LMFDB - Embedded newform 990.2.t.a.131.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [990,2,Mod(131,990)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(990, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 0, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("990.131"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.t (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,-24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			131.4
Character	$\chi$	$=$	990.131
Dual form			990.2.t.a.461.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.62493 - 0.599680i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(0.293125 + 1.70707i) q^{6} +(-3.18423 + 1.83842i) q^{7} +1.00000 q^{8} +(2.28077 + 1.94887i) q^{9} +1.00000i q^{10} +(0.851809 + 3.20537i) q^{11} +(1.33180 - 1.10739i) q^{12} +(1.88953 + 1.09092i) q^{13} +(3.18423 + 1.83842i) q^{14} +(1.10739 + 1.33180i) q^{15} +(-0.500000 - 0.866025i) q^{16} +1.68359 q^{17} +(0.547388 - 2.94964i) q^{18} -7.86116i q^{19} +(0.866025 - 0.500000i) q^{20} +(6.27660 - 1.07777i) q^{21} +(2.35003 - 2.34038i) q^{22} +(-4.34269 - 2.50725i) q^{23} +(-1.62493 - 0.599680i) q^{24} +(0.500000 + 0.866025i) q^{25} -2.18184i q^{26} +(-2.53738 - 4.53450i) q^{27} -3.67683i q^{28} +(3.65719 + 6.33444i) q^{29} +(0.599680 - 1.62493i) q^{30} +(2.78313 - 4.82052i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.538072 - 5.71931i) q^{33} +(-0.841796 - 1.45803i) q^{34} +3.67683 q^{35} +(-2.82816 + 1.00077i) q^{36} -9.84289 q^{37} +(-6.80796 + 3.93058i) q^{38} +(-2.41614 - 2.90578i) q^{39} +(-0.866025 - 0.500000i) q^{40} +(-2.91945 + 5.05664i) q^{41} +(-4.07168 - 4.89681i) q^{42} +(-2.89355 + 1.67059i) q^{43} +(-3.20184 - 0.864999i) q^{44} +(-1.00077 - 2.82816i) q^{45} +5.01450i q^{46} +(4.46479 - 2.57775i) q^{47} +(0.293125 + 1.70707i) q^{48} +(3.25955 - 5.64570i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-2.73571 - 1.00962i) q^{51} +(-1.88953 + 1.09092i) q^{52} -4.66886i q^{53} +(-2.65830 + 4.46469i) q^{54} +(0.864999 - 3.20184i) q^{55} +(-3.18423 + 1.83842i) q^{56} +(-4.71418 + 12.7738i) q^{57} +(3.65719 - 6.33444i) q^{58} +(-12.1117 - 6.99268i) q^{59} +(-1.70707 + 0.293125i) q^{60} +(7.93110 - 4.57903i) q^{61} -5.56625 q^{62} +(-10.8453 - 2.01265i) q^{63} +1.00000 q^{64} +(-1.09092 - 1.88953i) q^{65} +(-5.22210 + 2.39367i) q^{66} +(6.87891 - 11.9146i) q^{67} +(-0.841796 + 1.45803i) q^{68} +(5.55299 + 6.67832i) q^{69} +(-1.83842 - 3.18423i) q^{70} +7.93786i q^{71} +(2.28077 + 1.94887i) q^{72} +4.80281i q^{73} +(4.92145 + 8.52419i) q^{74} +(-0.293125 - 1.70707i) q^{75} +(6.80796 + 3.93058i) q^{76} +(-8.60517 - 8.64067i) q^{77} +(-1.30841 + 3.54533i) q^{78} +(12.4035 - 7.16118i) q^{79} +1.00000i q^{80} +(1.40380 + 8.88984i) q^{81} +5.83891 q^{82} +(-2.79143 - 4.83489i) q^{83} +(-2.20492 + 5.97458i) q^{84} +(-1.45803 - 0.841796i) q^{85} +(2.89355 + 1.67059i) q^{86} +(-2.14403 - 12.4861i) q^{87} +(0.851809 + 3.20537i) q^{88} -12.9841i q^{89} +(-1.94887 + 2.28077i) q^{90} -8.02226 q^{91} +(4.34269 - 2.50725i) q^{92} +(-7.41314 + 6.16400i) q^{93} +(-4.46479 - 2.57775i) q^{94} +(-3.93058 + 6.80796i) q^{95} +(1.33180 - 1.10739i) q^{96} +(-7.38202 - 12.7860i) q^{97} -6.51910 q^{98} +(-4.30408 + 8.97078i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 24 q^{2} - 2 q^{3} - 24 q^{4} - 2 q^{6} + 48 q^{8} + 10 q^{9} - 6 q^{11} + 4 q^{12} + 24 q^{13} - 4 q^{15} - 24 q^{16} - 12 q^{17} - 8 q^{18} - 16 q^{21} + 12 q^{22} + 36 q^{23} - 2 q^{24} + 24 q^{25}+ \cdots - 48 q^{99}+O(q^{100}) $ 48 * q - 24 * q^2 - 2 * q^3 - 24 * q^4 - 2 * q^6 + 48 * q^8 + 10 * q^9 - 6 * q^11 + 4 * q^12 + 24 * q^13 - 4 * q^15 - 24 * q^16 - 12 * q^17 - 8 * q^18 - 16 * q^21 + 12 * q^22 + 36 * q^23 - 2 * q^24 + 24 * q^25 - 8 * q^27 + 8 * q^30 - 24 * q^32 + 2 * q^33 + 6 * q^34 - 2 * q^36 - 6 * q^38 - 40 * q^39 - 6 * q^41 + 8 * q^42 + 30 * q^43 - 6 * q^44 - 2 * q^48 + 24 * q^49 + 24 * q^50 + 22 * q^51 - 24 * q^52 + 22 * q^54 + 40 * q^57 - 54 * q^59 - 4 * q^60 - 38 * q^63 + 48 * q^64 + 8 * q^66 - 6 * q^67 + 6 * q^68 + 76 * q^69 + 10 * q^72 + 2 * q^75 + 6 * q^76 + 6 * q^77 + 32 * q^78 + 10 * q^81 + 12 * q^82 + 36 * q^83 + 8 * q^84 - 30 * q^86 - 44 * q^87 - 6 * q^88 + 24 * q^91 - 36 * q^92 - 68 * q^93 + 4 * q^96 + 6 * q^97 - 48 * q^98 - 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−1.62493	−	0.599680i	−0.938151	−	0.346225i
$3$	−1.62493	−	0.599680i	−0.938151	−	0.346225i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$6$	0.293125	+	1.70707i	0.119668	+	0.696907i
$7$	−3.18423	+	1.83842i	−1.20353	+	0.694856i	−0.961337	−	0.275373i	$-0.911199\pi$
$7$	−3.18423	+	1.83842i	−1.20353	+	0.694856i	−0.242188	+	0.970229i	$0.577865\pi$
$8$	1.00000			0.353553
$9$	2.28077	+	1.94887i	0.760256	+	0.649624i
$10$			1.00000i			0.316228i
$11$	0.851809	+	3.20537i	0.256830	+	0.966457i
$11$	0.851809	+	3.20537i	0.256830	+	0.966457i
$12$	1.33180	−	1.10739i	0.384458	−	0.319675i
$13$	1.88953	+	1.09092i	0.524061	+	0.302567i	0.738595	−	0.674150i	$-0.235490\pi$
$13$	1.88953	+	1.09092i	0.524061	+	0.302567i	−0.214534	+	0.976717i	$0.568823\pi$
$14$	3.18423	+	1.83842i	0.851021	+	0.491337i
$15$	1.10739	+	1.33180i	0.285926	+	0.343870i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.68359			0.408331			0.204166	−	0.978936i	$-0.434552\pi$
$17$	1.68359			0.408331			0.204166	+	0.978936i	$0.434552\pi$
$18$	0.547388	−	2.94964i	0.129021	−	0.695236i
$19$		−	7.86116i		−	1.80347i	−0.432285	−	0.901737i	$-0.642293\pi$
$19$		−	7.86116i		−	1.80347i	0.432285	−	0.901737i	$-0.357707\pi$
$20$	0.866025	−	0.500000i	0.193649	−	0.111803i
$21$	6.27660	−	1.07777i	1.36967	−	0.235189i
$22$	2.35003	−	2.34038i	0.501028	−	0.498970i
$23$	−4.34269	−	2.50725i	−0.905513	−	0.522798i	−0.0265280	−	0.999648i	$-0.508445\pi$
$23$	−4.34269	−	2.50725i	−0.905513	−	0.522798i	−0.878985	+	0.476850i	$0.841778\pi$
$24$	−1.62493	−	0.599680i	−0.331687	−	0.122409i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$		−	2.18184i		−	0.427894i
$27$	−2.53738	−	4.53450i	−0.488319	−	0.872665i
$28$		−	3.67683i		−	0.694856i
