LMFDB - Embedded newform 1001.2.i.d.716.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1001,2,Mod(144,1001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1001, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1001.144");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1001 = 7 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1001.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.99302524233$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$25$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			716.17
Character	$\chi$	$=$	1001.716
Dual form			1001.2.i.d.144.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.434546 - 0.752655i) q^{2} +(1.23247 + 2.13471i) q^{3} +(0.622340 + 1.07792i) q^{4} +(2.15910 - 3.73967i) q^{5} +2.14227 q^{6} +(-1.52058 - 2.16514i) q^{7} +2.81992 q^{8} +(-1.53799 + 2.66387i) q^{9} +O(q^{10})$	\(q+(0.434546 - 0.752655i) q^{2} +(1.23247 + 2.13471i) q^{3} +(0.622340 + 1.07792i) q^{4} +(2.15910 - 3.73967i) q^{5} +2.14227 q^{6} +(-1.52058 - 2.16514i) q^{7} +2.81992 q^{8} +(-1.53799 + 2.66387i) q^{9} +(-1.87646 - 3.25012i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(-1.53404 + 2.65703i) q^{12} -1.00000 q^{13} +(-2.29037 + 0.203620i) q^{14} +10.6442 q^{15} +(-0.0192947 + 0.0334194i) q^{16} +(1.53679 + 2.66181i) q^{17} +(1.33665 + 2.31515i) q^{18} +(3.03313 - 5.25354i) q^{19} +5.37478 q^{20} +(2.74787 - 5.91448i) q^{21} -0.869091 q^{22} +(-2.33356 + 4.04184i) q^{23} +(3.47548 + 6.01972i) q^{24} +(-6.82344 - 11.8185i) q^{25} +(-0.434546 + 0.752655i) q^{26} -0.187277 q^{27} +(1.38754 - 2.98653i) q^{28} +6.73380 q^{29} +(4.62537 - 8.01138i) q^{30} +(-1.30801 - 2.26554i) q^{31} +(2.83669 + 4.91330i) q^{32} +(1.23247 - 2.13471i) q^{33} +2.67123 q^{34} +(-11.3800 + 1.01171i) q^{35} -3.82861 q^{36} +(-4.45051 + 7.70850i) q^{37} +(-2.63607 - 4.56581i) q^{38} +(-1.23247 - 2.13471i) q^{39} +(6.08850 - 10.5456i) q^{40} +1.63987 q^{41} +(-3.25749 - 4.63831i) q^{42} -3.16556 q^{43} +(0.622340 - 1.07792i) q^{44} +(6.64134 + 11.5031i) q^{45} +(2.02807 + 3.51273i) q^{46} +(-3.91671 + 6.78394i) q^{47} -0.0951209 q^{48} +(-2.37567 + 6.58454i) q^{49} -11.8604 q^{50} +(-3.78812 + 6.56122i) q^{51} +(-0.622340 - 1.07792i) q^{52} +(-0.187459 - 0.324688i) q^{53} +(-0.0813802 + 0.140955i) q^{54} -4.31820 q^{55} +(-4.28792 - 6.10553i) q^{56} +14.9530 q^{57} +(2.92614 - 5.06823i) q^{58} +(-5.12480 - 8.87642i) q^{59} +(6.62428 + 11.4736i) q^{60} +(-2.02221 + 3.50256i) q^{61} -2.27356 q^{62} +(8.10630 - 0.720672i) q^{63} +4.85351 q^{64} +(-2.15910 + 3.73967i) q^{65} +(-1.07113 - 1.85526i) q^{66} +(5.71278 + 9.89483i) q^{67} +(-1.91282 + 3.31310i) q^{68} -11.5042 q^{69} +(-4.18366 + 9.00486i) q^{70} -14.2444 q^{71} +(-4.33701 + 7.51192i) q^{72} +(2.72448 + 4.71894i) q^{73} +(3.86790 + 6.69939i) q^{74} +(16.8194 - 29.1321i) q^{75} +7.55056 q^{76} +(-1.11478 + 2.39943i) q^{77} -2.14227 q^{78} +(4.84566 - 8.39293i) q^{79} +(0.0833184 + 0.144312i) q^{80} +(4.38315 + 7.59184i) q^{81} +(0.712597 - 1.23425i) q^{82} +4.95076 q^{83} +(8.08547 - 0.718821i) q^{84} +13.2724 q^{85} +(-1.37558 + 2.38258i) q^{86} +(8.29923 + 14.3747i) q^{87} +(-1.40996 - 2.44213i) q^{88} +(0.609347 - 1.05542i) q^{89} +11.5439 q^{90} +(1.52058 + 2.16514i) q^{91} -5.80907 q^{92} +(3.22418 - 5.58444i) q^{93} +(3.40398 + 5.89586i) q^{94} +(-13.0977 - 22.6859i) q^{95} +(-6.99230 + 12.1110i) q^{96} +7.28506 q^{97} +(3.92355 + 4.64935i) q^{98} +3.07598 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - 6 q^{2} + 2 q^{3} - 30 q^{4} + q^{5} + 4 q^{6} + q^{7} + 42 q^{8} - 37 q^{9}+O(q^{10}) $ 50 * q - 6 * q^2 + 2 * q^3 - 30 * q^4 + q^5 + 4 * q^6 + q^7 + 42 * q^8 - 37 * q^9	\( 50 q - 6 q^{2} + 2 q^{3} - 30 q^{4} + q^{5} + 4 q^{6} + q^{7} + 42 q^{8} - 37 q^{9} + 3 q^{10} - 25 q^{11} - 9 q^{12} - 50 q^{13} + 22 q^{14} - 32 q^{16} + q^{17} - 44 q^{18} - 5 q^{19} + 8 q^{20} + 2 q^{21} + 12 q^{22} - 15 q^{23} + 4 q^{24} - 50 q^{25} + 6 q^{26} - 34 q^{27} + 12 q^{28} + 48 q^{29} - q^{30} + 12 q^{31} - 48 q^{32} + 2 q^{33} - 16 q^{34} + 20 q^{35} + 60 q^{36} - 33 q^{37} - 16 q^{38} - 2 q^{39} + 21 q^{40} + 24 q^{41} - 42 q^{42} + 76 q^{43} - 30 q^{44} + 22 q^{45} - 39 q^{46} - 4 q^{47} + 164 q^{48} + 23 q^{49} + 32 q^{50} - 51 q^{51} + 30 q^{52} - 2 q^{53} - 10 q^{54} - 2 q^{55} - 72 q^{56} + 76 q^{57} - 17 q^{58} + 4 q^{59} + 33 q^{60} + 22 q^{61} + 84 q^{62} - 19 q^{63} + 82 q^{64} - q^{65} - 2 q^{66} - 24 q^{67} - 14 q^{68} - 60 q^{69} - 124 q^{70} + 18 q^{71} - 102 q^{72} - 11 q^{73} - 39 q^{74} + 16 q^{75} + 116 q^{76} + q^{77} - 4 q^{78} - 19 q^{79} + 33 q^{80} - 73 q^{81} + 32 q^{82} + 32 q^{83} - 109 q^{84} + 28 q^{85} - 27 q^{86} + 11 q^{87} - 21 q^{88} - 13 q^{89} + 80 q^{90} - q^{91} - 17 q^{93} + 56 q^{94} - 15 q^{95} - 55 q^{96} + 68 q^{97} - 22 q^{98} + 74 q^{99}+O(q^{100}) \) 50 * q - 6 * q^2 + 2 * q^3 - 30 * q^4 + q^5 + 4 * q^6 + q^7 + 42 * q^8 - 37 * q^9 + 3 * q^10 - 25 * q^11 - 9 * q^12 - 50 * q^13 + 22 * q^14 - 32 * q^16 + q^17 - 44 * q^18 - 5 * q^19 + 8 * q^20 + 2 * q^21 + 12 * q^22 - 15 * q^23 + 4 * q^24 - 50 * q^25 + 6 * q^26 - 34 * q^27 + 12 * q^28 + 48 * q^29 - q^30 + 12 * q^31 - 48 * q^32 + 2 * q^33 - 16 * q^34 + 20 * q^35 + 60 * q^36 - 33 * q^37 - 16 * q^38 - 2 * q^39 + 21 * q^40 + 24 * q^41 - 42 * q^42 + 76 * q^43 - 30 * q^44 + 22 * q^45 - 39 * q^46 - 4 * q^47 + 164 * q^48 + 23 * q^49 + 32 * q^50 - 51 * q^51 + 30 * q^52 - 2 * q^53 - 10 * q^54 - 2 * q^55 - 72 * q^56 + 76 * q^57 - 17 * q^58 + 4 * q^59 + 33 * q^60 + 22 * q^61 + 84 * q^62 - 19 * q^63 + 82 * q^64 - q^65 - 2 * q^66 - 24 * q^67 - 14 * q^68 - 60 * q^69 - 124 * q^70 + 18 * q^71 - 102 * q^72 - 11 * q^73 - 39 * q^74 + 16 * q^75 + 116 * q^76 + q^77 - 4 * q^78 - 19 * q^79 + 33 * q^80 - 73 * q^81 + 32 * q^82 + 32 * q^83 - 109 * q^84 + 28 * q^85 - 27 * q^86 + 11 * q^87 - 21 * q^88 - 13 * q^89 + 80 * q^90 - q^91 - 17 * q^93 + 56 * q^94 - 15 * q^95 - 55 * q^96 + 68 * q^97 - 22 * q^98 + 74 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1001\mathbb{Z}\right)^\times$.

$n$	$365$	$430$	$925$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.434546	−	0.752655i	0.307270	−	0.532208i	−0.670494	−	0.741915i	$-0.733918\pi$
$2$	0.434546	−	0.752655i	0.307270	−	0.532208i	0.977764	+	0.209707i	$0.0672511\pi$
$3$	1.23247	+	2.13471i	0.711570	+	1.23247i	0.964268	+	0.264930i	$0.0853487\pi$
$3$	1.23247	+	2.13471i	0.711570	+	1.23247i	−0.252698	+	0.967545i	$0.581318\pi$
$4$	0.622340	+	1.07792i	0.311170	+	0.538962i
$5$	2.15910	−	3.73967i	0.965580	−	1.67243i	0.257530	−	0.966270i	$-0.417092\pi$
$5$	2.15910	−	3.73967i	0.965580	−	1.67243i	0.708050	−	0.706162i	$-0.249575\pi$
$6$	2.14227			0.874577
$7$	−1.52058	−	2.16514i	−0.574725	−	0.818346i
$7$	−1.52058	−	2.16514i	−0.574725	−	0.818346i
$8$	2.81992			0.996994
$9$	−1.53799	+	2.66387i	−0.512663	+	0.887958i
$10$	−1.87646	−	3.25012i	−0.593388	−	1.02778i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$	−1.53404	+	2.65703i	−0.442838	+	0.767018i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$	−2.29037	+	0.203620i	−0.612126	+	0.0544197i
$15$	10.6442			2.74831
$16$	−0.0192947	+	0.0334194i	−0.00482367	+	0.00835485i
$17$	1.53679	+	2.66181i	0.372727	+	0.645583i	0.989984	−	0.141179i	$-0.0450894\pi$
$17$	1.53679	+	2.66181i	0.372727	+	0.645583i	−0.617257	+	0.786762i	$0.711756\pi$
$18$	1.33665	+	2.31515i	0.315052	+	0.545686i
$19$	3.03313	−	5.25354i	0.695848	−	1.20524i	−0.274045	−	0.961717i	$-0.588362\pi$
$19$	3.03313	−	5.25354i	0.695848	−	1.20524i	0.969894	−	0.243528i	$-0.0783048\pi$
$20$	5.37478			1.20184
$21$	2.74787	−	5.91448i	0.599634	−	1.29064i
$22$	−0.869091			−0.185291
$23$	−2.33356	+	4.04184i	−0.486580	+	0.842782i	−0.999881	−	0.0154270i	$-0.995089\pi$
$23$	−2.33356	+	4.04184i	−0.486580	+	0.842782i	0.513301	+	0.858209i	$0.328423\pi$
$24$	3.47548	+	6.01972i	0.709430	+	1.22877i
$25$	−6.82344	−	11.8185i	−1.36469	−	2.36371i
$26$	−0.434546	+	0.752655i	−0.0852214	+	0.147608i
$27$	−0.187277			−0.0360414
$28$	1.38754	−	2.98653i	0.262221	−	0.564400i
$29$	6.73380			1.25043			0.625217	−	0.780451i	$-0.285010\pi$
$29$	6.73380			1.25043			0.625217	+	0.780451i	$0.285010\pi$
$30$	4.62537	−	8.01138i	0.844473	−	1.46267i
$31$	−1.30801	−	2.26554i	−0.234925	−	0.406903i	0.724326	−	0.689458i	$-0.242151\pi$
$31$	−1.30801	−	2.26554i	−0.234925	−	0.406903i	−0.959251	+	0.282555i	$0.908818\pi$
$32$	2.83669	+	4.91330i	0.501461	+	0.868556i
$33$	1.23247	−	2.13471i	0.214546	−	0.371605i
$34$	2.67123			0.458112
$35$	−11.3800	+	1.01171i	−1.92357	+	0.171011i
$36$	−3.82861			−0.638101
$37$	−4.45051	+	7.70850i	−0.731659	+	1.26727i	0.224515	+	0.974471i	$0.427920\pi$
$37$	−4.45051	+	7.70850i	−0.731659	+	1.26727i	−0.956174	+	0.292799i	$0.905413\pi$
$38$	−2.63607	−	4.56581i	−0.427627	−	0.740672i
$39$	−1.23247	−	2.13471i	−0.197354	−	0.341827i
$40$	6.08850	−	10.5456i	0.962677	−	1.66740i
$41$	1.63987			0.256104			0.128052	−	0.991767i	$-0.459128\pi$
$41$	1.63987			0.256104			0.128052	+	0.991767i	$0.459128\pi$
$42$	−3.25749	−	4.63831i	−0.502641	−	0.715707i
$43$	−3.16556			−0.482743			−0.241372	−	0.970433i	$-0.577597\pi$
