	−	0.0740374i
$439$	−2.95690	−	5.12150i	−0.141125	−	0.244436i	0.786795	−	0.617214i	$-0.211739\pi$
$439$	−2.95690	−	5.12150i	−0.141125	−	0.244436i	−0.927921	+	0.372778i	$0.878405\pi$
$440$	0.579684	−	0.334681i	0.0276354	−	0.0159553i
$441$	−15.1198			−0.719990
$442$	7.22611	+	5.12410i	0.343711	+	0.243729i
$443$	3.56976			0.169605			0.0848023	−	0.996398i	$-0.472974\pi$
$443$	3.56976			0.169605			0.0848023	+	0.996398i	$0.472974\pi$
$444$	−20.5672	+	11.8745i	−0.976076	+	0.563538i
$445$	0.625098	+	1.08270i	0.0296325	+	0.0513250i
$446$	−34.7625	+	60.2104i	−1.64605	+	2.85104i
$447$		−	11.1279i		−	0.526331i
$448$	−30.7627	−	17.7608i	−1.45340	−	0.839121i
$449$	21.2457	+	12.2662i	1.00265	+	0.578878i	0.909030	−	0.416731i	$-0.136824\pi$
$449$	21.2457	+	12.2662i	1.00265	+	0.578878i	0.0936155	+	0.995608i	$0.470158\pi$
$450$			12.0859i			0.569735i
$451$	0.598528	−	1.03668i	0.0281836	−	0.0488154i
$452$	−25.3626	−	43.9294i	−1.19296	−	2.06626i
$453$	6.57887	−	3.79831i	0.309102	−	0.178460i
$454$	20.8431			0.978216
$455$	−2.01165	−	4.38186i	−0.0943077	−	0.205425i
$456$	−0.680709			−0.0318771
$457$	3.27812	−	1.89262i	0.153344	−	0.0885331i	−0.421365	−	0.906891i	$-0.638449\pi$
$457$	3.27812	−	1.89262i	0.153344	−	0.0885331i	0.574709	+	0.818358i	$0.305115\pi$
$458$	−27.8285	−	48.2004i	−1.30034	−	2.25226i
$459$	−0.500000	+	0.866025i	−0.0233380	+	0.0404226i
$460$		−	9.90301i		−	0.461730i
$461$	−3.54546	−	2.04697i	−0.165128	−	0.0953369i	0.415158	−	0.909749i	$-0.363726\pi$
$461$	−3.54546	−	2.04697i	−0.165128	−	0.0953369i	−0.580287	+	0.814412i	$0.697060\pi$
$462$	4.70865	+	2.71854i	0.219066	+	0.126478i
$463$		−	20.9704i		−	0.974577i	−0.873241	−	0.487289i	$-0.837986\pi$
$463$		−	20.9704i		−	0.974577i	0.873241	−	0.487289i	$-0.162014\pi$
$464$	13.7799	−	23.8674i	0.639714	−	1.10802i
$465$	0.511911	+	0.886656i	0.0237393	+	0.0411177i
$466$	−37.5368	+	21.6719i	−1.73886	+	1.00393i
$467$	11.4563			0.530132			0.265066	−	0.964230i	$-0.414606\pi$
$467$	11.4563			0.530132			0.265066	+	0.964230i	$0.414606\pi$
$468$	14.4902	+	1.35463i	0.669811	+	0.0626177i
$469$	−45.4785			−2.10000
$470$	−0.787206	+	0.454494i	−0.0363111	+	0.0209642i
$471$	−7.12357	−	12.3384i	−0.328237	−	0.568523i
$472$	5.25453	−	9.10111i	0.241859	−	0.418912i
$473$		−	3.10574i		−	0.142802i
$474$	32.2683	+	18.6301i	1.48213	+	0.855710i
$475$	0.579607	+	0.334636i	0.0265942	+	0.0153542i
$476$		−	18.9838i		−	0.870121i
$477$	3.61228	−	6.25665i	0.165395	−	0.286472i
$478$	16.8934	+	29.2603i	0.772687	+	1.33833i
$479$	33.1586	−	19.1441i	1.51505	−	0.874717i	0.515211	−	0.857064i	$-0.327714\pi$
$479$	33.1586	−	19.1441i	1.51505	−	0.874717i	0.999844	−	0.0176538i	$-0.00561967\pi$
$480$	−0.102602			−0.00468314
$481$	1.97460	−	21.1219i	0.0900339	−	0.963077i
$482$	3.22898			0.147076
$483$	35.1455	−	20.2913i	1.59918	−	0.923284i
$484$	21.7533	+	37.6778i	0.988787	+	1.71263i
$485$	1.73713	−	3.00880i	0.0788791	−	0.136623i
$486$			2.45691i			0.111448i
$487$	1.33466	+	0.770565i	0.0604791	+	0.0349176i	0.529935	−	0.848038i	$-0.322216\pi$
$487$	1.33466	+	0.770565i	0.0604791	+	0.0349176i	−0.469456	+	0.882956i	$0.655550\pi$
$488$	−13.9323	−	8.04383i	−0.630687	−	0.364127i
$489$		−	16.5719i		−	0.749407i
$490$	−5.28117	+	9.14725i	−0.238579	+	0.413231i
$491$	10.9048	+	18.8876i	0.492125	+	0.852385i	0.999959	−	0.00907007i	$-0.00288713\pi$
$491$	10.9048	+	18.8876i	0.492125	+	0.852385i	−0.507834	+	0.861455i	$0.669554\pi$
$492$	−8.89307	+	5.13442i	−0.400931	+	0.231477i
$493$	−6.53128			−0.294154
$494$	0.697157	−	0.983144i	0.0313666	−	0.0442337i
$495$	−0.133786			−0.00601325
$496$	13.1585	−	7.59705i	0.590833	−	0.341118i
$497$	−32.4155	−	56.1453i	−1.45403	−	2.51846i
$498$	15.9767	−	27.6725i	0.715934	−	1.24003i
$499$		−	0.502152i		−	0.0224794i	−0.999937	−	0.0112397i	$-0.996422\pi$
$499$		−	0.502152i		−	0.0224794i	0.999937	−	0.0112397i	$-0.00357778\pi$
$500$	9.85880	+	5.69198i	0.440899	+	0.254553i
$501$	6.49824	+	3.75176i	0.290320	+	0.167616i
$502$			34.2127i			1.52699i
$503$	−7.49497	+	12.9817i	−0.334184	+	0.578824i	−0.983328	−	0.181842i	$-0.941794\pi$
$503$	−7.49497	+	12.9817i	−0.334184	+	0.578824i	0.649144	+	0.760666i	$0.275127\pi$
$504$	−11.7655	−	20.3784i	−0.524076	−	0.907726i
$505$	−0.778454	+	0.449441i	−0.0346407	+	0.0199998i
$506$	−9.97524			−0.443454
$507$	−8.47412	+	9.85846i	−0.376349	+	0.437830i
$508$	−62.9842			−2.79447
$509$	−10.4793	+	6.05024i	−0.464488	+	0.268172i	−0.713929	−	0.700218i	$-0.753086\pi$
$509$	−10.4793	+	6.05024i	−0.464488	+	0.268172i	0.249442	+	0.968390i	$0.419753\pi$
$510$	0.349288	+	0.604985i	0.0154668	+	0.0267892i
$511$	1.71249	−	2.96613i	0.0757563	−	0.131214i
$512$		−	40.7009i		−	1.79874i
$513$	0.117827	+	0.0680272i	0.00520217	+	0.00300347i
$514$	49.1404	+	28.3712i	2.16749	+	1.25140i
$515$		−	5.03517i		−	0.221876i
$516$	−13.3212	+	23.0729i	−0.586431	+	1.01573i