$29$	3.65719	+	6.33444i	0.679124	+	1.17628i	0.975245	+	0.221126i	$0.0709733\pi$
$29$	3.65719	+	6.33444i	0.679124	+	1.17628i	−0.296122	+	0.955150i	$0.595693\pi$
$30$	0.599680	−	1.62493i	0.109486	−	0.296670i
$31$	2.78313	−	4.82052i	0.499864	−	0.865790i	−0.500136	−	0.865947i	$-0.666717\pi$
$31$	2.78313	−	4.82052i	0.499864	−	0.865790i	1.00000		0.000156599i	$4.98469e-5\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	0.538072	−	5.71931i	0.0936663	−	0.995604i
$34$	−0.841796	−	1.45803i	−0.144367	−	0.250051i
$35$	3.67683			0.621498
$36$	−2.82816	+	1.00077i	−0.471359	+	0.166795i
$37$	−9.84289			−1.61816			−0.809081	−	0.587698i	$-0.800034\pi$
$37$	−9.84289			−1.61816			−0.809081	+	0.587698i	$0.800034\pi$
$38$	−6.80796	+	3.93058i	−1.10440	+	0.637624i
$39$	−2.41614	−	2.90578i	−0.386892	−	0.465296i
$40$	−0.866025	−	0.500000i	−0.136931	−	0.0790569i
$41$	−2.91945	+	5.05664i	−0.455942	+	0.789715i	−0.998742	−	0.0501472i	$-0.984031\pi$
$41$	−2.91945	+	5.05664i	−0.455942	+	0.789715i	0.542800	+	0.839862i	$0.317364\pi$
$42$	−4.07168	−	4.89681i	−0.628273	−	0.755594i
$43$	−2.89355	+	1.67059i	−0.441262	+	0.254763i	−0.704133	−	0.710068i	$-0.748664\pi$
$43$	−2.89355	+	1.67059i	−0.441262	+	0.254763i	0.262871	+	0.964831i	$0.415331\pi$
$44$	−3.20184	−	0.864999i	−0.482695	−	0.130403i
$45$	−1.00077	−	2.82816i	−0.149186	−	0.421597i
$46$			5.01450i			0.739348i
$47$	4.46479	−	2.57775i	0.651256	−	0.376003i	−0.137681	−	0.990477i	$-0.543965\pi$
$47$	4.46479	−	2.57775i	0.651256	−	0.376003i	0.788937	+	0.614474i	$0.210632\pi$
$48$	0.293125	+	1.70707i	0.0423089	+	0.246394i
$49$	3.25955	−	5.64570i	0.465650	−	0.806529i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	−2.73571	−	1.00962i	−0.383076	−	0.141375i
$52$	−1.88953	+	1.09092i	−0.262030	+	0.151283i
$53$		−	4.66886i		−	0.641317i	−0.947195	−	0.320658i	$-0.896096\pi$
$53$		−	4.66886i		−	0.641317i	0.947195	−	0.320658i	$-0.103904\pi$
$54$	−2.65830	+	4.46469i	−0.361749	+	0.607567i
$55$	0.864999	−	3.20184i	0.116636	−	0.431736i
$56$	−3.18423	+	1.83842i	−0.425511	+	0.245669i
$57$	−4.71418	+	12.7738i	−0.624408	+	1.69193i
$58$	3.65719	−	6.33444i	0.480213	−	0.831753i
$59$	−12.1117	−	6.99268i	−1.57681	−	0.910370i	−0.995301	−	0.0968274i	$-0.969131\pi$
$59$	−12.1117	−	6.99268i	−1.57681	−	0.910370i	−0.581506	−	0.813542i	$-0.697536\pi$
$60$	−1.70707	+	0.293125i	−0.220381	+	0.0378423i
$61$	7.93110	−	4.57903i	1.01547	−	0.586284i	0.102684	−	0.994714i	$-0.467257\pi$
$61$	7.93110	−	4.57903i	1.01547	−	0.586284i	0.912790	+	0.408430i	$0.133924\pi$
$62$	−5.56625			−0.706915
$63$	−10.8453	−	2.01265i	−1.36638	−	0.253570i
$64$	1.00000			0.125000
$65$	−1.09092	−	1.88953i	−0.135312	−	0.234367i
$66$	−5.22210	+	2.39367i	−0.642796	+	0.294640i
$67$	6.87891	−	11.9146i	0.840393	−	1.45560i	−0.0491705	−	0.998790i	$-0.515658\pi$
$67$	6.87891	−	11.9146i	0.840393	−	1.45560i	0.889563	−	0.456812i	$-0.151009\pi$
$68$	−0.841796	+	1.45803i	−0.102083	+	0.176813i
$69$	5.55299	+	6.67832i	0.668502	+	0.803975i
$70$	−1.83842	−	3.18423i	−0.219733	−	0.380588i
$71$			7.93786i			0.942050i	0.882120	+	0.471025i	$0.156116\pi$