$43$	−3.16556			−0.482743			−0.241372	+	0.970433i	$0.577597\pi$
$44$	0.622340	−	1.07792i	0.0938213	−	0.162503i
$45$	6.64134	+	11.5031i	0.990033	+	1.71479i
$46$	2.02807	+	3.51273i	0.299023	+	0.517923i
$47$	−3.91671	+	6.78394i	−0.571310	+	0.989539i	0.425121	+	0.905136i	$0.360231\pi$
$47$	−3.91671	+	6.78394i	−0.571310	+	0.989539i	−0.996432	+	0.0844023i	$0.973102\pi$
$48$	−0.0951209			−0.0137295
$49$	−2.37567	+	6.58454i	−0.339382	+	0.940649i
$50$	−11.8604			−1.67731
$51$	−3.78812	+	6.56122i	−0.530443	+	0.918754i
$52$	−0.622340	−	1.07792i	−0.0863030	−	0.149481i
$53$	−0.187459	−	0.324688i	−0.0257495	−	0.0445994i	0.852864	−	0.522134i	$-0.174864\pi$
$53$	−0.187459	−	0.324688i	−0.0257495	−	0.0445994i	−0.878613	+	0.477535i	$0.841531\pi$
$54$	−0.0813802	+	0.140955i	−0.0110744	+	0.0191815i
$55$	−4.31820			−0.582266
$56$	−4.28792	−	6.10553i	−0.572997	−	0.815886i
$57$	14.9530			1.98058
$58$	2.92614	−	5.06823i	0.384221	−	0.665491i
$59$	−5.12480	−	8.87642i	−0.667193	−	1.15561i	−0.978686	−	0.205363i	$-0.934162\pi$
$59$	−5.12480	−	8.87642i	−0.667193	−	1.15561i	0.311493	−	0.950248i	$-0.399171\pi$
$60$	6.62428	+	11.4736i	0.855191	+	1.48123i
$61$	−2.02221	+	3.50256i	−0.258917	+	0.448457i	−0.965952	−	0.258721i	$-0.916699\pi$
$61$	−2.02221	+	3.50256i	−0.258917	+	0.448457i	0.707035	+	0.707178i	$0.250032\pi$
$62$	−2.27356			−0.288742
$63$	8.10630	−	0.720672i	1.02130	−	0.0907962i
$64$	4.85351			0.606689
$65$	−2.15910	+	3.73967i	−0.267804	+	0.463849i
$66$	−1.07113	−	1.85526i	−0.131847	−	0.228366i
$67$	5.71278	+	9.89483i	0.697927	+	1.20885i	0.969184	+	0.246338i	$0.0792275\pi$
$67$	5.71278	+	9.89483i	0.697927	+	1.20885i	−0.271257	+	0.962507i	$0.587439\pi$
$68$	−1.91282	+	3.31310i	−0.231963	+	0.401772i
$69$	−11.5042			−1.38494
$70$	−4.18366	+	9.00486i	−0.500043	+	1.07629i
$71$	−14.2444			−1.69050			−0.845249	−	0.534373i	$-0.820548\pi$
$71$	−14.2444			−1.69050			−0.845249	+	0.534373i	$0.820548\pi$
$72$	−4.33701	+	7.51192i	−0.511121	+	0.885288i
$73$	2.72448	+	4.71894i	0.318876	+	0.552310i	0.980254	−	0.197743i	$-0.0633612\pi$
$73$	2.72448	+	4.71894i	0.318876	+	0.552310i	−0.661377	+	0.750053i	$0.730028\pi$
$74$	3.86790	+	6.69939i	0.449634	+	0.778789i
$75$	16.8194	−	29.1321i	1.94214	−	3.36389i
$76$	7.55056			0.866109
$77$	−1.11478	+	2.39943i	−0.127041	+	0.273441i
$78$	−2.14227			−0.242564
$79$	4.84566	−	8.39293i	0.545179	−	0.944278i	−0.453416	−	0.891299i	$-0.649795\pi$
$79$	4.84566	−	8.39293i	0.545179	−	0.944278i	0.998596	−	0.0529794i	$-0.0168718\pi$
$80$	0.0833184	+	0.144312i	0.00931528	+	0.0161345i
$81$	4.38315	+	7.59184i	0.487017	+	0.843538i
$82$	0.712597	−	1.23425i	0.0786932	−	0.136301i
$83$	4.95076			0.543417			0.271708	−	0.962380i	$-0.412411\pi$
$83$	4.95076			0.543417			0.271708	+	0.962380i	$0.412411\pi$
$84$	8.08547	−	0.718821i	0.882197	−	0.0784298i
$85$	13.2724			1.43959
$86$	−1.37558	+	2.38258i	−0.148333	+	0.256920i
$87$	8.29923	+	14.3747i	0.889771	+	1.54113i
$88$	−1.40996	−	2.44213i	−0.150302	−	0.260331i
$89$	0.609347	−	1.05542i	0.0645906	−	0.111874i	−0.831922	−	0.554893i	$-0.812759\pi$
$89$	0.609347	−	1.05542i	0.0645906	−	0.111874i	0.896512	+	0.443019i	$0.146093\pi$
$90$	11.5439			1.21683
$91$	1.52058	+	2.16514i	0.159400	+	0.226968i
$92$	−5.80907			−0.605637
$93$	3.22418	−	5.58444i	0.334332	−	0.579079i
$94$	3.40398	+	5.89586i	0.351093	+	0.608111i
$95$	−13.0977	−	22.6859i	−1.34379	−	2.32752i
$96$	−6.99230	+	12.1110i	−0.713649	+	1.23608i
$97$	7.28506			0.739686			0.369843	−	0.929094i	$-0.379412\pi$
$97$	7.28506			0.739686			0.369843	+	0.929094i	$0.379412\pi$
$98$	3.92355	+	4.64935i	0.396339	+	0.469655i
$99$	3.07598			0.309147
$100$	8.49300	−	14.7103i	0.849300	−	1.47103i
$101$	2.37473	+	4.11315i	0.236294	+	0.409274i	0.959648	−	0.281204i	$-0.0907337\pi$
$101$	2.37473	+	4.11315i	0.236294	+	0.409274i	−0.723354	+	0.690478i	$0.757400\pi$
$102$	3.29222	+	5.70230i	0.325979	+	0.564611i
$103$	−7.96222	+	13.7910i	−0.784541	+	1.35887i	0.144732	+	0.989471i	$0.453768\pi$
$103$	−7.96222	+	13.7910i	−0.784541	+	1.35887i	−0.929273	+	0.369394i	$0.879565\pi$
$104$	−2.81992			−0.276516
$105$	−16.1853	−	23.0461i	−1.57952	−	2.24907i
$106$	−0.325838			−0.0316482
$107$	6.82560	−	11.8223i	0.659855	−	1.14290i	−0.320797	−	0.947148i	$-0.603951\pi$
$107$	6.82560	−	11.8223i	0.659855	−	1.14290i	0.980653	−	0.195755i	$-0.0627158\pi$
$108$	−0.116550	−	0.201870i	−0.0112150	−	0.0194249i
$109$	−0.104953	−	0.181784i	−0.0100527	−	0.0174118i	0.860955	−	0.508681i	$-0.169867\pi$
$109$	−0.104953	−	0.181784i	−0.0100527	−	0.0174118i	−0.871008	+	0.491269i	$0.836533\pi$
$110$	−1.87646	+	3.25012i	−0.178913	+	0.309887i
$111$	−21.9405			−2.08250
$112$	0.101697	−	0.00904113i	0.00960945	−	0.000854307i
$113$	−8.16695			−0.768282			−0.384141	−	0.923274i	$-0.625502\pi$
$113$	−8.16695			−0.768282			−0.384141	+	0.923274i	$0.625502\pi$
$114$	6.49778	−	11.2545i	0.608573	−	1.05408i
$115$	10.0768	+	17.4535i	0.939664	+	1.62755i
$116$	4.19071	+	7.25852i	0.389098	+	0.673937i
$117$	1.53799	−	2.66387i	0.142187	−	0.246275i
$118$	−8.90785			−0.820034
$119$	3.42636	−	7.37486i	0.314094	−	0.676053i
$120$	30.0157			2.74005
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	1.75748	+	3.04405i	0.159115	+	0.275595i
$123$	2.02109	+	3.50064i	0.182236	+	0.315642i
$124$	1.62805	−	2.81987i	0.146203	−	0.253232i
$125$	−37.3390			−3.33970
$126$	2.98014	−	6.41441i	0.265492	−	0.571441i
$127$	−7.88710			−0.699867			−0.349934	−	0.936775i	$-0.613796\pi$
$127$	−7.88710			−0.699867			−0.349934	+	0.936775i	$0.613796\pi$
$128$	−3.56431	+	6.17357i	−0.315044	+	0.545672i
$129$	−3.90147	−	6.75755i	−0.343506	−	0.594969i
$130$	1.87646	+	3.25012i	0.164576	+	0.285054i
$131$	−8.76156	+	15.1755i	−0.765501	+	1.32589i	0.174480	+	0.984661i	$0.444175\pi$
$131$	−8.76156	+	15.1755i	−0.765501	+	1.32589i	−0.939981	+	0.341226i	$0.889158\pi$
$132$	3.06807			0.267042
$133$	−15.9868	+	1.42127i	−1.38623	+	0.123240i
$134$	9.92986			0.857809
$135$	−0.404349	+	0.700353i	−0.0348008	+	0.0602768i
$136$	4.33364	+	7.50609i	0.371607	+	0.643642i
$137$	2.82834	+	4.89883i	0.241641	+	0.418535i	0.961182	−	0.275915i	$-0.0889809\pi$
$137$	2.82834	+	4.89883i	0.241641	+	0.418535i	−0.719541	+	0.694450i	$0.755648\pi$
$138$	−4.99910	+	8.65870i	−0.425552	+	0.737077i
$139$	−3.47904			−0.295088			−0.147544	−	0.989055i	$-0.547137\pi$
$139$	−3.47904			−0.295088			−0.147544	+	0.989055i	$0.547137\pi$
$140$	−8.17279	−	11.6372i	−0.690727	−	0.983520i
$141$	−19.3090			−1.62611
$142$	−6.18984	+	10.7211i	−0.519440	+	0.899696i
$143$	0.500000	+	0.866025i	0.0418121	+	0.0724207i
$144$	−0.0593500	−	0.102797i	−0.00494583	−	0.00856644i
$145$	14.5389	−	25.1822i	1.20739	−	2.09127i
$146$	4.73565			0.391925
$147$	−16.9840	+	3.04391i	−1.40082	+	0.251058i
$148$	−11.0789			−0.910681
$149$	−5.84324	+	10.1208i	−0.478696	+	0.829127i	−0.999702	−	0.0244269i	$-0.992224\pi$
$149$	−5.84324	+	10.1208i	−0.478696	+	0.829127i	0.521005	+	0.853554i	$0.325557\pi$
$150$	−14.6176	−	25.3185i	−1.19352	−	2.06724i
$151$	−10.1493	−	17.5791i	−0.825937	−	1.43056i	−0.901201	−	0.433400i	$-0.857314\pi$
$151$	−10.1493	−	17.5791i	−0.825937	−	1.43056i	0.0752649	−	0.997164i	$-0.476020\pi$
$152$	8.55320	−	14.8146i	0.693756	−	1.20162i
$153$	−9.45428			−0.764333
$154$	1.32152	+	1.88171i	0.106491	+	0.151632i
$155$	−11.2965			−0.907356
$156$	1.53404	−	2.65703i	0.122821	−	0.212733i
$157$	0.928889	+	1.60888i	0.0741334	+	0.128403i	0.900709	−	0.434423i	$-0.143048\pi$
$157$	0.928889	+	1.60888i	0.0741334	+	0.128403i	−0.826576	+	0.562826i	$0.809714\pi$
$158$	−4.21132	−	7.29422i	−0.335035	−	0.580297i
$159$	0.462077	−	0.800341i	0.0366451	−	0.0634711i
$160$	24.4988			1.93680
$161$	12.2995	−	1.09346i	0.969337	−	0.0861768i
$162$	7.61872			0.598583
$163$	0.389451	−	0.674550i	0.0305042	−	0.0528348i	−0.850370	−	0.526185i	$-0.823622\pi$
$163$	0.389451	−	0.674550i	0.0305042	−	0.0528348i	0.880874	+	0.473350i	$0.156955\pi$
$164$	1.02055	+	1.76765i	0.0796919	+	0.138030i
$165$	−5.32208	−	9.21811i	−0.414323	−	0.717629i
$166$	2.15133	−	3.72622i	0.166976	−	0.289210i
$167$	−4.83343			−0.374022			−0.187011	−	0.982358i	$-0.559880\pi$
$167$	−4.83343			−0.374022			−0.187011	+	0.982358i	$0.559880\pi$
$168$	7.74878	−	16.6784i	0.597831	−	1.28676i
$169$	1.00000			0.0769231
$170$	5.76745	−	9.98952i	0.442343	−	0.766161i
$171$	9.32984	+	16.1598i	0.713471	+	1.23577i
$172$	−1.97005	−	3.41224i	−0.150215	−	0.260180i
$173$	12.2030	−	21.1362i	0.927777	−	1.60696i	0.140743	−	0.990046i	$-0.455051\pi$
$173$	12.2030	−	21.1362i	0.927777	−	1.60696i	0.787034	−	0.616910i	$-0.211616\pi$
$174$	14.4256			1.09360
$175$	−15.2132	+	32.7447i	−1.15001	+	2.47527i
$176$	0.0385894			0.00290878
$177$	12.6324	−	21.8799i	0.949508	−	1.64460i
$178$	−0.529578	−	0.917256i	−0.0396935	−	0.0687512i
$179$	3.82502	+	6.62512i	0.285895	+	0.495185i	0.972826	−	0.231538i	$-0.0743758\pi$
$179$	3.82502	+	6.62512i	0.285895	+	0.495185i	−0.686931	+	0.726723i	$0.741042\pi$
$180$	−8.26635	+	14.3177i	−0.616137	+	1.06718i
$181$	9.31027			0.692027			0.346014	−	0.938229i	$-0.387535\pi$
$181$	9.31027			0.692027			0.346014	+	0.938229i	$0.387535\pi$
$182$	2.29037	−	0.203620i	0.169773	−	0.0150933i
$183$	−9.96927			−0.736950