$517$	0.306126	+	0.530226i	0.0134634	+	0.0233193i
$518$	−58.8791	+	33.9939i	−2.58700	+	1.49360i
$519$	25.6628			1.12647
$520$	2.96691	−	4.18399i	0.130107	−	0.183480i
$521$	43.3795			1.90049			0.950246	−	0.311501i	$-0.100832\pi$
$521$	43.3795			1.90049			0.950246	+	0.311501i	$0.100832\pi$
$522$	−13.8969	+	8.02337i	−0.608250	+	0.351173i
$523$	−12.4807	−	21.6172i	−0.545743	−	0.945255i	−0.998560	−	0.0536510i	$-0.982914\pi$
$523$	−12.4807	−	21.6172i	−0.545743	−	0.945255i	0.452817	−	0.891604i	$-0.350419\pi$
$524$	17.9341	−	31.0627i	0.783453	−	1.35698i
$525$			23.1356i			1.00972i
$526$	13.9894	+	8.07680i	0.609968	+	0.352165i
$527$	−3.11838	−	1.80040i	−0.135839	−	0.0784266i
$528$			1.98547i			0.0864063i
$529$	−25.7278	+	44.5618i	−1.11860	+	1.93747i
$530$	−2.52345	−	4.37075i	−0.109612	−	0.189853i
$531$	−1.81905	+	1.05023i	−0.0789402	+	0.0455761i
$532$	−2.58283			−0.111980
$533$	0.853799	−	9.13294i	0.0369821	−	0.395591i
$534$	−10.8029			−0.467488
$535$	−0.741271	+	0.427973i	−0.0320479	+	0.0185029i
$536$	−24.1899	−	41.8982i	−1.04485	−	1.80973i
$537$	−7.12667	+	12.3437i	−0.307538	+	0.532672i
$538$			24.3440i			1.04955i
$539$	6.16116	+	3.55715i	0.265380	+	0.153217i
$540$	0.993915	+	0.573837i	0.0427713	+	0.0246940i
$541$			13.1990i			0.567471i	0.958903	+	0.283735i	$0.0915737\pi$
$541$			13.1990i			0.567471i	−0.958903	+	0.283735i	$0.908426\pi$
$542$	7.40317	−	12.8227i	0.317993	−	0.550781i
$543$	1.92095	+	3.32718i	0.0824359	+	0.142783i
$544$	0.312509	−	0.180427i	0.0133987	−	0.00773575i
$545$	−1.85887			−0.0796250
$546$	41.4821	+	3.87799i	1.77527	+	0.165962i
$547$	−28.7221			−1.22807			−0.614033	−	0.789280i	$-0.710454\pi$
$547$	−28.7221			−1.22807			−0.614033	+	0.789280i	$0.710454\pi$
$548$	24.4648	−	14.1248i	1.04509	−	0.603381i
$549$	1.60773	+	2.78468i	0.0686164	+	0.118847i
$550$	2.84338	−	4.92488i	0.121242	−	0.209998i
$551$			0.888610i			0.0378560i
$552$	37.3876	+	21.5858i	1.59132	+	0.918751i
$553$	61.7701	+	35.6630i	2.62673	+	1.51654i
$554$		−	9.14635i		−	0.388591i
$555$	0.836464	−	1.44880i	0.0355059	−	0.0614981i
$556$	−8.55717	−	14.8215i	−0.362905	−	0.628570i
$557$	−9.10251	+	5.25534i	−0.385686	+	0.222676i	−0.680289	−	0.732944i	$-0.738146\pi$
$557$	−9.10251	+	5.25534i	−0.385686	+	0.222676i	0.294603	+	0.955620i	$0.404812\pi$
$558$	−8.84682			−0.374516
$559$	−9.92923	−	21.6283i	−0.419962	−	0.914778i
$560$	−5.64277			−0.238451
$561$	0.407490	−	0.235264i	0.0172042	−	0.00993287i
$562$	1.74134	+	3.01608i	0.0734538	+	0.127226i
$563$	8.30365	−	14.3823i	0.349957	−	0.606143i	−0.636284	−	0.771455i	$-0.719529\pi$
$563$	8.30365	−	14.3823i	0.349957	−	0.606143i	0.986241	+	0.165311i	$0.0528628\pi$
$564$		−	5.25214i		−	0.221155i
$565$	3.09448	+	1.78660i	0.130186	+	0.0751628i
$566$	43.7436	+	25.2554i	1.83868	+	1.06156i
$567$			4.70317i			0.197514i
$568$	34.4835	−	59.7272i	1.44690	−	2.50610i
$569$	−20.7749	−	35.9832i	−0.870929	−	1.50849i	−0.861037	−	0.508543i	$-0.830184\pi$
$569$	−20.7749	−	35.9832i	−0.870929	−	1.50849i	−0.00989281	−	0.999951i	$-0.503149\pi$
$570$	0.0823109	−	0.0475222i	0.00344763	−	0.00199049i
$571$	14.1358			0.591564			0.295782	−	0.955255i	$-0.404420\pi$
$571$	14.1358			0.591564			0.295782	+	0.955255i	$0.404420\pi$
$572$	−5.58592	−	3.96103i	−0.233559	−	0.165619i
$573$	−7.45189			−0.311307
$574$	−25.4588	+	14.6986i	−1.06263	+	0.613510i
$575$	−21.2231	−	36.7595i	−0.885065	−	1.53298i
$576$	−3.77636	+	6.54084i	−0.157348	+	0.272535i
$577$		−	0.447505i		−	0.0186299i	−0.999957	−	0.00931495i	$-0.997035\pi$
$577$		−	0.447505i		−	0.0186299i	0.999957	−	0.00931495i	$-0.00296508\pi$
$578$	−2.12774	−	1.22845i	−0.0885024	−	0.0510969i
$579$	2.89705	+	1.67261i	0.120397	+	0.0695113i
$580$			7.49578i			0.311245i
$581$	30.5837	−	52.9725i	1.26882	−	2.19767i
$582$	15.0105	+	25.9990i	0.622206	+	1.07769i
$583$	−2.94393	+	1.69968i	−0.121925	+	0.0703936i
$584$	3.64349			0.150769
$585$	−0.931683	+	0.427723i	−0.0385204	+	0.0176842i
$586$	−65.2198			−2.69420
$587$	10.6734	−	6.16228i	0.440538	−	0.254345i	−0.263288	−	0.964717i	$-0.584807\pi$
$587$	10.6734	−	6.16228i	0.440538	−	0.254345i	0.703826	+	0.710373i	$0.251474\pi$
$588$	−30.5147	−	52.8529i	−1.25840	−	2.17962i
$589$	−0.244952	+	0.424270i	−0.0100931	+	0.0174817i
$590$			1.46733i			0.0604092i
$591$	−11.9020	−	6.87162i	−0.489583	−	0.282661i
$592$	−21.5010	−	12.4136i	−0.883685	−	0.510196i
$593$			32.0563i			1.31639i	0.752846	+	0.658196i	$0.228680\pi$
$593$			32.0563i			1.31639i	−0.752846	+	0.658196i	$0.771320\pi$
$594$	0.578023	−	1.00116i	0.0237166	−	0.0410783i
$595$	0.668630	+	1.15810i	0.0274112	+	0.0474776i
$596$	38.8988	−	22.4582i	1.59336	−	0.919925i
$597$	8.13323			0.332871
$598$	−69.4672	+	31.8914i	−2.84073	+	1.30414i
$599$	27.0434			1.10496			0.552481	−	0.833525i	$-0.313681\pi$
$599$	27.0434			1.10496			0.552481	+	0.833525i	$0.313681\pi$