$184$	−6.58045	+	11.3977i	−0.485117	+	0.840248i
$185$	19.2182	+	33.2869i	1.41295	+	2.44730i
$186$	−2.80210	−	4.85339i	−0.205460	−	0.355868i
$187$	1.53679	−	2.66181i	0.112382	−	0.194650i
$188$	−9.75010			−0.711099
$189$	0.284769	+	0.405480i	0.0207139	+	0.0294943i
$190$	−22.7662			−1.65163
$191$	2.59106	−	4.48785i	0.187482	−	0.324729i	−0.756928	−	0.653499i	$-0.773301\pi$
$191$	2.59106	−	4.48785i	0.187482	−	0.324729i	0.944410	+	0.328769i	$0.106634\pi$
$192$	5.98183	+	10.3608i	0.431701	+	0.747729i
$193$	−10.5474	−	18.2687i	−0.759222	−	1.31501i	−0.943248	−	0.332089i	$-0.892246\pi$
$193$	−10.5474	−	18.2687i	−0.759222	−	1.31501i	0.184026	−	0.982921i	$-0.441087\pi$
$194$	3.16569	−	5.48314i	0.227283	−	0.393666i
$195$	−10.6442			−0.762244
$196$	−8.57612	+	1.53703i	−0.612580	+	0.109788i
$197$	−2.59763			−0.185074			−0.0925368	−	0.995709i	$-0.529498\pi$
$197$	−2.59763			−0.185074			−0.0925368	+	0.995709i	$0.529498\pi$
$198$	1.33665	−	2.31515i	0.0949917	−	0.164530i
$199$	1.66800	+	2.88907i	0.118242	+	0.204801i	0.919071	−	0.394092i	$-0.128941\pi$
$199$	1.66800	+	2.88907i	0.118242	+	0.204801i	−0.800829	+	0.598893i	$0.795608\pi$
$200$	−19.2416	−	33.3274i	−1.36058	−	2.35660i
$201$	−14.0817	+	24.3902i	−0.993248	+	1.72036i
$202$	4.12771			0.290425
$203$	−10.2393	−	14.5796i	−0.718656	−	1.02329i
$204$	−9.42999			−0.660232
$205$	3.54064	−	6.13257i	0.247289	−	0.428317i
$206$	6.91990	+	11.9856i	0.482132	+	0.835077i
$207$	−7.17797	−	12.4326i	−0.498903	−	0.864125i
$208$	0.0192947	−	0.0334194i	0.00133785	−	0.00231722i
$209$	−6.06627			−0.419612
$210$	−24.3790	+	2.16736i	−1.68231	+	0.149562i
$211$	−13.5896			−0.935547			−0.467773	−	0.883848i	$-0.654944\pi$
$211$	−13.5896			−0.935547			−0.467773	+	0.883848i	$0.654944\pi$
$212$	0.233326	−	0.404133i	0.0160249	−	0.0277560i
$213$	−17.5558	−	30.4076i	−1.20291	−	2.08350i
$214$	−5.93207	−	10.2746i	−0.405508	−	0.702360i
$215$	−6.83476	+	11.8382i	−0.466127	+	0.807356i
$216$	−0.528105			−0.0359330
$217$	−2.91628	+	6.27696i	−0.197970	+	0.426108i
$218$	−0.182428			−0.0123556
$219$	−6.71571	+	11.6319i	−0.453806	+	0.786014i
$220$	−2.68739	−	4.65470i	−0.181184	−	0.313820i
$221$	−1.53679	−	2.66181i	−0.103376	−	0.179052i
$222$	−9.53417	+	16.5137i	−0.639892	+	1.10832i
$223$	17.8007			1.19202			0.596011	−	0.802976i	$-0.296751\pi$
$223$	17.8007			1.19202			0.596011	+	0.802976i	$0.296751\pi$
$224$	6.32456	−	13.6129i	0.422577	−	0.909550i
$225$	41.9775			2.79850
$226$	−3.54891	+	6.14690i	−0.236070	+	0.408886i
$227$	2.49387	+	4.31952i	0.165524	+	0.286696i	0.936841	−	0.349755i	$-0.113735\pi$
$227$	2.49387	+	4.31952i	0.165524	+	0.286696i	−0.771317	+	0.636451i	$0.780402\pi$
$228$	9.30588	+	16.1183i	0.616297	+	1.06746i
$229$	7.89196	−	13.6693i	0.521516	−	0.903291i	−0.478171	−	0.878267i	$-0.658700\pi$
$229$	7.89196	−	13.6693i	0.521516	−	0.903291i	0.999687	−	0.0250248i	$-0.00796648\pi$
$230$	17.5153			1.15492
$231$	−6.49602	+	0.577515i	−0.427407	+	0.0379977i
$232$	18.9888			1.24668
$233$	1.75336	−	3.03690i	0.114866	−	0.198954i	−0.802860	−	0.596168i	$-0.796689\pi$
$233$	1.75336	−	3.03690i	0.114866	−	0.198954i	0.917726	+	0.397213i	$0.130023\pi$
$234$	−1.33665	−	2.31515i	−0.0873797	−	0.151346i
$235$	16.9131	+	29.2944i	1.10329	+	1.91096i
$236$	6.37874	−	11.0483i	0.415221	−	0.719184i
$237$	23.8886			1.55173
$238$	−4.06182	−	5.78359i	−0.263289	−	0.374894i
$239$	−14.3966			−0.931239			−0.465619	−	0.884985i	$-0.654168\pi$
$239$	−14.3966			−0.931239			−0.465619	+	0.884985i	$0.654168\pi$
$240$	−0.205376	+	0.355721i	−0.0132569	+	0.0229617i
$241$	−5.20448	−	9.01443i	−0.335250	−	0.580671i	0.648283	−	0.761400i	$-0.275488\pi$
$241$	−5.20448	−	9.01443i	−0.335250	−	0.580671i	−0.983533	+	0.180729i	$0.942154\pi$
$242$	0.434546	+	0.752655i	0.0279337	+	0.0483825i
$243$	−11.0852	+	19.2001i	−0.711113	+	1.23168i
$244$	−5.03400			−0.322269
$245$	19.4947	+	23.1009i	1.24547	+	1.47586i
$246$	3.51303			0.223983
$247$	−3.03313	+	5.25354i	−0.192994	+	0.334275i
$248$	−3.68849	−	6.38864i	−0.234219	−	0.405679i
$249$	6.10169	+	10.5684i	0.386679	+	0.669747i
$250$	−16.2255	+	28.1034i	−1.02619	+	1.77741i
$251$	−21.0293			−1.32736			−0.663680	−	0.748017i	$-0.731006\pi$
$251$	−21.0293			−1.32736			−0.663680	+	0.748017i	$0.731006\pi$
$252$	5.82170	+	8.28947i	0.366733	+	0.522188i
$253$	4.66711			0.293419
$254$	−3.42731	+	5.93627i	−0.215048	+	0.372475i
$255$	16.3579	+	28.3327i	1.02437	+	1.77426i
$256$	7.95122	+	13.7719i	0.496951	+	0.860745i
$257$	8.92664	−	15.4614i	0.556829	−	0.964456i	−0.440930	−	0.897542i	$-0.645351\pi$
$257$	8.92664	−	15.4614i	0.556829	−	0.964456i	0.997759	−	0.0669142i	$-0.0213154\pi$
$258$	−6.78147			−0.422196
$259$	23.4573	−	2.08542i	1.45757	−	0.129582i
$260$	−5.37478			−0.333330
$261$	−10.3565	+	17.9380i	−0.641051	+	1.11033i
$262$	7.61460	+	13.1889i	0.470431	+	0.814811i
$263$	−12.1805	−	21.0972i	−0.751080	−	1.30091i	−0.947300	−	0.320348i	$-0.896200\pi$
$263$	−12.1805	−	21.0972i	−0.751080	−	1.30091i	0.196220	−	0.980560i	$-0.437133\pi$
$264$	3.47548	−	6.01972i	0.213901	−	0.370488i
$265$	−1.61897			−0.0994526
$266$	−5.87726	+	12.6501i	−0.360358	+	0.775630i
$267$	3.00402			0.183843
$268$	−7.11059	+	12.3159i	−0.434348	+	0.752313i
$269$	13.0996	+	22.6892i	0.798699	+	1.38339i	0.920464	+	0.390828i	$0.127811\pi$
$269$	13.0996	+	22.6892i	0.798699	+	1.38339i	−0.121764	+	0.992559i	$0.538855\pi$
$270$	0.351416	+	0.608671i	0.0213865	+	0.0370425i
$271$	−2.97422	+	5.15151i	−0.180671	+	0.312932i	−0.942109	−	0.335306i	$-0.891160\pi$
$271$	−2.97422	+	5.15151i	−0.180671	+	0.312932i	0.761438	+	0.648238i	$0.224494\pi$
$272$	−0.118608			−0.00719166
$273$	−2.74787	+	5.91448i	−0.166309	+	0.357960i
$274$	4.91617			0.296997
$275$	−6.82344	+	11.8185i	−0.411469	+	0.712685i
$276$	−7.15953	−	12.4007i	−0.430953	−	0.746432i
$277$	−3.82166	−	6.61932i	−0.229622	−	0.397716i	0.728074	−	0.685498i	$-0.240416\pi$
$277$	−3.82166	−	6.61932i	−0.229622	−	0.397716i	−0.957696	+	0.287782i	$0.907082\pi$
$278$	−1.51180	+	2.61852i	−0.0906718	+	0.157048i
$279$	8.04681			0.481750
$280$	−32.0907	+	2.85296i	−1.91779	+	0.170497i
$281$	−3.15916			−0.188459			−0.0942297	−	0.995550i	$-0.530039\pi$
$281$	−3.15916			−0.188459			−0.0942297	+	0.995550i	$0.530039\pi$
$282$	−8.39063	+	14.5330i	−0.499655	+	0.865427i
$283$	14.7591	+	25.5635i	0.877339	+	1.51959i	0.854251	+	0.519861i	$0.174016\pi$
$283$	14.7591	+	25.5635i	0.877339	+	1.51959i	0.0230880	+	0.999733i	$0.492650\pi$
$284$	−8.86485	−	15.3544i	−0.526032	−	0.911115i
$285$	32.2851	−	55.9195i	1.91241	−	3.31238i
$286$	0.869091			0.0513904
$287$	−2.49355	−	3.55054i	−0.147190	−	0.209582i
$288$	−17.4512			−1.02832
$289$	3.77653	−	6.54114i	0.222149	−	0.384773i
$290$	−12.6357	−	21.8856i	−0.741992	−	1.28517i
$291$	8.97865	+	15.5515i	0.526338	+	0.911644i
$292$	−3.39111	+	5.87357i	−0.198450	+	0.343725i
$293$	28.9433			1.69088			0.845441	−	0.534068i	$-0.179337\pi$
$293$	28.9433			1.69088			0.845441	+	0.534068i	$0.179337\pi$
$294$	−5.08932	+	14.1058i	−0.296815	+	0.822669i
$295$	−44.2599			−2.57691
$296$	−12.5501	+	21.7374i	−0.729459	+	1.26346i
$297$	0.0936383	+	0.162186i	0.00543344	+	0.00941100i
$298$	5.07831	+	8.79588i	0.294178	+	0.509532i
$299$	2.33356	−	4.04184i	0.134953	−	0.233746i
$300$	41.8696			2.41734
$301$	4.81349	+	6.85388i	0.277445	+	0.395051i
$302$	−17.6413			−1.01514
$303$	−5.85359	+	10.1387i	−0.336280	+	0.582454i
$304$	0.117047	+	0.202731i	0.00671309	+	0.0116274i
$305$	8.73229	+	15.1248i	0.500010	+	0.866042i
$306$	−4.10832	+	7.11581i	−0.234857	+	0.406784i
$307$	−1.67213			−0.0954337			−0.0477169	−	0.998861i	$-0.515195\pi$
$307$	−1.67213			−0.0954337			−0.0477169	+	0.998861i	$0.515195\pi$
$308$	−3.28018	+	0.291617i	−0.186905	+	0.0166164i
$309$	−39.2530			−2.23302
$310$	−4.90884	+	8.50237i	−0.278804	+	0.482902i
$311$	−14.7516	−	25.5505i	−0.836487	−	1.44884i	−0.892814	−	0.450425i	$-0.851272\pi$
$311$	−14.7516	−	25.5505i	−0.836487	−	1.44884i	0.0563276	−	0.998412i	$-0.482061\pi$
$312$	−3.47548	−	6.01972i	−0.196761	−	0.340799i
$313$	−16.5589	+	28.6809i	−0.935967	+	1.62114i	−0.163067	+	0.986615i	$0.552139\pi$
$313$	−16.5589	+	28.6809i	−0.935967	+	1.62114i	−0.772900	+	0.634528i	$0.781195\pi$
$314$	1.61458			0.0911159
$315$	14.8072	−	31.8709i	0.834293	−	1.79572i
$316$	12.0626			0.678574
$317$	7.23171	−	12.5257i	0.406173	−	0.703513i	−0.588284	−	0.808655i	$-0.700196\pi$
$317$	7.23171	−	12.5257i	0.406173	−	0.703513i	0.994457	+	0.105142i	$0.0335296\pi$
$318$	−0.401587	−	0.695569i	−0.0225199	−	0.0390056i
$319$	−3.36690	−	5.83164i	−0.188510	−	0.326509i
$320$	10.4792	−	18.1505i	0.585806	−	1.01465i
$321$	33.6495			1.87813
$322$	4.52170	−	9.73245i	0.251985	−	0.542368i
$323$	18.6452			1.03745
$324$	−5.45562	+	9.44941i	−0.303090	+	0.524967i
$325$	6.82344	+	11.8185i	0.378496	+	0.655575i
$326$	−0.338469	−	0.586245i	−0.0187461	−	0.0324691i
$327$	0.258704	−	0.448089i	0.0143064	−	0.0247794i
$328$	4.62430			0.255334
$329$	20.6438	−	1.83530i	1.13813	−	0.101183i
$330$	−9.25074			−0.509236
$331$	−3.35648	+	5.81359i	−0.184489	+	0.319544i	−0.943404	−	0.331646i	$-0.892396\pi$
$331$	−3.35648	+	5.81359i	−0.184489	+	0.319544i	0.758916	+	0.651189i	$0.225730\pi$
$332$	3.08106	+	5.33655i	0.169095	+	0.292881i
$333$	−13.6896	−	23.7112i	−0.750188	−	1.29936i
$334$	−2.10035	+	3.63791i	−0.114926	+	0.199058i
$335$	49.3379			2.69562
$336$	0.144639	+	0.205950i	0.00789070	+	0.0112355i
$337$	6.53587			0.356031			0.178016	−	0.984028i	$-0.443032\pi$
$337$	6.53587			0.356031			0.178016	+	0.984028i	$0.443032\pi$
$338$	0.434546	−	0.752655i	0.0236362	−	0.0409390i
$339$	−10.0656	−	17.4341i	−0.546686	−	0.946889i
$340$	8.25993	+	14.3066i	0.447958	+	0.775886i
$341$	−1.30801	+	2.26554i	−0.0708327	+	0.122686i
$342$	16.2170			0.876914
$343$	17.8689	−	4.86866i	0.964828	−	0.262883i
$344$	−8.92664			−0.481292
$345$	−24.8387	+	43.0220i	−1.33727	+	2.31622i
$346$	−10.6055	−	18.3693i	−0.570156	−	0.987539i
$347$	−11.9032	−	20.6169i	−0.638996	−	1.10677i	−0.985653	−	0.168782i	$-0.946017\pi$
$347$	−11.9032	−	20.6169i	−0.638996	−	1.10677i	0.346657	−	0.937992i	$-0.387317\pi$
$348$	−10.3299	+	17.8919i	−0.553740	+	0.959106i
$349$	27.9522			1.49625			0.748123	−	0.663560i	$-0.230955\pi$
$349$	27.9522			1.49625			0.748123	+	0.663560i	$0.230955\pi$
$350$	18.0347	+	25.6794i	0.963993	+	1.37262i
$351$	0.187277			0.00999608
$352$	2.83669	−	4.91330i	0.151196	−	0.261880i
$353$	−3.70093	−	6.41021i	−0.196981	−	0.341181i	0.750567	−	0.660794i	$-0.229780\pi$
$353$	−3.70093	−	6.41021i	−0.196981	−	0.341181i	−0.947548	+	0.319613i	$0.896447\pi$
$354$	−10.9787	−	19.0157i	−0.583511	−	1.01067i
$355$	−30.7551	+	53.2694i	−1.63231	+	2.82724i
$356$	1.51688			0.0803947
$357$	19.9661	−	1.77504i	1.05672	−	0.0939452i
$358$	6.64858			0.351388
$359$	−10.4751	+	18.1435i	−0.552857	+	0.957576i	0.445210	+	0.895426i	$0.353129\pi$
$359$	−10.4751	+	18.1435i	−0.552857	+	0.957576i	−0.998067	+	0.0621500i	$0.980204\pi$
$360$	18.7281	+	32.4380i	0.987057	+	1.70963i
$361$	−8.89979	−	15.4149i	−0.468410	−	0.811310i
$362$	4.04574	−	7.00743i	0.212639	−	0.368302i
$363$	−2.46495			−0.129376
$364$	−1.38754	+	2.98653i	−0.0727269	+	0.156536i
$365$	23.5297			1.23160
$366$	−4.33210	+	7.50342i	−0.226443	+	0.392210i
$367$	−5.22914	−	9.05713i	−0.272959	−	0.472779i	0.696659	−	0.717402i	$-0.254669\pi$
$367$	−5.22914	−	9.05713i	−0.272959	−	0.472779i	−0.969618	+	0.244624i	$0.921336\pi$
$368$	−0.0900505	−	0.155972i	−0.00469421	−	0.00813061i
$369$	−2.52209	+	4.36840i	−0.131295	+	0.227410i
$370$	33.4047			1.73663
$371$	−0.417950	+	0.899590i	−0.0216989	+	0.0467044i
$372$	8.02614			0.416136
$373$	12.1764	−	21.0901i	0.630468	−	1.09200i	−0.356988	−	0.934109i	$-0.616196\pi$
$373$	12.1764	−	21.0901i	0.630468	−	1.09200i	0.987456	−	0.157894i	$-0.0504705\pi$
$374$	−1.33561	−	2.31335i	−0.0690630	−	0.119621i
$375$	−46.0193	−	79.7078i	−2.37643	−	4.11609i
$376$	−11.0448	+	19.1302i	−0.569593	+	0.986564i
$377$	−6.73380			−0.346808
$378$	0.428932	−	0.0381332i	0.0220619	−	0.00196136i
$379$	22.1844			1.13954			0.569768	−	0.821805i	$-0.307033\pi$
$379$	22.1844			1.13954			0.569768	+	0.821805i	$0.307033\pi$
$380$	16.3024	−	28.2366i	0.836297	−	1.44851i
$381$	−9.72065	−	16.8367i	−0.498004	−	0.862568i
$382$	−2.25187	−	3.90035i	−0.115216	−	0.199559i
$383$	15.6926	−	27.1804i	0.801855	−	1.38885i	−0.116539	−	0.993186i	$-0.537180\pi$
$383$	15.6926	−	27.1804i	0.801855	−	1.38885i	0.918394	−	0.395667i	$-0.129487\pi$
$384$	−17.5717			−0.896702
$385$	6.56617	+	9.34952i	0.334643	+	0.476496i
$386$	−18.3334			−0.933145
$387$	4.86859	−	8.43265i	0.247484	−	0.428656i
$388$	4.53378	+	7.85275i	0.230168	+	0.398663i
$389$	0.359796	+	0.623185i	0.0182424	+	0.0315967i	0.875002	−	0.484118i	$-0.160860\pi$
$389$	0.359796	+	0.623185i	0.0182424	+	0.0315967i	−0.856760	+	0.515715i	$0.827526\pi$
$390$	−4.62537	+	8.01138i	−0.234215	+	0.405672i
$391$	−14.3448			−0.725447
$392$	−6.69921	+	18.5679i	−0.338361	+	0.937821i
$393$	−43.1936			−2.17883
$394$	−1.12879	+	1.95512i	−0.0568676	+	0.0984976i
$395$	−20.9245	−	36.2424i	−1.05283	−	1.82355i
$396$	1.91430	+	3.31567i	0.0961974	+	0.166619i
$397$	−2.30769	+	3.99703i	−0.115820	+	0.200605i	−0.918107	−	0.396332i	$-0.870283\pi$
$397$	−2.30769	+	3.99703i	−0.115820	+	0.200605i	0.802287	+	0.596938i	$0.203616\pi$
$398$	2.89930			0.145329
$399$	−22.7373	−	32.3754i	−1.13829	−	1.62080i
$400$	0.526625			0.0263312
$401$	−9.47673	+	16.4142i	−0.473245	+	0.819685i	−0.999531	−	0.0306231i	$-0.990251\pi$
$401$	−9.47673	+	16.4142i	−0.473245	+	0.819685i	0.526286	+	0.850308i	$0.323584\pi$
$402$	12.2383	+	21.1974i	0.610391	+	1.05723i
$403$	1.30801	+	2.26554i	0.0651566	+	0.112854i
$404$	−2.95578	+	5.11956i	−0.147055	+	0.254708i
$405$	37.8547			1.88101
$406$	−15.4229	+	1.37114i	−0.765424	+	0.0680483i
$407$	8.90101			0.441207
$408$	−10.6822	+	18.5021i	−0.528848	+	0.915992i
$409$	−5.80309	−	10.0513i	−0.286945	−	0.497002i	0.686134	−	0.727475i	$-0.259306\pi$
$409$	−5.80309	−	10.0513i	−0.286945	−	0.497002i	−0.973079	+	0.230472i	$0.925973\pi$
$410$	−3.07714	−	5.32976i	−0.151969	−	0.263218i
$411$	−6.97172	+	12.0754i	−0.343889	+	0.595634i
$412$	−19.8208			−0.976503
$413$	−11.4260	+	24.5932i	−0.562238	+	1.21015i
$414$	−12.4766			−0.613192
$415$	10.6892	−	18.5142i	0.524712	−	0.908828i
$416$	−2.83669	−	4.91330i	−0.139080	−	0.240894i
$417$	−4.28783	−	7.42673i	−0.209976	−	0.363689i
$418$	−2.63607	+	4.56581i	−0.128934	+	0.223321i
$419$	−12.0489			−0.588626			−0.294313	−	0.955709i	$-0.595091\pi$
$419$	−12.0489			−0.588626			−0.294313	+	0.955709i	$0.595091\pi$
$420$	14.7692	−	31.7890i	0.720663	−	1.55115i
$421$	−18.9718			−0.924630			−0.462315	−	0.886716i	$-0.652981\pi$
$421$	−18.9718			−0.924630			−0.462315	+	0.886716i	$0.652981\pi$
$422$	−5.90530	+	10.2283i	−0.287466	+	0.497905i
$423$	−12.0477	−	20.8672i	−0.585779	−	1.01460i
$424$	−0.528620	−	0.915597i	−0.0256721	−	0.0444653i
$425$	20.9724	−	36.3253i	1.01731	−	1.76204i
$426$	−30.5153			−1.47847
$427$	10.6585	−	0.947568i	0.515799	−	0.0458560i
$428$	16.9914			0.821309
$429$	−1.23247	+	2.13471i	−0.0595044	+	0.103065i
$430$	5.94004	+	10.2884i	0.286454	+	0.496153i
$431$	−4.08490	−	7.07525i	−0.196762	−	0.340803i	0.750714	−	0.660627i	$-0.229709\pi$
$431$	−4.08490	−	7.07525i	−0.196762	−	0.340803i	−0.947477	+	0.319824i	$0.896376\pi$
$432$	0.00361344	−	0.00625867i	0.000173852	−	0.000301120i
$433$	29.4188			1.41378			0.706890	−	0.707324i	$-0.250098\pi$
$433$	29.4188			1.41378			0.706890	+	0.707324i	$0.250098\pi$
$434$	3.45713	+	4.92258i	0.165947	+	0.236291i
$435$	71.6755			3.43658
$436$	0.130633	−	0.226263i	0.00625620	−	0.0108360i
$437$	14.1560	+	24.5189i	0.677172	+	1.17290i
$438$	5.83656	+	10.1092i	0.278882	+	0.483038i
$439$	−16.4896	+	28.5609i	−0.787007	+	1.36314i	0.140785	+	0.990040i	$0.455037\pi$
$439$	−16.4896	+	28.5609i	−0.787007	+	1.36314i	−0.927792	+	0.373097i	$0.878296\pi$
$440$	−12.1770			−0.580516
$441$	−13.8866	−	16.4554i	−0.661268	−	0.783592i
$442$	−2.67123			−0.127057
$443$	−12.6471	+	21.9054i	−0.600881	+	1.04076i	0.391807	+	0.920048i	$0.371850\pi$
$443$	−12.6471	+	21.9054i	−0.600881	+	1.04076i	−0.992688	+	0.120709i	$0.961483\pi$
$444$	−13.6545	−	23.6503i	−0.648013	−	1.12239i
$445$	−2.63128	−	4.55752i	−0.124735	−	0.216047i
$446$	7.73521	−	13.3978i	0.366273	−	0.634403i
$447$	−28.8066			−1.36250
$448$	−7.38015	−	10.5085i	−0.348679	−	0.496482i
$449$	−4.60539			−0.217342			−0.108671	−	0.994078i	$-0.534659\pi$
$449$	−4.60539			−0.217342			−0.108671	+	0.994078i	$0.534659\pi$
$450$	18.2411	−	31.5946i	0.859895	−	1.48938i
$451$	−0.819933	−	1.42017i	−0.0386092	−	0.0668730i
$452$	−5.08262	−	8.80336i	−0.239066	−	0.414075i
$453$	25.0175	−	43.3315i	1.17542	−	2.03589i
$454$	4.33481			0.203443
$455$	11.3800	−	1.01171i	0.533503	−	0.0474299i
$456$	42.1664			1.97462
$457$	1.20814	−	2.09256i	0.0565144	−	0.0978858i	−0.836384	−	0.548144i	$-0.815335\pi$
$457$	1.20814	−	2.09256i	0.0565144	−	0.0978858i	0.892898	+	0.450258i	$0.148668\pi$
$458$	−6.85884	−	11.8799i	−0.320492	−	0.555109i
$459$	−0.287805	−	0.498494i	−0.0134336	−	0.0232677i
$460$	−12.5424	+	21.7240i	−0.584791	+	1.01289i
$461$	−13.6537			−0.635914			−0.317957	−	0.948105i	$-0.602997\pi$
$461$	−13.6537			−0.635914			−0.317957	+	0.948105i	$0.602997\pi$
$462$	−2.38815	+	5.14022i	−0.111107	+	0.239145i
$463$	−10.7298			−0.498654			−0.249327	−	0.968419i	$-0.580209\pi$
$463$	−10.7298			−0.498654			−0.249327	+	0.968419i	$0.580209\pi$
$464$	−0.129927	+	0.225039i	−0.00603169	+	0.0104472i
$465$	−13.9226	−	24.1147i	−0.645647	−	1.11829i
$466$	−1.52383	−	2.63934i	−0.0705899	−	0.122265i
$467$	1.00464	−	1.74008i	0.0464891	−	0.0805215i	−0.841844	−	0.539720i	$-0.818530\pi$
$467$	1.00464	−	1.74008i	0.0464891	−	0.0805215i	0.888334	+	0.459199i	$0.151863\pi$
$468$	3.82861			0.176977
$469$	12.7370	−	27.4149i	0.588138	−	1.26590i
$470$	29.3981			1.35603
$471$	−2.28966	+	3.96581i	−0.105502	+	0.182735i
$472$	−14.4516	−	25.0308i	−0.665187	−	1.15214i
$473$	1.58278	+	2.74146i	0.0727763	+	0.126052i
$474$	10.3807	−	17.9799i	0.476801	−	0.825844i
$475$	−82.7856			−3.79846
$476$	10.0819	−	0.896310i	0.462104	−	0.0410823i
$477$	1.15324			0.0528032
$478$	−6.25598	+	10.8357i	−0.286142	+	0.495612i
$479$	7.24932	+	12.5562i	0.331230	+	0.573707i	0.982753	−	0.184922i	$-0.0592032\pi$
$479$	7.24932	+	12.5562i	0.331230	+	0.573707i	−0.651524	+	0.758628i	$0.725870\pi$