$600$	−21.3143	+	12.3058i	−0.870151	+	0.502382i
$601$	−3.97582	−	6.88633i	−0.162177	−	0.280899i	0.773472	−	0.633830i	$-0.218518\pi$
$601$	−3.97582	−	6.88633i	−0.162177	−	0.280899i	−0.935649	+	0.352931i	$0.885185\pi$
$602$	−38.1354	+	66.0524i	−1.55428	+	2.69210i
$603$			9.66976i			0.393783i
$604$	26.5549	+	15.3315i	1.08050	+	0.623828i
$605$	−2.65411	−	1.53235i	−0.107905	−	0.0622989i
$606$		−	7.76721i		−	0.315521i
$607$	20.8360	−	36.0890i	0.845708	−	1.46481i	−0.0392975	−	0.999228i	$-0.512512\pi$
$607$	20.8360	−	36.0890i	0.845708	−	1.46481i	0.885005	−	0.465581i	$-0.154155\pi$
$608$	−0.0245479	−	0.0425182i	−0.000995549	−	0.00172434i
$609$	−26.6023	+	15.3589i	−1.07798	+	0.622372i
$610$	2.24625			0.0909480
$611$	3.82701	+	2.71377i	0.154824	+	0.109787i
$612$	−4.03639			−0.163161
$613$	8.50704	−	4.91154i	0.343596	−	0.198375i	−0.318265	−	0.948002i	$-0.603100\pi$
$613$	8.50704	−	4.91154i	0.343596	−	0.198375i	0.661861	+	0.749626i	$0.269767\pi$
$614$	16.6216	+	28.7894i	0.670792	+	1.16185i
$615$	0.361680	−	0.626447i	0.0145843	−	0.0252608i
$616$			11.0720i			0.446103i
$617$	23.0624	+	13.3151i	0.928455	+	0.536044i	0.886323	−	0.463068i	$-0.153251\pi$
$617$	23.0624	+	13.3151i	0.928455	+	0.536044i	0.0421326	+	0.999112i	$0.486585\pi$
$618$	37.6797	+	21.7544i	1.51570	+	0.875090i
$619$			18.1787i			0.730665i	0.930877	+	0.365333i	$0.119045\pi$
$619$			18.1787i			0.730665i	−0.930877	+	0.365333i	$0.880955\pi$
$620$	−2.06627	+	3.57889i	−0.0829835	+	0.143732i
$621$	−4.31438	−	7.47273i	−0.173130	−	0.299870i
$622$	−6.13269	+	3.54071i	−0.245898	+	0.141969i
$623$	−20.6797			−0.828513
$624$	6.34765	+	13.8267i	0.254109	+	0.553511i
$625$	23.7939			0.951755
$626$	−52.0933	+	30.0761i	−2.08207	+	1.20208i
$627$	−0.0320088	−	0.0554408i	−0.00127831	−	0.00221409i
$628$	28.7535	−	49.8025i	1.14739	−	1.98734i
$629$			5.88371i			0.234599i
$630$	2.84535	+	1.64276i	0.113361	+	0.0654492i
$631$	−1.77632	−	1.02556i	−0.0707141	−	0.0408268i	0.464226	−	0.885717i	$-0.346333\pi$
$631$	−1.77632	−	1.02556i	−0.0707141	−	0.0408268i	−0.534940	+	0.844890i	$0.679666\pi$
$632$			75.8763i			3.01820i
$633$	−7.96336	+	13.7929i	−0.316515	+	0.548220i
$634$	37.7586	+	65.3997i	1.49958	+	2.59736i
$635$	3.84233	−	2.21837i	0.152478	−	0.0880334i
$636$	29.1611			1.15631
$637$	54.2785	+	5.07426i	2.15059	+	0.201050i
$638$	7.55046			0.298925
$639$	−11.9378	+	6.89227i	−0.472251	+	0.272654i
$640$	2.74068	+	4.74699i	0.108335	+	0.187641i
$641$	−16.3951	+	28.3971i	−0.647567	+	1.12162i	0.336136	+	0.941814i	$0.390880\pi$
$641$	−16.3951	+	28.3971i	−0.647567	+	1.12162i	−0.983702	+	0.179805i	$0.942453\pi$
$642$		−	7.39621i		−	0.291905i
$643$	−26.0108	−	15.0173i	−1.02576	−	0.592226i	−0.109996	−	0.993932i	$-0.535084\pi$
$643$	−26.0108	−	15.0173i	−1.02576	−	0.592226i	−0.915769	+	0.401706i	$0.868417\pi$
$644$	141.861	+	81.9034i	5.59010	+	3.22745i
$645$		−	1.87674i		−	0.0738967i
$646$	−0.167136	+	0.289489i	−0.00657590	+	0.0113898i
$647$	1.91234	+	3.31226i	0.0751817	+	0.130219i	0.901165	−	0.433476i	$-0.142713\pi$
$647$	1.91234	+	3.31226i	0.0751817	+	0.130219i	−0.825984	+	0.563694i	$0.809380\pi$
$648$	−4.33291	+	2.50161i	−0.170213	+	0.0982724i
$649$	0.988328			0.0387953
$650$	4.05608	−	43.3872i	0.159092	−	1.70178i
$651$	−16.9352			−0.663741
$652$	57.9289	−	33.4453i	2.26867	−	1.30982i
$653$	−1.82465	−	3.16038i	−0.0714040	−	0.123675i	0.828113	−	0.560561i	$-0.189415\pi$
$653$	−1.82465	−	3.16038i	−0.0714040	−	0.123675i	−0.899517	+	0.436886i	$0.856081\pi$
$654$	8.03121	−	13.9105i	0.314045	−	0.543942i
$655$			2.52663i			0.0987236i
$656$	−9.29684	−	5.36753i	−0.362980	−	0.209567i
$657$	−0.630666	−	0.364115i	−0.0246046	−	0.0142055i
$658$		−	15.0357i		−	0.586151i
$659$	−17.2013	+	29.7935i	−0.670066	+	1.16059i	0.307818	+	0.951445i	$0.400401\pi$
$659$	−17.2013	+	29.7935i	−0.670066	+	1.16059i	−0.977885	+	0.209144i	$0.932932\pi$
$660$	−0.270007	−	0.467666i	−0.0105100	−	0.0182039i
$661$	29.2207	−	16.8706i	1.13656	−	0.656191i	0.190980	−	0.981594i	$-0.438833\pi$
$661$	29.2207	−	16.8706i	1.13656	−	0.656191i	0.945575	+	0.325403i	$0.105500\pi$
$662$	19.1141			0.742890
$663$	2.08559	−	2.94114i	0.0809976	−	0.114224i
$664$	65.0696			2.52519
$665$	0.157565	−	0.0909701i	0.00611010	−	0.00352767i
$666$	7.22787	+	12.5190i	0.280074	+	0.485103i
$667$	28.1784	−	48.8065i	1.09107	−	1.88979i
$668$			30.2871i			1.17184i
$669$	24.5066	+	14.1489i	0.947479	+	0.547027i
$670$	5.85006	+	3.37754i	0.226008	+	0.130486i
$671$		−	1.51297i		−	0.0584076i
$672$	0.848579	−	1.46978i	0.0327346	−	0.0566981i
$673$	25.2759	+	43.7792i	0.974316	+	1.68756i	0.682174	+	0.731189i	$0.261034\pi$
$673$	25.2759	+	43.7792i	0.974316	+	1.68756i	0.292141	+	0.956375i	$0.405632\pi$
$674$	42.9329	−	24.7873i	1.65371	−	0.954772i
$675$	4.91916			0.189338
$676$	−51.5638	−	9.72595i	−1.98322	−	0.374075i
$677$	15.3060			0.588259			0.294130	−	0.955766i	$-0.404970\pi$