$480$	30.1942	+	52.2979i	1.37817	+	2.38706i
$481$	4.45051	−	7.70850i	0.202926	−	0.351477i
$482$	−9.04634			−0.412050
$483$	17.4931	+	24.9082i	0.795962	+	1.13336i
$484$	−1.24468			−0.0565764
$485$	15.7292	−	27.2437i	0.714225	−	1.23707i
$486$	9.63402	+	16.6866i	0.437008	+	0.756920i
$487$	−15.4929	−	26.8346i	−0.702052	−	1.21599i	−0.967745	−	0.251933i	$-0.918934\pi$
$487$	−15.4929	−	26.8346i	−0.702052	−	1.21599i	0.265692	−	0.964058i	$-0.414399\pi$
$488$	−5.70246	+	9.87696i	−0.258138	+	0.447109i
$489$	1.91996			0.0868234
$490$	25.8584	−	4.63439i	1.16816	−	0.209361i
$491$	−10.2575			−0.462913			−0.231457	−	0.972845i	$-0.574349\pi$
$491$	−10.2575			−0.462913			−0.231457	+	0.972845i	$0.574349\pi$
$492$	−2.51562	+	4.35717i	−0.113413	+	0.196437i
$493$	10.3485	+	17.9241i	0.466071	+	0.807259i
$494$	2.63607	+	4.56581i	0.118602	+	0.205425i
$495$	6.64134	−	11.5031i	0.298506	−	0.517028i
$496$	0.100951			0.00453281
$497$	21.6597	+	30.8411i	0.971572	+	1.38341i
$498$	10.6058			0.475259
$499$	18.5871	−	32.1939i	0.832074	−	1.44120i	−0.0643160	−	0.997930i	$-0.520487\pi$
$499$	18.5871	−	32.1939i	0.832074	−	1.44120i	0.896390	−	0.443265i	$-0.146180\pi$
$500$	−23.2375	−	40.2486i	−1.03921	−	1.79997i
$501$	−5.95709	−	10.3180i	−0.266143	−	0.460973i
$502$	−9.13821	+	15.8278i	−0.407858	+	0.706431i
$503$	4.45664			0.198712			0.0993559	−	0.995052i	$-0.468322\pi$
$503$	4.45664			0.198712			0.0993559	+	0.995052i	$0.468322\pi$
$504$	22.8591	−	2.03224i	1.01823	−	0.0905232i
$505$	20.5091			0.912644
$506$	2.02807	−	3.51273i	0.0901589	−	0.156160i
$507$	1.23247	+	2.13471i	0.0547361	+	0.0948057i
$508$	−4.90846	−	8.50170i	−0.217778	−	0.377202i
$509$	10.2417	−	17.7392i	0.453957	−	0.786277i	−0.544670	−	0.838650i	$-0.683345\pi$
$509$	10.2417	−	17.7392i	0.453957	−	0.786277i	0.998628	+	0.0523731i	$0.0166785\pi$
$510$	28.4330			1.25903
$511$	6.07438	−	13.0744i	0.268715	−	0.578378i
$512$	−0.436571			−0.0192939
$513$	−0.568035	+	0.983865i	−0.0250793	+	0.0434387i
$514$	−7.75807	−	13.4374i	−0.342194	−	0.592697i
$515$	34.3825	+	59.5522i	1.51507	+	2.62418i
$516$	4.85609	−	8.41099i	0.213777	−	0.370273i
$517$	7.83341			0.344513
$518$	8.62368	−	18.5615i	0.378903	−	0.815546i
$519$	60.1595			2.64071
$520$	−6.08850	+	10.5456i	−0.266998	+	0.462455i
$521$	2.92289	+	5.06260i	0.128054	+	0.221796i	0.922923	−	0.384985i	$-0.125794\pi$
$521$	2.92289	+	5.06260i	0.128054	+	0.221796i	−0.794868	+	0.606782i	$0.792460\pi$
$522$	9.00074	+	15.5897i	0.393952	+	0.682344i
$523$	5.71759	−	9.90316i	0.250013	−	0.433035i	−0.713516	−	0.700639i	$-0.752898\pi$
$523$	5.71759	−	9.90316i	0.250013	−	0.433035i	0.963529	+	0.267604i	$0.0862318\pi$
$524$	−21.8107			−0.952804
$525$	−88.6504	+	7.88127i	−3.86902	+	0.343967i
$526$	−21.1719			−0.923138
$527$	4.02028	−	6.96333i	0.175126	−	0.303327i
$528$	0.0475604	+	0.0823771i	0.00206980	+	0.00358500i
$529$	0.609022	+	1.05486i	0.0264792	+	0.0458633i
$530$	−0.703517	+	1.21853i	−0.0305588	+	0.0529294i
$531$	31.5276			1.36818
$532$	−11.4812	−	16.3480i	−0.497775	−	0.708777i
$533$	−1.63987			−0.0710305
$534$	1.30538	−	2.26099i	0.0564894	−	0.0978426i
$535$	−29.4743	−	51.0510i	−1.27429	−	2.20713i
$536$	16.1096	+	27.9027i	0.695829	+	1.20521i
$537$	−9.42847	+	16.3306i	−0.406869	+	0.704717i
$538$	22.7696			0.981666
$539$	6.89022	−	1.23488i	0.296783	−	0.0531900i
$540$	−1.00657			−0.0433159
$541$	2.37445	−	4.11266i	0.102085	−	0.176817i	−0.810458	−	0.585796i	$-0.800782\pi$
$541$	2.37445	−	4.11266i	0.102085	−	0.176817i	0.912544	+	0.408979i	$0.134115\pi$
$542$	2.58487	+	4.47713i	0.111030	+	0.192309i
$543$	11.4747	+	19.8747i	0.492426	+	0.852906i
$544$	−8.71882	+	15.1014i	−0.373816	+	0.647469i
$545$	−0.906419			−0.0388267
$546$	3.25749	+	4.63831i	0.139408	+	0.198501i
$547$	42.2663			1.80718			0.903589	−	0.428401i	$-0.140923\pi$
$547$	42.2663			1.80718			0.903589	+	0.428401i	$0.140923\pi$
$548$	−3.52038	+	6.09748i	−0.150383	+	0.260471i
$549$	−6.22026	−	10.7738i	−0.265474	−	0.459814i
$550$	5.93019	+	10.2714i	0.252864	+	0.437974i
$551$	20.4245	−	35.3763i	0.870113	−	1.50708i
$552$	−32.4410			−1.38078
$553$	−25.5401	+	2.27059i	−1.08608	+	0.0965551i
$554$	−6.64275			−0.282223
$555$	−47.3719	+	82.0505i	−2.01082	+	3.48285i
$556$	−2.16514	−	3.75014i	−0.0918226	−	0.159041i
$557$	−8.57758	−	14.8568i	−0.363444	−	0.629503i	0.625081	−	0.780559i	$-0.285066\pi$
$557$	−8.57758	−	14.8568i	−0.363444	−	0.629503i	−0.988525	+	0.151057i	$0.951732\pi$
$558$	3.49671	−	6.05647i	0.148027	−	0.256391i
$559$	3.16556			0.133889
$560$	0.185763	−	0.399834i	0.00784991	−	0.0168961i
$561$	7.57624			0.319869
$562$	−1.37280	+	2.37776i	−0.0579080	+	0.100300i
$563$	17.3190	+	29.9974i	0.729910	+	1.26424i	0.956921	+	0.290349i	$0.0937714\pi$
$563$	17.3190	+	29.9974i	0.729910	+	1.26424i	−0.227011	+	0.973892i	$0.572895\pi$
$564$	−12.0167	−	20.8136i	−0.505996	−	0.876411i
$565$	−17.6333	+	30.5417i	−0.741838	+	1.28490i
$566$	25.6540			1.07832
$567$	9.77247	−	21.0341i	0.410405	−	0.883351i
$568$	−40.1681			−1.68542
$569$	11.7736	−	20.3924i	0.493573	−	0.854894i	−0.506400	−	0.862299i	$-0.669024\pi$
$569$	11.7736	−	20.3924i	0.493573	−	0.854894i	0.999973	+	0.00740537i	$0.00235722\pi$
$570$	−28.0587	−	48.5991i	−1.17525	−	2.03559i
$571$	9.22389	+	15.9763i	0.386008	+	0.668585i	0.991908	−	0.126955i	$-0.0405204\pi$
$571$	9.22389	+	15.9763i	0.386008	+	0.668585i	−0.605901	+	0.795540i	$0.707187\pi$
$572$	−0.622340	+	1.07792i	−0.0260213	+	0.0450703i
$573$	12.7737			0.533627
$574$	−3.75589	+	0.333910i	−0.156768	+	0.0139371i
$575$	63.6915			2.65612
$576$	−7.46464	+	12.9291i	−0.311027	+	0.538714i
$577$	11.9935	+	20.7734i	0.499298	+	0.864809i	1.00000		0.000810545i	$-0.000258004\pi$
$577$	11.9935	+	20.7734i	0.499298	+	0.864809i	−0.500702	+	0.865620i	$0.666925\pi$
$578$	−3.28215	−	5.68485i	−0.136519	−	0.236459i
$579$	25.9989	−	45.0314i	1.08048	−	1.87144i
$580$	36.1927			1.50282
$581$	−7.52803	−	10.7191i	−0.312315	−	0.444703i
$582$	15.6065			0.646912
$583$	−0.187459	+	0.324688i	−0.00776376	+	0.0134472i
$584$	7.68283	+	13.3071i	0.317918	+	0.550650i
$585$	−6.64134	−	11.5031i	−0.274586	−	0.475597i
$586$	12.5772	−	21.7843i	0.519558	−	0.899901i
$587$	20.2547			0.836000			0.418000	−	0.908447i	$-0.362731\pi$
$587$	20.2547			0.836000			0.418000	+	0.908447i	$0.362731\pi$
$588$	−13.8510	−	16.4132i	−0.571204	−	0.676867i
$589$	−15.8695			−0.653890
$590$	−19.2329	+	33.3124i	−0.791808	+	1.37145i
$591$	−3.20151	−	5.54519i	−0.131693	−	0.228098i
$592$	−0.171742	−	0.297466i	−0.00705856	−	0.0122258i
$593$	−20.3398	+	35.2296i	−0.835256	+	1.44671i	0.0585666	+	0.998284i	$0.481347\pi$
$593$	−20.3398	+	35.2296i	−0.835256	+	1.44671i	−0.893822	+	0.448422i	$0.851986\pi$
$594$	0.162760			0.00667814
$595$	−20.1817	−	28.7366i	−0.827370	−	1.17808i
$596$	−14.5459			−0.595824
$597$	−4.11155	+	7.12141i	−0.168274	+	0.291460i
$598$	−2.02807	−	3.51273i	−0.0829341	−	0.143646i
$599$	10.2146	+	17.6923i	0.417359	+	0.722886i	0.995673	−	0.0929277i	$-0.0296226\pi$
$599$	10.2146	+	17.6923i	0.417359	+	0.722886i	−0.578314	+	0.815814i	$0.696289\pi$
$600$	47.4295	−	82.1503i	1.93630	−	3.35377i
$601$	−14.7102			−0.600042			−0.300021	−	0.953933i	$-0.596994\pi$
$601$	−14.7102			−0.600042			−0.300021	+	0.953933i	$0.596994\pi$
$602$	7.25029	−	0.644571i	0.295500	−	0.0262708i
$603$	−35.1448			−1.43120
$604$	12.6326	−	21.8803i	0.514013	−	0.890297i
$605$	2.15910	+	3.73967i	0.0877800	+	0.152039i
$606$	5.08730	+	8.81146i	0.206657	+	0.357941i
$607$	0.814745	−	1.41118i	0.0330695	−	0.0572780i	−0.849017	−	0.528366i	$-0.822805\pi$
$607$	0.814745	−	1.41118i	0.0330695	−	0.0572780i	0.882086	+	0.471088i	$0.156138\pi$
$608$	34.4163			1.39576
$609$	18.5036	−	39.8269i	0.749803	−	1.61387i
$610$	15.1783			0.614552
$611$	3.91671	−	6.78394i	0.158453	−	0.274449i
$612$	−5.88378	−	10.1910i	−0.237838	−	0.411947i
$613$	1.02097	+	1.76838i	0.0412367	+	0.0714241i	0.885907	−	0.463863i	$-0.153537\pi$
$613$	1.02097	+	1.76838i	0.0412367	+	0.0714241i	−0.844670	+	0.535287i	$0.820204\pi$
$614$	−0.726618	+	1.25854i	−0.0293239	+	0.0507905i
$615$	17.4550			0.703853
$616$	−3.14359	+	6.76621i	−0.126659	+	0.272619i
$617$	−16.9937			−0.684140			−0.342070	−	0.939674i	$-0.611128\pi$
$617$	−16.9937			−0.684140			−0.342070	+	0.939674i	$0.611128\pi$
$618$	−17.0572	+	29.5439i	−0.686141	+	1.18843i
$619$	8.62453	+	14.9381i	0.346649	+	0.600414i	0.985652	−	0.168790i	$-0.0539861\pi$
$619$	8.62453	+	14.9381i	0.346649	+	0.600414i	−0.639003	+	0.769204i	$0.720653\pi$
$620$	−7.03026	−	12.1768i	−0.282342	−	0.489031i
$621$	0.437020	−	0.756942i	0.0175370	−	0.0303750i
$622$	−25.6410			−1.02811
$623$	−3.21169	+	0.285528i	−0.128674	+	0.0114395i
$624$	0.0951209			0.00380788
$625$	−46.5014	+	80.5428i	−1.86006	+	3.22171i
$626$	14.3912	+	24.9264i	0.575190	+	0.996258i
$627$	−7.47652	−	12.9497i	−0.298583	−	0.517162i
$628$	−1.15617	+	2.00254i	−0.0461362	+	0.0799102i
$629$	−27.3580			−1.09084
$630$	−17.5534	−	24.9941i	−0.699343	−	0.995789i
$631$	33.8602			1.34795			0.673976	−	0.738753i	$-0.264585\pi$
$631$	33.8602			1.34795			0.673976	+	0.738753i	$0.264585\pi$
$632$	13.6644	−	23.6674i	0.543540	−	0.941439i
$633$	−16.7488	−	29.0098i	−0.665707	−	1.15304i