$677$	15.3060			0.588259			0.294130	+	0.955766i	$0.404970\pi$
$678$	−26.7393	+	15.4380i	−1.02692	+	0.592892i
$679$	28.7341	+	49.7689i	1.10271	+	1.90995i
$680$	−0.711287	+	1.23198i	−0.0272766	+	0.0472445i
$681$		−	8.48348i		−	0.325088i
$682$	3.60499	+	2.08134i	0.138042	+	0.0796988i
$683$	−33.5452	−	19.3673i	−1.28357	−	0.741070i	−0.306072	−	0.952008i	$-0.599015\pi$
$683$	−33.5452	−	19.3673i	−1.28357	−	0.741070i	−0.977499	+	0.210938i	$0.932348\pi$
$684$			0.549168i			0.0209980i
$685$	−0.994981	+	1.72336i	−0.0380163	+	0.0658461i
$686$	−46.9130	−	81.2558i	−1.79115	−	3.10236i
$687$	−19.6183	+	11.3267i	−0.748486	+	0.432139i
$688$	−27.8519			−1.06184
$689$	−15.0675	+	21.2484i	−0.574025	+	0.809501i
$690$	−6.02786			−0.229477
$691$	22.2082	−	12.8219i	0.844840	−	0.487768i	−0.0140666	−	0.999901i	$-0.504478\pi$
$691$	22.2082	−	12.8219i	0.844840	−	0.487768i	0.858906	+	0.512133i	$0.171144\pi$
$692$	51.7926	+	89.7074i	1.96886	+	3.41016i
$693$	1.10649	−	1.91649i	0.0420320	−	0.0728016i
$694$		−	65.4784i		−	2.48553i
$695$	1.04406	+	0.602786i	0.0396033	+	0.0228650i
$696$	−28.2994	−	16.3387i	−1.07269	−	0.619317i
$697$			2.54407i			0.0963633i
$698$	−30.1454	+	52.2134i	−1.14102	+	1.97631i
$699$	8.82080	+	15.2781i	0.333633	+	0.577870i
$700$	−80.8732	+	46.6921i	−3.05672	+	1.76480i
$701$	1.06049			0.0400540			0.0200270	−	0.999799i	$-0.493625\pi$
$701$	1.06049			0.0400540			0.0200270	+	0.999799i	$0.493625\pi$
$702$	0.824548	−	8.82004i	0.0311205	−	0.332891i
$703$	0.800505			0.0301916
$704$	3.07765	−	1.77688i	0.115993	−	0.0669689i
$705$	0.184986	+	0.320406i	0.00696698	+	0.0120672i
$706$	−26.0866	+	45.1833i	−0.981782	+	1.70050i
$707$		−	14.8685i		−	0.559187i
$708$	−7.34240	−	4.23914i	−0.275944	−	0.159317i
$709$	−27.0130	−	15.5959i	−1.01449	−	0.585718i	−0.101989	−	0.994785i	$-0.532521\pi$
$709$	−27.0130	−	15.5959i	−1.01449	−	0.585718i	−0.912504	+	0.409067i	$0.865854\pi$
$710$			9.62957i			0.361391i
$711$	7.58276	−	13.1337i	0.284376	−	0.492553i
$712$	−10.9995	−	19.0516i	−0.412222	−	0.713990i
$713$	26.9078	−	15.5352i	1.00770	−	0.581799i
$714$	−11.5552			−0.432444
$715$	0.480280	+	0.0448993i	0.0179614	+	0.00167914i
$716$	−57.5320			−2.15007
$717$	11.9094	−	6.87589i	0.444765	−	0.256785i
$718$	−37.7964	−	65.4653i	−1.41055	−	2.44314i
$719$	−5.48495	+	9.50021i	−0.204554	+	0.354298i	−0.949991	−	0.312279i	$-0.898908\pi$
$719$	−5.48495	+	9.50021i	−0.204554	+	0.354298i	0.745437	+	0.666577i	$0.232241\pi$
$720$			1.19978i			0.0447132i
$721$	72.1289	+	41.6436i	2.68622	+	1.55089i
$722$	−40.3877	−	23.3179i	−1.50308	−	0.867801i
$723$		−	1.31425i		−	0.0488773i
$724$	−7.75370	+	13.4298i	−0.288164	+	0.499115i
$725$	16.0642	+	27.8240i	0.596609	+	1.03336i
$726$	22.9341	−	13.2410i	0.851164	−	0.491420i
$727$	−24.7789			−0.919000			−0.459500	−	0.888178i	$-0.651971\pi$
$727$	−24.7789			−0.919000			−0.459500	+	0.888178i	$0.651971\pi$
$728$	35.3978	+	77.1049i	1.31193	+	2.85770i
$729$	1.00000			0.0370370
$730$	−0.440569	+	0.254362i	−0.0163062	+	0.00941438i
$731$	3.30027	+	5.71623i	0.122065	+	0.211422i
$732$	−6.48943	+	11.2400i	−0.239856	+	0.415443i
$733$			27.5830i			1.01880i	0.860529	+	0.509401i	$0.170133\pi$
$733$			27.5830i			1.01880i	−0.860529	+	0.509401i	$0.829867\pi$
$734$	71.8417	+	41.4778i	2.65173	+	1.53097i
$735$	3.72308	+	2.14952i	0.137328	+	0.0792862i
$736$			3.11373i			0.114773i
$737$	2.27495	−	3.94033i	0.0837989	−	0.145144i
$738$	3.12526	+	5.41312i	0.115043	+	0.199260i
$739$	−40.9399	+	23.6366i	−1.50600	+	0.869488i	−0.506021	+	0.862521i	$0.668884\pi$
$739$	−40.9399	+	23.6366i	−1.50600	+	0.869488i	−0.999976	+	0.00696648i	$0.997782\pi$
$740$	6.75259			0.248230
$741$	−0.400155	−	0.283754i	−0.0147001	−	0.0104240i
$742$	83.4815			3.06470
$743$	30.4873	−	17.6019i	1.11847	−	0.645749i	0.177461	−	0.984128i	$-0.443212\pi$
$743$	30.4873	−	17.6019i	1.11847	−	0.645749i	0.941010	+	0.338379i	$0.109878\pi$
$744$	−9.00778	−	15.6019i	−0.330241	−	0.571995i
$745$	−1.58201	+	2.74012i	−0.0579603	+	0.100390i
$746$		−	17.5166i		−	0.641329i
$747$	−11.2631	−	6.50278i	−0.412097	−	0.237924i
$748$	1.64479	+	0.949619i	0.0601394	+	0.0347215i
$749$		−	14.1583i		−	0.517333i
$750$	3.46465	−	6.00094i	0.126511	−	0.219124i
$751$	−2.52194	−	4.36812i	−0.0920267	−	0.159395i	0.816337	−	0.577576i	$-0.196001\pi$
$751$	−2.52194	−	4.36812i	−0.0920267	−	0.159395i	−0.908364	+	0.418181i	$0.862668\pi$
$752$	4.75500	−	2.74530i	0.173397	−	0.100111i
$753$	13.9251			0.507460
$754$	52.5811	−	24.1392i	1.91489	−	0.879099i
$755$	−2.15996			−0.0786091
$756$	−16.4405	+	9.49190i	−0.597934	+	0.345217i
$757$	−8.89366	−	15.4043i	−0.323245	−	0.559877i	0.657910	−	0.753096i	$-0.271441\pi$
$757$	−8.89366	−	15.4043i	−0.323245	−	0.559877i	−0.981156	+	0.193219i	$0.938107\pi$
$758$	4.15586	−	7.19816i	0.150948	−	0.261449i
$759$			4.06008i			0.147372i