$634$	−6.28502	−	10.8860i	−0.249610	−	0.432337i
$635$	−17.0291	+	29.4952i	−0.675777	+	1.17048i
$636$	1.15028			0.0456114
$637$	2.37567	−	6.58454i	0.0941275	−	0.260889i
$638$	−5.85228			−0.231694
$639$	21.9077	−	37.9452i	0.866655	−	1.50109i
$640$	15.3914	+	26.6587i	0.608399	+	1.05378i
$641$	18.8702	+	32.6842i	0.745329	+	1.29095i	0.950041	+	0.312126i	$0.101041\pi$
$641$	18.8702	+	32.6842i	0.745329	+	1.29095i	−0.204711	+	0.978822i	$0.565626\pi$
$642$	14.6222	−	25.3265i	0.577094	−	0.999556i
$643$	−12.5479			−0.494841			−0.247420	−	0.968908i	$-0.579583\pi$
$643$	−12.5479			−0.494841			−0.247420	+	0.968908i	$0.579583\pi$
$644$	8.83315	+	12.5774i	0.348075	+	0.495621i
$645$	−33.6947			−1.32673
$646$	8.10219	−	14.0334i	0.318776	−	0.552137i
$647$	−6.28305	−	10.8826i	−0.247012	−	0.427838i	0.715683	−	0.698425i	$-0.246115\pi$
$647$	−6.28305	−	10.8826i	−0.247012	−	0.427838i	−0.962695	+	0.270587i	$0.912782\pi$
$648$	12.3601	+	21.4084i	0.485552	+	0.841002i
$649$	−5.12480	+	8.87642i	−0.201166	+	0.348430i
$650$	11.8604			0.465202
$651$	−16.9937	+	1.51079i	−0.666036	+	0.0592125i
$652$	0.969485			0.0379680
$653$	−4.31018	+	7.46545i	−0.168670	+	0.292146i	−0.937953	−	0.346764i	$-0.887281\pi$
$653$	−4.31018	+	7.46545i	−0.168670	+	0.292146i	0.769282	+	0.638909i	$0.220614\pi$
$654$	−0.224838	−	0.389430i	−0.00879185	−	0.0152279i
$655$	37.8342	+	65.5307i	1.47830	+	2.56050i
$656$	−0.0316407	+	0.0548033i	−0.00123536	+	0.00213971i
$657$	−16.7609			−0.653904
$658$	7.58935	−	16.3352i	0.295864	−	0.636813i
$659$	−26.1704			−1.01946			−0.509728	−	0.860336i	$-0.670254\pi$
$659$	−26.1704			−1.01946			−0.509728	+	0.860336i	$0.670254\pi$
$660$	6.62428	−	11.4736i	0.257850	−	0.446609i
$661$	10.1422	+	17.5667i	0.394484	+	0.683266i	0.993035	−	0.117818i	$-0.0375900\pi$
$661$	10.1422	+	17.5667i	0.394484	+	0.683266i	−0.598551	+	0.801085i	$0.704257\pi$
$662$	2.91708	+	5.05254i	0.113376	+	0.196372i
$663$	3.78812	−	6.56122i	0.147118	−	0.254816i
$664$	13.9608			0.541783
$665$	−29.2020	+	62.8540i	−1.13240	+	2.43737i
$666$	−23.7951			−0.922042
$667$	−15.7137	+	27.2169i	−0.608437	+	1.05384i
$668$	−3.00804	−	5.21008i	−0.116385	−	0.201584i
$669$	21.9389	+	37.9993i	0.848207	+	1.46914i
$670$	21.4396	−	37.1344i	0.828283	−	1.43463i
$671$	4.04441			0.156133
$672$	36.8544	−	3.27646i	1.42169	−	0.126392i
$673$	15.3876			0.593150			0.296575	−	0.955010i	$-0.404156\pi$
$673$	15.3876			0.593150			0.296575	+	0.955010i	$0.404156\pi$
$674$	2.84013	−	4.91925i	0.109398	−	0.189483i
$675$	1.27787	+	2.21334i	0.0491852	+	0.0851913i
$676$	0.622340	+	1.07792i	0.0239362	+	0.0414586i
$677$	1.96267	−	3.39944i	0.0754314	−	0.130651i	−0.825842	−	0.563901i	$-0.809300\pi$
$677$	1.96267	−	3.39944i	0.0754314	−	0.130651i	0.901274	+	0.433250i	$0.142633\pi$
$678$	−17.4958			−0.671922
$679$	−11.0775	−	15.7732i	−0.425116	−	0.605319i
$680$	37.4271			1.43526
$681$	−6.14727	+	10.6474i	−0.235564	+	0.408009i
$682$	1.13678	+	1.96896i	0.0435295	+	0.0753954i
$683$	22.3226	+	38.6640i	0.854152	+	1.47944i	0.877429	+	0.479706i	$0.159257\pi$
$683$	22.3226	+	38.6640i	0.854152	+	1.47944i	−0.0232767	+	0.999729i	$0.507410\pi$
$684$	−11.6127	+	20.1137i	−0.444022	+	0.769068i
$685$	24.4267			0.933296
$686$	4.10041	−	15.5647i	0.156554	−	0.594265i
$687$	38.9066			1.48438
$688$	0.0610785	−	0.105791i	0.00232860	−	0.00403325i
$689$	0.187459	+	0.324688i	0.00714162	+	0.0123696i
$690$	21.5871	+	37.3900i	0.821808	+	1.42341i
$691$	10.6370	−	18.4238i	0.404649	−	0.700873i	−0.589632	−	0.807672i	$-0.700727\pi$
$691$	10.6370	−	18.4238i	0.404649	−	0.700873i	0.994281	+	0.106800i	$0.0340604\pi$
$692$	30.3777			1.15479
$693$	−4.67727	−	6.65992i	−0.177675	−	0.252989i
$694$	−20.6899			−0.785378
$695$	−7.51159	+	13.0105i	−0.284931	+	0.493515i
$696$	23.4032	+	40.5355i	0.887096	+	1.53650i
$697$	2.52014	+	4.36501i	0.0954570	+	0.165336i
$698$	12.1465	−	21.0384i	0.459752	−	0.796314i
$699$	8.64387			0.326941
$700$	−44.7642	+	3.97966i	−1.69193	+	0.150417i
$701$	4.24150			0.160199			0.0800996	−	0.996787i	$-0.474476\pi$
$701$	4.24150			0.160199			0.0800996	+	0.996787i	$0.474476\pi$
$702$	0.0813802	−	0.140955i	0.00307150	−	0.00531999i
$703$	26.9980	+	46.7618i	1.01825	+	1.76366i
$704$	−2.42676	−	4.20326i	−0.0914618	−	0.158416i
$705$	−41.6900	+	72.2092i	−1.57014	+	2.71956i
$706$	−6.43290			−0.242105
$707$	5.29459	−	11.3960i	0.199123	−	0.428591i
$708$	31.4466			1.18183
$709$	7.79957	−	13.5092i	0.292919	−	0.507350i	−0.681580	−	0.731744i	$-0.738707\pi$
$709$	7.79957	−	13.5092i	0.292919	−	0.507350i	0.974499	+	0.224393i	$0.0720401\pi$
$710$	26.7290	+	46.2959i	1.00312	+	1.73746i
$711$	14.9051	+	25.8164i	0.558986	+	0.968192i
$712$	1.71831	−	2.97620i	0.0643964	−	0.111538i
$713$	12.2093			0.457240
$714$	7.34019	−	15.7989i	0.274700	−	0.591260i
$715$	4.31820			0.161492
$716$	−4.76092	+	8.24616i	−0.177924	+	0.308173i
$717$	−17.7434	−	30.7326i	−0.662641	−	1.14773i
$718$	9.10386	+	15.7683i	0.339753	+	0.588469i
$719$	12.6112	−	21.8432i	0.470318	−	0.814614i	−0.529106	−	0.848556i	$-0.677473\pi$
$719$	12.6112	−	21.8432i	0.470318	−	0.814614i	0.999424	+	0.0339416i	$0.0108060\pi$
$720$	−0.512571			−0.0191024
$721$	41.9666	−	3.73095i	1.56292	−	0.138948i
$722$	−15.4695			−0.575714
$723$	12.8288	−	22.2201i	0.477108	−	0.826375i
$724$	5.79416	+	10.0358i	0.215338	+	0.372977i
$725$	−45.9476	−	79.5836i	−1.70645	−	2.95566i
$726$	−1.07113	+	1.85526i	−0.0397535	+	0.0688550i
$727$	2.90577			0.107769			0.0538844	−	0.998547i	$-0.482840\pi$
$727$	2.90577			0.107769			0.0538844	+	0.998547i	$0.482840\pi$
$728$	4.28792	+	6.10553i	0.158921	+	0.226286i
$729$	−28.3498			−1.04999
$730$	10.2247	−	17.7098i	0.378435	−	0.655468i
$731$	−4.86481	−	8.42610i	−0.179932	−	0.311651i
$732$	−6.20428	−	10.7461i	−0.229317	−	0.397188i
$733$	−8.32294	+	14.4158i	−0.307415	+	0.532458i	−0.977796	−	0.209559i	$-0.932797\pi$
$733$	−8.32294	+	14.4158i	−0.307415	+	0.532458i	0.670381	+	0.742017i	$0.266131\pi$
$734$	−9.08920			−0.335488
$735$	−25.2870	+	70.0869i	−0.932725	+	2.58519i
$736$	−26.4783			−0.976004
$737$	5.71278	−	9.89483i	0.210433	−	0.364481i
$738$	2.19193	+	3.79654i	0.0806861	+	0.139752i
$739$	−6.79770	−	11.7740i	−0.250057	−	0.433112i	0.713484	−	0.700672i	$-0.247116\pi$
$739$	−6.79770	−	11.7740i	−0.250057	−	0.433112i	−0.963541	+	0.267559i	$0.913783\pi$
$740$	−23.9205	+	41.4315i	−0.879335	+	1.52305i
$741$	−14.9530			−0.549314
$742$	0.495463	+	0.705485i	0.0181890	+	0.0258992i
$743$	−32.0224			−1.17479			−0.587394	−	0.809301i	$-0.699846\pi$
$743$	−32.0224			−1.17479			−0.587394	+	0.809301i	$0.699846\pi$
$744$	9.09193	−	15.7477i	0.333326	−	0.577338i
$745$	25.2323	+	43.7036i	0.924439	+	1.60118i
$746$	−10.5824	−	18.3292i	−0.387448	−	0.671080i
$747$	−7.61421	+	13.1882i	−0.278589	+	0.482531i
$748$	3.82563			0.139879
$749$	−35.9758	+	3.19835i	−1.31453	+	0.116865i
$750$	−79.9900			−2.92082
$751$	−24.7409	+	42.8525i	−0.902808	+	1.56371i	−0.0789741	+	0.996877i	$0.525164\pi$
$751$	−24.7409	+	42.8525i	−0.902808	+	1.56371i	−0.823833	+	0.566832i	$0.808169\pi$
$752$	−0.151143	−	0.261788i	−0.00551163	−	0.00954642i
$753$	−25.9181	−	44.8915i	−0.944509	−	1.63594i
$754$	−2.92614	+	5.06823i	−0.106564	+	0.184574i
$755$	−87.6533			−3.19003
$756$	−0.259854	+	0.559306i	−0.00945079	+	0.0203418i
$757$	4.26919			0.155166			0.0775832	−	0.996986i	$-0.475280\pi$
$757$	4.26919			0.155166			0.0775832	+	0.996986i	$0.475280\pi$
$758$	9.64014	−	16.6972i	0.350146	−	0.606470i
$759$	5.75210	+	9.96293i	0.208788	+	0.361631i
$760$	−36.9345	−	63.9724i	−1.33975	−	2.32052i
$761$	9.85280	−	17.0656i	0.357164	−	0.618626i	−0.630322	−	0.776334i	$-0.717077\pi$
$761$	9.85280	−	17.0656i	0.357164	−	0.618626i	0.987486	+	0.157708i	$0.0504104\pi$
$762$	−16.8963			−0.612087
$763$	−0.233999	+	0.503656i	−0.00847133	+	0.0182336i
$764$	6.45008			0.233356
$765$	−20.4128	+	35.3559i	−0.738025	+	1.27830i
$766$	−13.6383	−	23.6222i	−0.492772	−	0.853506i
$767$	5.12480	+	8.87642i	0.185046	+	0.320509i
$768$	−19.5994	+	33.9471i	−0.707231	+	1.22496i
$769$	32.8588			1.18492			0.592459	−	0.805601i	$-0.298157\pi$
$769$	32.8588			1.18492			0.592459	+	0.805601i	$0.298157\pi$
$770$	9.89027	−	0.879272i	0.356420	−	0.0316868i
$771$	44.0075			1.58489
$772$	13.1282	−	22.7387i	0.472494	−	0.818384i
$773$	−26.7680	−	46.3635i	−0.962777	−	1.66758i	−0.715472	−	0.698641i	$-0.753788\pi$
$773$	−26.7680	−	46.3635i	−0.962777	−	1.66758i	−0.247305	−	0.968938i	$-0.579545\pi$
$774$	−4.23125	−	7.32874i	−0.152089	−	0.263426i
$775$	−17.8502	+	30.9175i	−0.641199	+	1.11059i
$776$	20.5433			0.737462
$777$	33.3624	+	47.5044i	1.19687	+	1.70421i
$778$	0.625391			0.0224213
$779$	4.97393	−	8.61511i	0.178210	−	0.308668i
$780$	−6.62428	−	11.4736i	−0.237187	−	0.410821i
$781$	7.12219	+	12.3360i	0.254852	+	0.441417i
$782$	−6.23346	+	10.7967i	−0.222908	+	0.386088i
$783$	−1.26108			−0.0450674
$784$	−0.174213	−	0.206440i	−0.00622191	−	0.00737286i
$785$	8.02226			0.286327
$786$	−18.7696	+	32.5099i	−0.669489	+	1.15959i
$787$	1.30773	+	2.26506i	0.0466156	+	0.0807406i	0.888392	−	0.459086i	$-0.151823\pi$
$787$	1.30773	+	2.26506i	0.0466156	+	0.0807406i	−0.841776	+	0.539827i	$0.818490\pi$