$760$	0.167617	+	0.0967737i	0.00608011	+	0.00351035i
$761$	−9.17927	−	5.29965i	−0.332748	−	0.192112i	0.324312	−	0.945950i	$-0.394867\pi$
$761$	−9.17927	−	5.29965i	−0.332748	−	0.192112i	−0.657061	+	0.753838i	$0.728200\pi$
$762$			38.3378i			1.38883i
$763$	15.3739	−	26.6283i	0.556571	−	0.964009i
$764$	−15.0394	−	26.0489i	−0.544105	−	0.942417i
$765$	0.246239	−	0.142166i	0.00890278	−	0.00514002i
$766$	29.0551			1.04980
$767$	6.88267	−	3.15974i	0.248519	−	0.114092i
$768$	−32.2588			−1.16404
$769$	7.48640	−	4.32227i	0.269966	−	0.155865i	−0.358906	−	0.933374i	$-0.616850\pi$
$769$	7.48640	−	4.32227i	0.269966	−	0.155865i	0.628872	+	0.777509i	$0.283517\pi$
$770$	−0.772967	−	1.33882i	−0.0278558	−	0.0482477i
$771$	11.5475	−	20.0009i	0.415874	−	0.720315i
$772$			13.5026i			0.485969i
$773$	4.24967	+	2.45355i	0.152850	+	0.0882480i	0.574474	−	0.818523i	$-0.305207\pi$
$773$	4.24967	+	2.45355i	0.152850	+	0.0882480i	−0.421624	+	0.906771i	$0.638540\pi$
$774$	14.0442	+	8.10845i	0.504810	+	0.291452i
$775$			17.7129i			0.636266i
$776$	−30.5672	+	52.9440i	−1.09730	+	1.90058i
$777$	13.8360	+	23.9647i	0.496365	+	0.859730i
$778$	−4.82774	+	2.78729i	−0.173083	+	0.0999294i
$779$	0.346131			0.0124014
$780$	−3.37547	−	2.39358i	−0.120861	−	0.0857039i
$781$	6.48603			0.232088
$782$	18.3598	−	10.6000i	0.656545	−	0.379056i
$783$	3.26564	+	5.65626i	0.116704	+	0.202138i
$784$	31.9001	−	55.2526i	1.13929	−	1.97331i
$785$			4.05092i			0.144583i
$786$	−18.9075	−	10.9163i	−0.674409	−	0.389370i
$787$	34.8968	+	20.1477i	1.24394	+	0.718186i	0.969893	−	0.243531i	$-0.0783058\pi$
$787$	34.8968	+	20.1477i	1.24394	+	0.718186i	0.274042	+	0.961718i	$0.411639\pi$
$788$		−	55.4730i		−	1.97615i
$789$	3.28739	−	5.69392i	0.117034	−	0.202709i
$790$	−5.29714	−	9.17491i	−0.188464	−	0.326429i
$791$	−51.1862	+	29.5523i	−1.81997	+	1.05076i
$792$	2.35416			0.0836513
$793$	−4.83705	−	10.5363i	−0.171769	−	0.374154i
$794$	−57.5906			−2.04382
$795$	−1.77896	+	1.02709i	−0.0630934	+	0.0364270i
$796$	16.4144	+	28.4306i	0.581794	+	1.00770i
$797$	3.25324	−	5.63477i	0.115236	−	0.199594i	−0.802638	−	0.596466i	$-0.796571\pi$
$797$	3.25324	−	5.63477i	0.115236	−	0.199594i	0.917874	+	0.396872i	$0.129904\pi$
$798$			1.57214i			0.0556532i
$799$	−1.12687	−	0.650599i	−0.0398658	−	0.0230166i
$800$	−1.53728	−	0.887549i	−0.0543511	−	0.0313796i
$801$			4.39696i			0.155359i
$802$	10.7424	−	18.6064i	0.379327	−	0.657014i
$803$	0.171327	+	0.296747i	0.00604599	+	0.0104720i
$804$	−33.8018	+	19.5155i	−1.19210	+	0.688257i
$805$	−11.5389			−0.406693
$806$	31.7592	+	2.96903i	1.11867	+	0.104580i
$807$	9.90841			0.348793
$808$	13.6980	−	7.90853i	0.481893	−	0.278221i
$809$	11.4865	+	19.8952i	0.403844	+	0.699479i	0.994186	−	0.107674i	$-0.0343404\pi$
$809$	11.4865	+	19.8952i	0.403844	+	0.699479i	−0.590342	+	0.807153i	$0.701007\pi$
$810$	0.349288	−	0.604985i	0.0122727	−	0.0212570i
$811$			37.2329i			1.30742i	0.756743	+	0.653712i	$0.226789\pi$
$811$			37.2329i			1.30742i	−0.756743	+	0.653712i	$0.773211\pi$
$812$	−107.377	−	61.9943i	−3.76820	−	2.17557i
$813$	−5.21903	−	3.01321i	−0.183039	−	0.105678i
$814$		−	6.80184i		−	0.238404i
$815$	−2.35596	+	4.08064i	−0.0825256	+	0.142939i
$816$	−2.10982	−	3.65432i	−0.0738586	−	0.127927i
$817$	0.777718	−	0.449016i	0.0272089	−	0.0157091i
$818$	76.8408			2.68667
$819$	1.57840	−	16.8839i	0.0551538	−	0.589971i
$820$	2.91976			0.101962
$821$	−13.8362	+	7.98832i	−0.482886	+	0.278794i	−0.721618	−	0.692291i	$-0.756601\pi$
$821$	−13.8362	+	7.98832i	−0.482886	+	0.278794i	0.238733	+	0.971085i	$0.423268\pi$
$822$	−8.59761	−	14.8915i	−0.299876	−	0.519400i
$823$	25.0448	−	43.3788i	0.873006	−	1.51209i	0.0141340	−	0.999900i	$-0.495501\pi$
$823$	25.0448	−	43.3788i	0.873006	−	1.51209i	0.858872	−	0.512190i	$-0.171166\pi$
$824$			88.6007i			3.08655i
$825$	−2.00451	−	1.15730i	−0.0697880	−	0.0402921i
$826$	−21.0196	−	12.1357i	−0.731365	−	0.422254i
$827$			10.4238i			0.362471i	0.983440	+	0.181235i	$0.0580096\pi$
$827$			10.4238i			0.362471i	−0.983440	+	0.181235i	$0.941990\pi$
$828$	17.4145	−	30.1628i	0.605196	−	1.04823i
$829$	−28.7361	−	49.7723i	−0.998045	−	1.72866i	−0.553151	−	0.833081i	$-0.686575\pi$
$829$	−28.7361	−	49.7723i	−0.998045	−	1.72866i	−0.444893	−	0.895584i	$-0.646758\pi$
$830$	−7.86817	+	4.54269i	−0.273108	+	0.157679i
$831$	−3.72271			−0.129139
$832$	15.7519	−	22.2136i	0.546098	−	0.770118i
$833$	−15.1198			−0.523870
$834$	−9.02167	+	5.20866i	−0.312395	+	0.180361i
$835$	−1.06675	−	1.84766i	−0.0369162	−	0.0639408i
$836$	0.129200	−	0.223781i	0.00446847	−	0.00773961i
$837$			3.60080i			0.124462i
$838$	−36.5389	−	21.0958i	−1.26222	−	0.728741i
$839$	35.7196	+	20.6227i	1.23318	+	0.711975i	0.967691	−	0.252140i	$-0.0811342\pi$
$839$	35.7196	+	20.6227i	1.23318	+	0.711975i	0.265486	+	0.964115i	$0.414468\pi$
$840$			6.69060i			0.230848i
$841$	−6.82882	+	11.8279i	−0.235476	+	0.407857i