$788$	−1.61661	−	2.80005i	−0.0575894	−	0.0997477i
$789$	30.0242	−	52.0035i	1.06889	−	1.85137i
$790$	−36.3707			−1.29401
$791$	12.4185	+	17.6826i	0.441551	+	0.628721i
$792$	8.67402			0.308218
$793$	2.02221	−	3.50256i	0.0718106	−	0.124380i
$794$	2.00559	+	3.47379i	0.0711758	+	0.123280i
$795$	−1.99534	−	3.45603i	−0.0707675	−	0.122573i
$796$	−2.07613	+	3.59597i	−0.0735866	+	0.127456i
$797$	−13.2158			−0.468126			−0.234063	−	0.972221i	$-0.575202\pi$
$797$	−13.2158			−0.468126			−0.234063	+	0.972221i	$0.575202\pi$
$798$	−34.2479	+	3.04474i	−1.21236	+	0.107783i
$799$	−24.0767			−0.851772
$800$	38.7120	−	67.0511i	1.36868	−	2.37062i
$801$	1.87434	+	3.24644i	0.0662264	+	0.114707i
$802$	8.23614	+	14.2654i	0.290828	+	0.503729i
$803$	2.72448	−	4.71894i	0.0961449	−	0.166528i
$804$	−35.0545			−1.23628
$805$	22.4667	−	48.3571i	0.791847	−	1.70436i
$806$	2.27356			0.0800827
$807$	−32.2899	+	55.9278i	−1.13666	+	1.96875i
$808$	6.69655	+	11.5988i	0.235584	+	0.408043i
$809$	−9.40866	−	16.2963i	−0.330791	−	0.572946i	0.651876	−	0.758325i	$-0.273982\pi$
$809$	−9.40866	−	16.2963i	−0.330791	−	0.572946i	−0.982667	+	0.185379i	$0.940649\pi$
$810$	16.4496	−	28.4915i	0.577979	−	1.00109i
$811$	6.22115			0.218454			0.109227	−	0.994017i	$-0.465162\pi$
$811$	6.22115			0.218454			0.109227	+	0.994017i	$0.465162\pi$
$812$	9.34342	−	20.1106i	0.327890	−	0.705745i
$813$	−14.6626			−0.514241
$814$	3.86790	−	6.69939i	0.135570	−	0.234814i
$815$	−1.68173	−	2.91284i	−0.0589085	−	0.102032i
$816$	−0.146181	−	0.253193i	−0.00511737	−	0.00886354i
$817$	−9.60156	+	16.6304i	−0.335916	+	0.581824i
$818$	−10.0868			−0.352678
$819$	−8.10630	+	0.720672i	−0.283257	+	0.0251823i
$820$	8.81392			0.307796
$821$	3.87601	−	6.71344i	0.135274	−	0.234301i	−0.790428	−	0.612555i	$-0.790142\pi$
$821$	3.87601	−	6.71344i	0.135274	−	0.234301i	0.925702	+	0.378254i	$0.123475\pi$
$822$	6.05906	+	10.4946i	0.211334	+	0.366041i
$823$	−7.49234	−	12.9771i	−0.261166	−	0.452354i	0.705386	−	0.708824i	$-0.250774\pi$
$823$	−7.49234	−	12.9771i	−0.261166	−	0.452354i	−0.966552	+	0.256470i	$0.917440\pi$
$824$	−22.4529	+	38.8895i	−0.782182	+	1.35478i
$825$	−33.6389			−1.17115
$826$	13.5451	+	19.2867i	0.471294	+	0.671072i
$827$	0.496348			0.0172597			0.00862986	−	0.999963i	$-0.497253\pi$
$827$	0.496348			0.0172597			0.00862986	+	0.999963i	$0.497253\pi$
$828$	8.93427	−	15.4746i	0.310487	−	0.537780i
$829$	10.8565	+	18.8040i	0.377062	+	0.653091i	0.990633	−	0.136548i	$-0.0436009\pi$
$829$	10.8565	+	18.8040i	0.377062	+	0.653091i	−0.613571	+	0.789639i	$0.710268\pi$
$830$	−9.28989	−	16.0906i	−0.322457	−	0.558511i
$831$	9.42021	−	16.3163i	0.326783	−	0.566006i
$832$	−4.85351			−0.168265
$833$	−21.1777	+	3.79551i	−0.733763	+	0.131507i
$834$	−7.45302			−0.258077
$835$	−10.4359	+	18.0755i	−0.361148	+	0.625527i
$836$	−3.77528	−	6.53898i	−0.130571	−	0.226155i
$837$	0.244959	+	0.424282i	0.00846704	+	0.0146653i
$838$	−5.23579	+	9.06865i	−0.180867	+	0.313271i
$839$	−27.3078			−0.942771			−0.471386	−	0.881927i	$-0.656246\pi$
$839$	−27.3078			−0.942771			−0.471386	+	0.881927i	$0.656246\pi$
$840$	−45.6413	−	64.9882i	−1.57477	−	2.24231i
$841$	16.3440			0.563586
$842$	−8.24412	+	14.2792i	−0.284111	+	0.492095i
$843$	−3.89358	−	6.74388i	−0.134102	−	0.232272i
$844$	−8.45736	−	14.6486i	−0.291114	−	0.504225i
$845$	2.15910	−	3.73967i	0.0742753	−	0.128649i
$846$	−20.9411			−0.719970
$847$	2.63536	−	0.234291i	0.0905519	−	0.00805032i
$848$	0.0144679			0.000496828
$849$	−36.3805	+	63.0128i	−1.24857	+	2.16260i
$850$	−18.2270	−	31.5700i	−0.625180	−	1.08284i
$851$	−20.7710	−	35.9765i	−0.712021	−	1.23326i
$852$	21.8514	−	37.8478i	0.748617	−	1.29664i
$853$	4.39310			0.150417			0.0752084	−	0.997168i	$-0.476038\pi$
$853$	4.39310			0.150417			0.0752084	+	0.997168i	$0.476038\pi$
$854$	3.91840	−	8.43391i	0.134085	−	0.288603i
$855$	80.5763			2.75565
$856$	19.2477	−	33.3379i	0.657872	−	1.13947i
$857$	26.8932	+	46.5804i	0.918654	+	1.59116i	0.801461	+	0.598047i	$0.204056\pi$
$857$	26.8932	+	46.5804i	0.918654	+	1.59116i	0.117193	+	0.993109i	$0.462610\pi$
$858$	1.07113	+	1.85526i	0.0365679	+	0.0633374i
$859$	24.6850	−	42.7556i	0.842240	−	1.45880i	−0.0457561	−	0.998953i	$-0.514570\pi$
$859$	24.6850	−	42.7556i	0.842240	−	1.45880i	0.887996	−	0.459850i	$-0.152097\pi$
$860$	−17.0142			−0.580179
$861$	4.50614	−	9.69895i	0.153569	−	0.330539i
$862$	−7.10029			−0.241837
$863$	−7.80233	+	13.5140i	−0.265595	+	0.460023i	−0.967719	−	0.252031i	$-0.918902\pi$
$863$	−7.80233	+	13.5140i	−0.265595	+	0.460023i	0.702125	+	0.712054i	$0.252235\pi$
$864$	−0.531246	−	0.920145i	−0.0180734	−	0.0313040i
$865$	−52.6950	−	91.2704i	−1.79168	−	3.10329i
$866$	12.7838	−	22.1422i	0.434412	−	0.752424i
$867$	18.6179			0.632297
$868$	−8.58100	+	0.762875i	−0.291258	+	0.0258937i
$869$	−9.69132			−0.328755
$870$	31.1463	−	53.9470i	1.05596	−	1.82897i
$871$	−5.71278	−	9.89483i	−0.193570	−	0.335273i
$872$	−0.295960	−	0.512618i	−0.0100225	−	0.0173594i
$873$	−11.2043	+	19.4065i	−0.379209	+	0.656810i
$874$	24.6057			0.832299
$875$	56.7769	+	80.8441i	1.91941	+	2.73303i
$876$	−16.7178			−0.564843
$877$	−3.43438	+	5.94851i	−0.115971	+	0.200867i	−0.918167	−	0.396193i	$-0.870331\pi$
$877$	−3.43438	+	5.94851i	−0.115971	+	0.200867i	0.802197	+	0.597060i	$0.203665\pi$
$878$	14.3310	+	24.8220i	0.483648	+	0.837703i
$879$	35.6718	+	61.7854i	1.20318	+	2.08397i
$880$	0.0833184	−	0.144312i	0.00280866	−	0.00486475i
$881$	17.1117			0.576509			0.288255	−	0.957554i	$-0.406925\pi$
$881$	17.1117			0.576509			0.288255	+	0.957554i	$0.406925\pi$
$882$	−18.4196	+	3.30121i	−0.620222	+	0.111157i
$883$	10.0024			0.336606			0.168303	−	0.985735i	$-0.446171\pi$
$883$	10.0024			0.336606			0.168303	+	0.985735i	$0.446171\pi$
$884$	1.91282	−	3.31310i	0.0643350	−	0.111431i
$885$	−54.5492	−	94.4820i	−1.83365	−	3.17598i
$886$	10.9915	+	19.0378i	0.369266	+	0.639587i
$887$	11.4019	−	19.7487i	0.382839	−	0.663096i	−0.608628	−	0.793456i	$-0.708280\pi$
$887$	11.4019	−	19.7487i	0.382839	−	0.663096i	0.991467	+	0.130360i	$0.0416132\pi$
$888$	−61.8707			−2.07624
$889$	11.9930	+	17.0767i	0.402231	+	0.572734i
$890$	−4.57365			−0.153309
$891$	4.38315	−	7.59184i	0.146841	−	0.254336i
$892$	11.0781	+	19.1878i	0.370922	+	0.642455i
$893$	23.7598	+	41.1532i	0.795091	+	1.37714i
$894$	−12.5178	+	21.6814i	−0.418657	+	0.725135i
$895$	33.0344			1.10422
$896$	18.7865	−	1.67017i	0.627612	−	0.0557965i
$897$	11.5042			0.384114
$898$	−2.00125	+	3.46627i	−0.0667826	+	0.115671i
$899$	−8.80787	−	15.2557i	−0.293759	−	0.508805i
$900$	26.1243	+	45.2485i	0.870809	+	1.50828i
$901$	0.576172	−	0.997958i	0.0191951	−	0.0332468i
$902$	−1.42519			−0.0474538
$903$	−8.69854	+	18.7226i	−0.289469	+	0.623050i
$904$	−23.0302			−0.765972
$905$	20.1018	−	34.8174i	0.668207	−	1.15737i
$906$	−21.7425	−	37.6590i	−0.722345	−	1.25114i
$907$	23.0726	+	39.9630i	0.766114	+	1.32695i	0.939655	+	0.342122i	$0.111146\pi$
$907$	23.0726	+	39.9630i	0.766114	+	1.32695i	−0.173541	+	0.984827i	$0.555521\pi$
$908$	−3.10407	+	5.37641i	−0.103012	+	0.178423i
$909$	−14.6092			−0.484557
$910$	4.18366	−	9.00486i	0.138687	−	0.298508i
$911$	−49.7516			−1.64835			−0.824173	−	0.566338i	$-0.808360\pi$
$911$	−49.7516			−1.64835			−0.824173	+	0.566338i	$0.808360\pi$
$912$	−0.288514	+	0.499721i	−0.00955366	+	0.0165474i
$913$	−2.47538	−	4.28749i	−0.0819231	−	0.141895i
$914$	−1.04998	−	1.81862i	−0.0347304	−	0.0601548i
$915$	−21.5247	+	37.2818i	−0.711583	+	1.23250i
$916$	19.6459			0.649120
$917$	46.1797	−	4.10550i	1.52499	−	0.135576i
$918$	−0.500258			−0.0165110
$919$	−3.91102	+	6.77408i	−0.129013	+	0.223456i	−0.923294	−	0.384093i	$-0.874514\pi$
$919$	−3.91102	+	6.77408i	−0.129013	+	0.223456i	0.794282	+	0.607550i	$0.207847\pi$
$920$	28.4157	+	49.2175i	0.936839	+	1.62265i
$921$	−2.06086	−	3.56952i	−0.0679077	−	0.117620i
$922$	−5.93314	+	10.2765i	−0.195397	+	0.338438i
$923$	14.2444			0.468860
$924$	−4.66525	−	6.64281i	−0.153476	−	0.218532i
$925$	121.471			3.99394
$926$	−4.66257	+	8.07580i	−0.153221	+	0.265387i
$927$	−24.4916	−	42.4207i	−0.804410	−	1.39328i
$928$	19.1017	+	33.0851i	0.627044	+	1.08607i
$929$	16.8475	−	29.1806i	0.552747	−	0.957386i	−0.445328	−	0.895368i	$-0.646913\pi$
$929$	16.8475	−	29.1806i	0.552747	−	0.957386i	0.998075	−	0.0620185i	$-0.0197538\pi$
$930$	−24.2001			−0.793553
$931$	27.3864	+	32.4525i	0.897554	+	1.06359i
$932$	4.36474			0.142972
$933$	36.3620	−	62.9808i	1.19044	−	2.06190i
$934$	−0.873122	−	1.51229i	−0.0285694	−	0.0494837i
$935$	−6.63619	−	11.4942i	−0.217027	−	0.375901i
$936$	4.33701	−	7.51192i	0.141760	−	0.245535i
$937$	2.95506			0.0965376			0.0482688	−	0.998834i	$-0.484630\pi$
$937$	2.95506			0.0965376			0.0482688	+	0.998834i	$0.484630\pi$
$938$	−15.0991	−	21.4995i	−0.493005	−	0.701985i
$939$	−81.6339			−2.66402
$940$	−21.0514	+	36.4622i	−0.686622	+	1.18926i
$941$	−27.2236	−	47.1527i	−0.887465	−	1.53714i	−0.842862	−	0.538131i	$-0.819131\pi$
$941$	−27.2236	−	47.1527i	−0.887465	−	1.53714i	−0.0446039	−	0.999005i	$-0.514203\pi$
$942$	1.98993	+	3.44665i	0.0648353	+	0.112298i
$943$	−3.82672	+	6.62808i	−0.124615	+	0.215840i
$944$	0.395526			0.0128733
$945$	2.13121	−	0.189470i	0.0693282	−	0.00616347i