$842$	−16.2457	−	28.1383i	−0.559862	−	0.969710i
$843$	1.22759	−	0.708751i	0.0422806	−	0.0244107i
$844$	−64.2864			−2.21283
$845$	3.48819	−	1.22280i	0.119998	−	0.0420658i
$846$	−3.19692			−0.109912
$847$	43.9019	−	25.3468i	1.50849	−	0.870926i
$848$	15.2425	+	26.4008i	0.523431	+	0.906609i
$849$	10.2793	−	17.8044i	0.352786	−	0.611044i
$850$			12.0859i			0.414543i
$851$	−43.9674	−	25.3846i	−1.50718	−	0.870173i
$852$	−48.1855	−	27.8199i	−1.65081	−	0.953094i
$853$		−	32.0321i		−	1.09676i	−0.836229	−	0.548380i	$-0.815245\pi$
$853$		−	32.0321i		−	1.09676i	0.836229	−	0.548380i	$-0.184755\pi$
$854$	−18.5777	+	32.1776i	−0.635717	+	1.10109i
$855$	−0.0193423	−	0.0335019i	−0.000661493	−	0.00114574i
$856$	13.0437	−	7.53077i	0.445824	−	0.257396i
$857$	15.8691			0.542078			0.271039	−	0.962568i	$-0.412633\pi$
$857$	15.8691			0.542078			0.271039	+	0.962568i	$0.412633\pi$
$858$	−2.41104	+	3.40009i	−0.0823115	+	0.116077i
$859$	−28.0067			−0.955578			−0.477789	−	0.878475i	$-0.658562\pi$
$859$	−28.0067			−0.955578			−0.477789	+	0.878475i	$0.658562\pi$
$860$	6.56037	−	3.78763i	0.223707	−	0.129157i
$861$	5.98258	+	10.3621i	0.203886	+	0.353141i
$862$	21.9728	−	38.0580i	0.748396	−	1.29626i
$863$		−	41.9771i		−	1.42892i	−0.699677	−	0.714459i	$-0.746673\pi$
$863$		−	41.9771i		−	1.42892i	0.699677	−	0.714459i	$-0.253327\pi$
$864$	−0.312509	−	0.180427i	−0.0106318	−	0.00613826i
$865$	−6.31919	−	3.64838i	−0.214859	−	0.124049i
$866$		−	52.8147i		−	1.79472i
$867$	−0.500000	+	0.866025i	−0.0169809	+	0.0294118i
$868$	−34.1784	−	59.1988i	−1.16009	−	2.00934i
$869$	−6.17980	+	3.56791i	−0.209635	+	0.121033i
$870$	4.56260			0.154687
$871$	3.24521	−	34.7135i	0.109960	−	1.17622i
$872$	32.7093			1.10768
$873$	10.5820	−	6.10952i	0.358146	−	0.206776i
$874$	−1.44218	−	2.49793i	−0.0487825	−	0.0844938i
$875$	6.63225	−	11.4874i	0.224211	−	0.388345i
$876$		−	2.93942i		−	0.0993138i
$877$	7.03065	+	4.05915i	0.237408	+	0.137068i	0.613985	−	0.789318i	$-0.289566\pi$
$877$	7.03065	+	4.05915i	0.237408	+	0.137068i	−0.376577	+	0.926385i	$0.622899\pi$
$878$	−12.5830	−	7.26483i	−0.424657	−	0.245176i
$879$			26.5455i			0.895357i
$880$	0.282266	−	0.488899i	0.00951518	−	0.0164808i
$881$	−23.4905	−	40.6868i	−0.791416	−	1.37077i	−0.925090	−	0.379747i	$-0.876011\pi$
$881$	−23.4905	−	40.6868i	−0.791416	−	1.37077i	0.133674	−	0.991025i	$-0.457322\pi$
$882$	−32.1710	+	18.5739i	−1.08325	+	0.625417i
$883$	−8.72799			−0.293720			−0.146860	−	0.989157i	$-0.546917\pi$
$883$	−8.72799			−0.293720			−0.146860	+	0.989157i	$0.546917\pi$
$884$	14.4902	+	1.35463i	0.487359	+	0.0455611i
$885$	0.597228			0.0200756
$886$	7.59554	−	4.38528i	0.255177	−	0.147327i
$887$	3.71857	+	6.44074i	0.124857	+	0.216259i	0.921677	−	0.387958i	$-0.126819\pi$
$887$	3.71857	+	6.44074i	0.124857	+	0.216259i	−0.796820	+	0.604217i	$0.793486\pi$
$888$	−14.7187	+	25.4936i	−0.493928	+	0.855509i
$889$			73.3887i			2.46138i
$890$	2.66010	+	1.53581i	0.0891667	+	0.0514804i
$891$	−0.407490	−	0.235264i	−0.0136514	−	0.00788166i
$892$			114.221i			3.82439i
$893$	−0.0885169	+	0.153316i	−0.00296211	+	0.00513052i
$894$	−13.6701	−	23.6773i	−0.457196	−	0.791887i
$895$	3.50972	−	2.02634i	0.117317	−	0.0677331i
$896$	−90.6677			−3.02900
$897$	12.9803	+	28.2743i	0.433400	+	0.944050i
$898$	60.2738			2.01136
$899$	−20.3670	+	11.7589i	−0.679279	+	0.392182i
$900$	9.92781	+	17.1955i	0.330927	+	0.573182i
$901$	3.61228	−	6.25665i	0.120342	−	0.208439i
$902$		−	2.94106i		−	0.0979264i
$903$	26.8844	+	15.5217i	0.894656	+	0.516530i
$904$	−54.4517	−	31.4377i	−1.81104	−	1.04560i
$905$		−	1.09238i		−	0.0363118i
$906$	9.33210	−	16.1637i	0.310038	−	0.537002i
$907$	−4.44315	−	7.69575i	−0.147532	−	0.255533i	0.782783	−	0.622295i	$-0.213800\pi$
$907$	−4.44315	−	7.69575i	−0.147532	−	0.255533i	−0.930315	+	0.366762i	$0.880466\pi$
$908$	29.6550	−	17.1213i	0.984135	−	0.568191i
$909$	−3.16138			−0.104856
$910$	−9.66319	−	6.85226i	−0.320332	−	0.227150i
$911$	−29.9919			−0.993677			−0.496839	−	0.867843i	$-0.665506\pi$
$911$	−29.9919			−0.993677			−0.496839	+	0.867843i	$0.665506\pi$
$912$	−0.497187	+	0.287051i	−0.0164635	+	0.00950520i
$913$	3.05975	+	5.29964i	0.101263	+	0.175392i
$914$	4.64999	−	8.05403i	0.153808	−	0.266404i
$915$		−	0.914260i		−	0.0302245i
$916$	−79.1872	−	45.7188i	−2.61642	−	1.51059i
$917$	−36.1940	−	20.8966i	−1.19523	−	0.690067i
$918$			2.45691i			0.0810900i
$919$	−16.6888	+	28.9059i	−0.550514	+	0.953518i	0.447724	+	0.894172i	$0.352235\pi$
$919$	−16.6888	+	28.9059i	−0.550514	+	0.953518i	−0.998237	+	0.0593457i	$0.981099\pi$
$920$	−6.13752	−	10.6305i	−0.202348	−	0.350477i
$921$	11.7177	−	6.76524i	0.386113	−	0.222922i
$922$	−10.0584			−0.331257
$923$	45.1684	−	20.7362i	1.48674	−	0.682540i
$924$	8.93243			0.293855
$925$	25.0653	−	14.4715i	0.824142	−	0.475818i
$926$	−25.7612	−	44.6196i	−0.846564	−	1.46629i