$946$	2.75116			0.0894480
$947$	8.49825	−	14.7194i	0.276156	−	0.478316i	−0.694270	−	0.719715i	$-0.744273\pi$
$947$	8.49825	−	14.7194i	0.276156	−	0.478316i	0.970426	+	0.241398i	$0.0776060\pi$
$948$	14.8668	+	25.7501i	0.482853	+	0.836325i
$949$	−2.72448	−	4.71894i	−0.0884404	−	0.153183i
$950$	−35.9741	+	62.3090i	−1.16715	+	2.02157i
$951$	35.6516			1.15608
$952$	9.66209	−	20.7966i	0.313150	−	0.674020i
$953$	51.8965			1.68109			0.840546	−	0.541739i	$-0.182234\pi$
$953$	51.8965			1.68109			0.840546	+	0.541739i	$0.182234\pi$
$954$	0.501135	−	0.867991i	0.0162248	−	0.0281022i
$955$	−11.1887	−	19.3794i	−0.362058	−	0.627104i
$956$	−8.95958	−	15.5185i	−0.289774	−	0.501903i
$957$	8.29923	−	14.3747i	0.268276	−	0.464668i
$958$	12.6006			0.407108
$959$	6.30594	−	13.5728i	0.203629	−	0.438289i
$960$	51.6615			1.66737
$961$	12.0782	−	20.9201i	0.389620	−	0.674842i
$962$	−3.86790	−	6.69939i	−0.124706	−	0.215997i
$963$	20.9954	+	36.3651i	0.676566	+	1.17185i
$964$	6.47792	−	11.2201i	0.208640	−	0.361375i
$965$	−91.0920			−2.93236
$966$	26.3488	−	2.34249i	0.847760	−	0.0753682i
$967$	−7.32442			−0.235537			−0.117769	−	0.993041i	$-0.537574\pi$
$967$	−7.32442			−0.235537			−0.117769	+	0.993041i	$0.537574\pi$
$968$	−1.40996	+	2.44213i	−0.0453179	+	0.0784929i
$969$	22.9797	+	39.8021i	0.738216	+	1.27863i
$970$	−13.6701	−	23.6773i	−0.438920	−	0.760232i
$971$	13.5367	−	23.4462i	0.434413	−	0.752426i	−0.562834	−	0.826570i	$-0.690289\pi$
$971$	13.5367	−	23.4462i	0.434413	−	0.752426i	0.997248	+	0.0741441i	$0.0236225\pi$
$972$	−27.5950			−0.885109
$973$	5.29016	+	7.53261i	0.169595	+	0.241484i
$974$	−26.9296			−0.862879
$975$	−16.8194	+	29.1321i	−0.538653	+	0.932974i
$976$	−0.0780357	−	0.135162i	−0.00249786	−	0.00432642i
$977$	4.26878	+	7.39374i	0.136570	+	0.236547i	0.926196	−	0.377042i	$-0.123059\pi$
$977$	4.26878	+	7.39374i	0.136570	+	0.236547i	−0.789626	+	0.613589i	$0.789725\pi$
$978$	0.834309	−	1.44507i	0.0266783	−	0.0462081i
$979$	−1.21869			−0.0389496
$980$	−12.7687	+	35.3905i	−0.407882	+	1.13051i
$981$	0.645667			0.0206146
$982$	−4.45734	+	7.72034i	−0.142239	+	0.246366i
$983$	−20.1593	−	34.9170i	−0.642982	−	1.11368i	−0.984764	−	0.173899i	$-0.944363\pi$
$983$	−20.1593	−	34.9170i	−0.642982	−	1.11368i	0.341781	−	0.939780i	$-0.388970\pi$
$984$	5.69933	+	9.87153i	0.181688	+	0.314693i
$985$	−5.60855	+	9.71429i	−0.178703	+	0.309523i
$986$	17.9875			0.572839
$987$	29.3608	+	41.8066i	0.934566	+	1.33072i
$988$	−7.55056			−0.240215
$989$	7.38702	−	12.7947i	0.234893	−	0.406847i
$990$	−5.77193	−	9.99728i	−0.183444	−	0.317735i
$991$	−12.9624	−	22.4515i	−0.411763	−	0.713195i	0.583319	−	0.812243i	$-0.301754\pi$
$991$	−12.9624	−	22.4515i	−0.411763	−	0.713195i	−0.995083	+	0.0990480i	$0.968420\pi$
$992$	7.42084	−	12.8533i	0.235612	−	0.408092i
$993$	−16.5471			−0.525106
$994$	32.6249	−	2.90044i	1.03480	−	0.0919964i
$995$	14.4056			0.456687
$996$	−7.59465	+	13.1543i	−0.240646	+	0.416811i
$997$	6.66791	+	11.5492i	0.211175	+	0.365766i	0.952082	−	0.305841i	$-0.0989377\pi$
$997$	6.66791	+	11.5492i	0.211175	+	0.365766i	−0.740908	+	0.671607i	$0.765604\pi$
$998$	−16.1539	−	27.9794i	−0.511343	−	0.885673i
$999$	0.833475	−	1.44362i	0.0263700	−	0.0456742i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1001.2.i.d.716.17	yes	50
7.2	even	3		7007.2.a.bh.1.9		25
7.4	even	3	inner	1001.2.i.d.144.17	✓	50
7.5	odd	6		7007.2.a.bi.1.9		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1001.2.i.d.144.17	✓	50	7.4	even	3	inner
1001.2.i.d.716.17	yes	50	1.1	even	1	trivial
7007.2.a.bh.1.9		25	7.2	even	3
7007.2.a.bi.1.9		25	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1001 = 7 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1001.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.434546 - 0.752655i) q^{2} +(1.23247 + 2.13471i) q^{3} +(0.622340 + 1.07792i) q^{4} +(2.15910 - 3.73967i) q^{5} +2.14227 q^{6} +(-1.52058 - 2.16514i) q^{7} +2.81992 q^{8} +(-1.53799 + 2.66387i) q^{9} +O(q^{10})\)	\(q+(0.434546 - 0.752655i) q^{2} +(1.23247 + 2.13471i) q^{3} +(0.622340 + 1.07792i) q^{4} +(2.15910 - 3.73967i) q^{5} +2.14227 q^{6} +(-1.52058 - 2.16514i) q^{7} +2.81992 q^{8} +(-1.53799 + 2.66387i) q^{9} +(-1.87646 - 3.25012i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(-1.53404 + 2.65703i) q^{12} -1.00000 q^{13} +(-2.29037 + 0.203620i) q^{14} +10.6442 q^{15} +(-0.0192947 + 0.0334194i) q^{16} +(1.53679 + 2.66181i) q^{17} +(1.33665 + 2.31515i) q^{18} +(3.03313 - 5.25354i) q^{19} +5.37478 q^{20} +(2.74787 - 5.91448i) q^{21} -0.869091 q^{22} +(-2.33356 + 4.04184i) q^{23} +(3.47548 + 6.01972i) q^{24} +(-6.82344 - 11.8185i) q^{25} +(-0.434546 + 0.752655i) q^{26} -0.187277 q^{27} +(1.38754 - 2.98653i) q^{28} +6.73380 q^{29} +(4.62537 - 8.01138i) q^{30} +(-1.30801 - 2.26554i) q^{31} +(2.83669 + 4.91330i) q^{32} +(1.23247 - 2.13471i) q^{33} +2.67123 q^{34} +(-11.3800 + 1.01171i) q^{35} -3.82861 q^{36} +(-4.45051 + 7.70850i) q^{37} +(-2.63607 - 4.56581i) q^{38} +(-1.23247 - 2.13471i) q^{39} +(6.08850 - 10.5456i) q^{40} +1.63987 q^{41} +(-3.25749 - 4.63831i) q^{42} -3.16556 q^{43} +(0.622340 - 1.07792i) q^{44} +(6.64134 + 11.5031i) q^{45} +(2.02807 + 3.51273i) q^{46} +(-3.91671 + 6.78394i) q^{47} -0.0951209 q^{48} +(-2.37567 + 6.58454i) q^{49} -11.8604 q^{50} +(-3.78812 + 6.56122i) q^{51} +(-0.622340 - 1.07792i) q^{52} +(-0.187459 - 0.324688i) q^{53} +(-0.0813802 + 0.140955i) q^{54} -4.31820 q^{55} +(-4.28792 - 6.10553i) q^{56} +14.9530 q^{57} +(2.92614 - 5.06823i) q^{58} +(-5.12480 - 8.87642i) q^{59} +(6.62428 + 11.4736i) q^{60} +(-2.02221 + 3.50256i) q^{61} -2.27356 q^{62} +(8.10630 - 0.720672i) q^{63} +4.85351 q^{64} +(-2.15910 + 3.73967i) q^{65} +(-1.07113 - 1.85526i) q^{66} +(5.71278 + 9.89483i) q^{67} +(-1.91282 + 3.31310i) q^{68} -11.5042 q^{69} +(-4.18366 + 9.00486i) q^{70} -14.2444 q^{71} +(-4.33701 + 7.51192i) q^{72} +(2.72448 + 4.71894i) q^{73} +(3.86790 + 6.69939i) q^{74} +(16.8194 - 29.1321i) q^{75} +7.55056 q^{76} +(-1.11478 + 2.39943i) q^{77} -2.14227 q^{78} +(4.84566 - 8.39293i) q^{79} +(0.0833184 + 0.144312i) q^{80} +(4.38315 + 7.59184i) q^{81} +(0.712597 - 1.23425i) q^{82} +4.95076 q^{83} +(8.08547 - 0.718821i) q^{84} +13.2724 q^{85} +(-1.37558 + 2.38258i) q^{86} +(8.29923 + 14.3747i) q^{87} +(-1.40996 - 2.44213i) q^{88} +(0.609347 - 1.05542i) q^{89} +11.5439 q^{90} +(1.52058 + 2.16514i) q^{91} -5.80907 q^{92} +(3.22418 - 5.58444i) q^{93} +(3.40398 + 5.89586i) q^{94} +(-13.0977 - 22.6859i) q^{95} +(-6.99230 + 12.1110i) q^{96} +7.28506 q^{97} +(3.92355 + 4.64935i) q^{98} +3.07598 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 6 q^{2} + 2 q^{3} - 30 q^{4} + q^{5} + 4 q^{6} + q^{7} + 42 q^{8} - 37 q^{9}+O(q^{10}) \) 50 * q - 6 * q^2 + 2 * q^3 - 30 * q^4 + q^5 + 4 * q^6 + q^7 + 42 * q^8 - 37 * q^9	\( 50 q - 6 q^{2} + 2 q^{3} - 30 q^{4} + q^{5} + 4 q^{6} + q^{7} + 42 q^{8} - 37 q^{9} + 3 q^{10} - 25 q^{11} - 9 q^{12} - 50 q^{13} + 22 q^{14} - 32 q^{16} + q^{17} - 44 q^{18} - 5 q^{19} + 8 q^{20} + 2 q^{21} + 12 q^{22} - 15 q^{23} + 4 q^{24} - 50 q^{25} + 6 q^{26} - 34 q^{27} + 12 q^{28} + 48 q^{29} - q^{30} + 12 q^{31} - 48 q^{32} + 2 q^{33} - 16 q^{34} + 20 q^{35} + 60 q^{36} - 33 q^{37} - 16 q^{38} - 2 q^{39} + 21 q^{40} + 24 q^{41} - 42 q^{42} + 76 q^{43} - 30 q^{44} + 22 q^{45} - 39 q^{46} - 4 q^{47} + 164 q^{48} + 23 q^{49} + 32 q^{50} - 51 q^{51} + 30 q^{52} - 2 q^{53} - 10 q^{54} - 2 q^{55} - 72 q^{56} + 76 q^{57} - 17 q^{58} + 4 q^{59} + 33 q^{60} + 22 q^{61} + 84 q^{62} - 19 q^{63} + 82 q^{64} - q^{65} - 2 q^{66} - 24 q^{67} - 14 q^{68} - 60 q^{69} - 124 q^{70} + 18 q^{71} - 102 q^{72} - 11 q^{73} - 39 q^{74} + 16 q^{75} + 116 q^{76} + q^{77} - 4 q^{78} - 19 q^{79} + 33 q^{80} - 73 q^{81} + 32 q^{82} + 32 q^{83} - 109 q^{84} + 28 q^{85} - 27 q^{86} + 11 q^{87} - 21 q^{88} - 13 q^{89} + 80 q^{90} - q^{91} - 17 q^{93} + 56 q^{94} - 15 q^{95} - 55 q^{96} + 68 q^{97} - 22 q^{98} + 74 q^{99}+O(q^{100}) \) 50 * q - 6 * q^2 + 2 * q^3 - 30 * q^4 + q^5 + 4 * q^6 + q^7 + 42 * q^8 - 37 * q^9 + 3 * q^10 - 25 * q^11 - 9 * q^12 - 50 * q^13 + 22 * q^14 - 32 * q^16 + q^17 - 44 * q^18 - 5 * q^19 + 8 * q^20 + 2 * q^21 + 12 * q^22 - 15 * q^23 + 4 * q^24 - 50 * q^25 + 6 * q^26 - 34 * q^27 + 12 * q^28 + 48 * q^29 - q^30 + 12 * q^31 - 48 * q^32 + 2 * q^33 - 16 * q^34 + 20 * q^35 + 60 * q^36 - 33 * q^37 - 16 * q^38 - 2 * q^39 + 21 * q^40 + 24 * q^41 - 42 * q^42 + 76 * q^43 - 30 * q^44 + 22 * q^45 - 39 * q^46 - 4 * q^47 + 164 * q^48 + 23 * q^49 + 32 * q^50 - 51 * q^51 + 30 * q^52 - 2 * q^53 - 10 * q^54 - 2 * q^55 - 72 * q^56 + 76 * q^57 - 17 * q^58 + 4 * q^59 + 33 * q^60 + 22 * q^61 + 84 * q^62 - 19 * q^63 + 82 * q^64 - q^65 - 2 * q^66 - 24 * q^67 - 14 * q^68 - 60 * q^69 - 124 * q^70 + 18 * q^71 - 102 * q^72 - 11 * q^73 - 39 * q^74 + 16 * q^75 + 116 * q^76 + q^77 - 4 * q^78 - 19 * q^79 + 33 * q^80 - 73 * q^81 + 32 * q^82 + 32 * q^83 - 109 * q^84 + 28 * q^85 - 27 * q^86 + 11 * q^87 - 21 * q^88 - 13 * q^89 + 80 * q^90 - q^91 - 17 * q^93 + 56 * q^94 - 15 * q^95 - 55 * q^96 + 68 * q^97 - 22 * q^98 + 74 * q^99

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