$927$	8.85438	−	15.3362i	0.290816	−	0.503708i
$928$		−	2.35684i		−	0.0773671i
$929$	−42.7623	−	24.6888i	−1.40298	−	0.810013i	−0.408286	−	0.912854i	$-0.633874\pi$
$929$	−42.7623	−	24.6888i	−1.40298	−	0.810013i	−0.994698	+	0.102841i	$0.967207\pi$
$930$	2.17843	+	1.25772i	0.0714336	+	0.0412422i
$931$			2.05711i			0.0674192i
$932$	−35.6042	+	61.6682i	−1.16625	+	2.02001i
$933$	1.44112	+	2.49610i	0.0471803	+	0.0817187i
$934$	24.3760	−	14.0735i	0.797606	−	0.460498i
$935$	−0.133786			−0.00437528
$936$	16.3943	−	7.52637i	0.535863	−	0.246007i
$937$	−35.3443			−1.15465			−0.577325	−	0.816515i	$-0.695903\pi$
$937$	−35.3443			−1.15465			−0.577325	+	0.816515i	$0.695903\pi$
$938$	−96.7666	+	55.8682i	−3.15954	+	1.82416i
$939$	12.2414	+	21.2028i	0.399484	+	0.691927i
$940$	−0.746676	+	1.29328i	−0.0243539	+	0.0421822i
$941$			35.7349i			1.16493i	0.812857	+	0.582463i	$0.197911\pi$
$941$			35.7349i			1.16493i	−0.812857	+	0.582463i	$0.802089\pi$
$942$	−30.3143	−	17.5019i	−0.987692	−	0.570244i
$943$	−19.0111	−	10.9761i	−0.619087	−	0.357430i
$944$		−	8.86321i		−	0.288473i
$945$	0.668630	−	1.15810i	0.0217506	−	0.0376731i
$946$	−3.81526	−	6.60822i	−0.124045	−	0.214852i
$947$	18.0861	−	10.4420i	0.587719	−	0.339320i	−0.176476	−	0.984305i	$-0.556470\pi$
$947$	18.0861	−	10.4420i	0.587719	−	0.339320i	0.764195	+	0.644985i	$0.223137\pi$
$948$	61.2139			1.98813
$949$	2.14183	+	1.51879i	0.0695267	+	0.0493020i
$950$	1.64434			0.0533494
$951$	26.6187	−	15.3683i	0.863172	−	0.498352i
$952$	−11.7655	−	20.3784i	−0.381321	−	0.660468i
$953$	−10.8659	+	18.8204i	−0.351983	+	0.609652i	−0.986597	−	0.163177i	$-0.947826\pi$
$953$	−10.8659	+	18.8204i	−0.351983	+	0.609652i	0.634614	+	0.772829i	$0.281159\pi$
$954$		−	17.7500i		−	0.574679i
$955$	1.83494	+	1.05941i	0.0593774	+	0.0342816i
$956$	48.0709	+	27.7538i	1.55473	+	0.897621i
$957$		−	3.07316i		−	0.0993411i
$958$	47.0353	−	81.4676i	1.51964	−	2.63210i
$959$	−16.4581	−	28.5062i	−0.531459	−	0.920515i
$960$	1.85977	−	1.07374i	0.0600238	−	0.0346548i
$961$	18.0342			0.581750
$962$	−21.7459	−	47.3678i	−0.701115	−	1.52720i
$963$	−3.01037			−0.0970080
$964$	4.59409	−	2.65240i	0.147966	−	0.0854281i
$965$	−0.475577	−	0.823723i	−0.0153094	−	0.0265166i
$966$	49.8537	−	86.3492i	1.60402	−	2.77824i
$967$			31.1613i			1.00208i	0.865424	+	0.501040i	$0.167049\pi$
$967$			31.1613i			1.00208i	−0.865424	+	0.501040i	$0.832951\pi$
$968$	46.7027	+	26.9638i	1.50108	+	0.866650i
$969$	0.117827	+	0.0680272i	0.00378514	+	0.00218535i
$970$		−	8.53594i		−	0.274072i
$971$	−18.4729	+	31.9959i	−0.592822	+	1.02680i	0.401028	+	0.916066i	$0.368653\pi$
$971$	−18.4729	+	31.9959i	−0.592822	+	1.02680i	−0.993850	+	0.110732i	$0.964680\pi$
$972$	2.01819	+	3.49561i	0.0647336	+	0.112122i
$973$	−17.2699	+	9.97075i	−0.553646	+	0.319648i
$974$	3.78641			0.121324
$975$	−17.6593	−	1.65089i	−0.565549	−	0.0528707i
$976$	−13.5681			−0.434305
$977$	−40.9976	+	23.6700i	−1.31163	+	0.757269i	−0.982366	−	0.186969i	$-0.940133\pi$
$977$	−40.9976	+	23.6700i	−1.31163	+	0.757269i	−0.329263	+	0.944238i	$0.606800\pi$
$978$	−20.3578	−	35.2607i	−0.650970	−	1.12751i
$979$	1.03445	−	1.79172i	0.0330611	−	0.0572636i
$980$			17.3526i			0.554308i
$981$	−5.66178	−	3.26883i	−0.180767	−	0.104366i
$982$	46.4050	+	26.7919i	1.48084	+	0.854965i
$983$			35.2475i			1.12422i	0.827063	+	0.562110i	$0.190010\pi$
$983$			35.2475i			1.12422i	−0.827063	+	0.562110i	$0.809990\pi$
$984$	−6.36425	+	11.0232i	−0.202885	+	0.351407i
$985$	1.95382	+	3.38412i	0.0622539	+	0.107827i
$986$	−13.8969	+	8.02337i	−0.442567	+	0.255516i
$987$	−6.11976			−0.194794
$988$	0.184303	−	1.97146i	0.00586346	−	0.0627204i
$989$	−56.9544			−1.81105
$990$	−0.284663	+	0.164350i	−0.00904719	+	0.00522340i
$991$	17.2571	+	29.8902i	0.548191	+	0.949494i	0.998399	+	0.0565705i	$0.0180166\pi$
$991$	17.2571	+	29.8902i	0.548191	+	0.949494i	−0.450208	+	0.892924i	$0.648650\pi$
$992$	0.649682	−	1.12528i	0.0206274	−	0.0357277i
$993$		−	7.77974i		−	0.246882i
$994$	−137.944	−	79.6419i	−4.37531	−	2.52609i
$995$	−2.00272	−	1.15627i	−0.0634903	−	0.0366562i
$996$		−	52.4955i		−	1.66338i
$997$	−3.28081	+	5.68253i	−0.103904	+	0.179968i	−0.913290	−	0.407310i	$-0.866467\pi$
$997$	−3.28081	+	5.68253i	−0.103904	+	0.179968i	0.809386	+	0.587277i	$0.199800\pi$
$998$	−0.616870	−	1.06845i	−0.0195267	−	0.0338212i
$999$	5.09545	−	2.94186i	0.161213	−	0.0930762i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	663.2.z.d.205.8	✓	16
13.2	odd	12		8619.2.a.bn.1.16		16
13.4	even	6	inner	663.2.z.d.511.8	yes	16
13.11	odd	12		8619.2.a.bn.1.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
663.2.z.d.205.8	✓	16	1.1	even	1	trivial
663.2.z.d.511.8	yes	16	13.4	even	6	inner
8619.2.a.bn.1.1		16	13.11	odd	12
8619.2.a.bn.1.16		16	13.2	odd	12

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:	\( N \)	\(=\)	\( 663 = 3 \cdot 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	663.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.12774 - 1.22845i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(2.01819 - 3.49561i) q^{4} +0.284332i q^{5} +(-2.12774 - 1.22845i) q^{6} +(-4.07306 - 2.35158i) q^{7} -5.00321i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(2.12774 - 1.22845i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(2.01819 - 3.49561i) q^{4} +0.284332i q^{5} +(-2.12774 - 1.22845i) q^{6} +(-4.07306 - 2.35158i) q^{7} -5.00321i q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.349288 + 0.604985i) q^{10} +(0.407490 - 0.235264i) q^{11} -4.03639 q^{12} +(2.08559 - 2.94114i) q^{13} -11.5552 q^{14} +(0.246239 - 0.142166i) q^{15} +(-2.10982 - 3.65432i) q^{16} +(-0.500000 + 0.866025i) q^{17} +2.45691i q^{18} +(0.117827 + 0.0680272i) q^{19} +(0.993915 + 0.573837i) q^{20} +4.70317i q^{21} +(0.578023 - 1.00116i) q^{22} +(-4.31438 - 7.47273i) q^{23} +(-4.33291 + 2.50161i) q^{24} +4.91916 q^{25} +(0.824548 - 8.82004i) q^{26} +1.00000 q^{27} +(-16.4405 + 9.49190i) q^{28} +(3.26564 + 5.65626i) q^{29} +(0.349288 - 0.604985i) q^{30} +3.60080i q^{31} +(-0.312509 - 0.180427i) q^{32} +(-0.407490 - 0.235264i) q^{33} +2.45691i q^{34} +(0.668630 - 1.15810i) q^{35} +(2.01819 + 3.49561i) q^{36} +(5.09545 - 2.94186i) q^{37} +0.334273 q^{38} +(-3.58990 - 0.335604i) q^{39} +1.42257 q^{40} +(2.20323 - 1.27203i) q^{41} +(5.77762 + 10.0071i) q^{42} +(3.30027 - 5.71623i) q^{43} -1.89924i q^{44} +(-0.246239 - 0.142166i) q^{45} +(-18.3598 - 10.6000i) q^{46} +1.30120i q^{47} +(-2.10982 + 3.65432i) q^{48} +(7.55989 + 13.0941i) q^{49} +(10.4667 - 6.04295i) q^{50} +1.00000 q^{51} +(-6.07197 - 13.2262i) q^{52} -7.22455 q^{53} +(2.12774 - 1.22845i) q^{54} +(0.0668932 + 0.115862i) q^{55} +(-11.7655 + 20.3784i) q^{56} -0.136054i q^{57} +(13.8969 + 8.02337i) q^{58} +(1.81905 + 1.05023i) q^{59} -1.14767i q^{60} +(1.60773 - 2.78468i) q^{61} +(4.42341 + 7.66157i) q^{62} +(4.07306 - 2.35158i) q^{63} +7.55271 q^{64} +(0.836260 + 0.593000i) q^{65} -1.15605 q^{66} +(8.37426 - 4.83488i) q^{67} +(2.01819 + 3.49561i) q^{68} +(-4.31438 + 7.47273i) q^{69} -3.28552i q^{70} +(11.9378 + 6.89227i) q^{71} +(4.33291 + 2.50161i) q^{72} +0.728230i q^{73} +(7.22787 - 12.5190i) q^{74} +(-2.45958 - 4.26011i) q^{75} +(0.475594 - 0.274584i) q^{76} -2.21298 q^{77} +(-8.05065 + 3.69594i) q^{78} -15.1655 q^{79} +(1.03904 - 0.599890i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.12526 - 5.41312i) q^{82} +13.0056i q^{83} +(16.4405 + 9.49190i) q^{84} +(-0.246239 - 0.142166i) q^{85} -16.2169i q^{86} +(3.26564 - 5.65626i) q^{87} +(-1.17708 - 2.03876i) q^{88} +(3.80788 - 2.19848i) q^{89} -0.698577 q^{90} +(-15.4111 + 7.07501i) q^{91} -34.8290 q^{92} +(3.11838 - 1.80040i) q^{93} +(1.59846 + 2.76862i) q^{94} +(-0.0193423 + 0.0335019i) q^{95} +0.360854i q^{96} +(-10.5820 - 6.10952i) q^{97} +(32.1710 + 18.5739i) q^{98} +0.470529i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} + 4 q^{4} - 8 q^{9}+O(q^{10}) \) 16 * q - 8 * q^3 + 4 * q^4 - 8 * q^9	\( 16 q - 8 q^{3} + 4 q^{4} - 8 q^{9} + q^{10} + 3 q^{11} - 8 q^{12} - 2 q^{13} - 26 q^{14} - 3 q^{15} - 8 q^{17} + 27 q^{20} + q^{22} - 21 q^{23} + 14 q^{25} + 2 q^{26} + 16 q^{27} - 33 q^{28} + 29 q^{29} + q^{30} - 15 q^{32} - 3 q^{33} + 15 q^{35} + 4 q^{36} - 18 q^{37} + 62 q^{38} + q^{39} + 4 q^{40} + 12 q^{41} + 13 q^{42} - 3 q^{43} + 3 q^{45} - 9 q^{46} + 2 q^{49} - 36 q^{50} + 16 q^{51} - 8 q^{52} - 26 q^{53} + 9 q^{55} - 37 q^{56} + 30 q^{58} - 3 q^{59} + 29 q^{61} - 20 q^{62} + 36 q^{64} - 16 q^{65} - 2 q^{66} + 33 q^{67} + 4 q^{68} - 21 q^{69} + 27 q^{71} + 17 q^{74} - 7 q^{75} - 48 q^{76} - 8 q^{77} - q^{78} - 14 q^{79} - 39 q^{80} - 8 q^{81} - 3 q^{82} + 33 q^{84} + 3 q^{85} + 29 q^{87} - 5 q^{88} - 3 q^{89} - 2 q^{90} - 70 q^{91} - 64 q^{92} - 6 q^{93} - 25 q^{94} - 27 q^{95} + 6 q^{97} + 102 q^{98}+O(q^{100}) \) 16 * q - 8 * q^3 + 4 * q^4 - 8 * q^9 + q^10 + 3 * q^11 - 8 * q^12 - 2 * q^13 - 26 * q^14 - 3 * q^15 - 8 * q^17 + 27 * q^20 + q^22 - 21 * q^23 + 14 * q^25 + 2 * q^26 + 16 * q^27 - 33 * q^28 + 29 * q^29 + q^30 - 15 * q^32 - 3 * q^33 + 15 * q^35 + 4 * q^36 - 18 * q^37 + 62 * q^38 + q^39 + 4 * q^40 + 12 * q^41 + 13 * q^42 - 3 * q^43 + 3 * q^45 - 9 * q^46 + 2 * q^49 - 36 * q^50 + 16 * q^51 - 8 * q^52 - 26 * q^53 + 9 * q^55 - 37 * q^56 + 30 * q^58 - 3 * q^59 + 29 * q^61 - 20 * q^62 + 36 * q^64 - 16 * q^65 - 2 * q^66 + 33 * q^67 + 4 * q^68 - 21 * q^69 + 27 * q^71 + 17 * q^74 - 7 * q^75 - 48 * q^76 - 8 * q^77 - q^78 - 14 * q^79 - 39 * q^80 - 8 * q^81 - 3 * q^82 + 33 * q^84 + 3 * q^85 + 29 * q^87 - 5 * q^88 - 3 * q^89 - 2 * q^90 - 70 * q^91 - 64 * q^92 - 6 * q^93 - 25 * q^94 - 27 * q^95 + 6 * q^97 + 102 * q^98

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