$71$			7.93786i			0.942050i	−0.882120	+	0.471025i	$0.843884\pi$
$72$	2.28077	+	1.94887i	0.268791	+	0.229677i
$73$			4.80281i			0.562127i	0.959689	+	0.281063i	$0.0906871\pi$
$73$			4.80281i			0.562127i	−0.959689	+	0.281063i	$0.909313\pi$
$74$	4.92145	+	8.52419i	0.572106	+	0.990917i
$75$	−0.293125	−	1.70707i	−0.0338471	−	0.197115i
$76$	6.80796	+	3.93058i	0.780927	+	0.450868i
$77$	−8.60517	−	8.64067i	−0.980650	−	0.984696i
$78$	−1.30841	+	3.54533i	−0.148148	+	0.401429i
$79$	12.4035	−	7.16118i	1.39551	−	0.805695i	0.401588	−	0.915821i	$-0.368459\pi$
$79$	12.4035	−	7.16118i	1.39551	−	0.805695i	0.993918	+	0.110125i	$0.0351252\pi$
$80$			1.00000i			0.111803i
$81$	1.40380	+	8.88984i	0.155978	+	0.987760i
$82$	5.83891			0.644800
$83$	−2.79143	−	4.83489i	−0.306399	−	0.530698i	0.671173	−	0.741301i	$-0.265791\pi$
$83$	−2.79143	−	4.83489i	−0.306399	−	0.530698i	−0.977572	+	0.210602i	$0.932457\pi$
$84$	−2.20492	+	5.97458i	−0.240577	+	0.651880i
$85$	−1.45803	−	0.841796i	−0.158146	−	0.0913056i
$86$	2.89355	+	1.67059i	0.312019	+	0.180144i
$87$	−2.14403	−	12.4861i	−0.229864	−	1.33866i
$88$	0.851809	+	3.20537i	0.0908031	+	0.341694i
$89$		−	12.9841i		−	1.37631i	−0.725565	−	0.688153i	$-0.758422\pi$
$89$		−	12.9841i		−	1.37631i	0.725565	−	0.688153i	$-0.241578\pi$
$90$	−1.94887	+	2.28077i	−0.205429	+	0.240414i
$91$	−8.02226			−0.840961
$92$	4.34269	−	2.50725i	0.452756	−	0.261399i
$93$	−7.41314	+	6.16400i	−0.768707	+	0.639177i
$94$	−4.46479	−	2.57775i	−0.460508	−	0.265874i
$95$	−3.93058	+	6.80796i	−0.403269	+	0.698482i
$96$	1.33180	−	1.10739i	0.135926	−	0.113022i
$97$	−7.38202	−	12.7860i	−0.749531	−	1.29823i	−0.948048	−	0.318128i	$-0.896946\pi$
$97$	−7.38202	−	12.7860i	−0.749531	−	1.29823i	0.198517	−	0.980097i	$-0.436388\pi$
$98$	−6.51910			−0.658528
$99$	−4.30408	+	8.97078i	−0.432576	+	0.901597i
$100$	−1.00000			−0.100000
$101$	0.670430	+	1.16122i	0.0667103	+	0.115546i	0.897451	−	0.441113i	$-0.145416\pi$
$101$	0.670430	+	1.16122i	0.0667103	+	0.115546i	−0.830741	+	0.556659i	$0.812083\pi$
$102$	0.493503	+	2.87400i	0.0488640	+	0.284569i
$103$	−0.170406	+	0.295152i	−0.0167906	+	0.0290822i	−0.874299	−	0.485388i	$-0.838678\pi$
$103$	−0.170406	+	0.295152i	−0.0167906	+	0.0290822i	0.857508	+	0.514471i	$0.172012\pi$
$104$	1.88953	+	1.09092i	0.185283	+	0.106973i
$105$	−5.97458	−	2.20492i	−0.583059	−	0.215178i
$106$	−4.04335	+	2.33443i	−0.392725	+	0.226740i
$107$	−6.18150			−0.597588			−0.298794	−	0.954318i	$-0.596584\pi$
$107$	−6.18150			−0.597588			−0.298794	+	0.954318i	$0.596584\pi$
$108$	5.19568	+	0.0698151i	0.499955	+	0.00671796i
$109$		−	6.26500i		−	0.600078i	−0.953927	−	0.300039i	$-0.903000\pi$
$109$		−	6.26500i		−	0.600078i	0.953927	−	0.300039i	$-0.0969997\pi$
$110$	−3.20537	+	0.851809i	−0.305620	+	0.0812168i
$111$	15.9940	+	5.90258i	1.51808	+	0.560249i
$112$	3.18423	+	1.83842i	0.300881	+	0.173714i
$113$	1.73318	+	1.00065i	0.163044	+	0.0941336i	0.579302	−	0.815113i	$-0.303325\pi$
$113$	1.73318	+	1.00065i	0.163044	+	0.0941336i	−0.416258	+	0.909247i	$0.636659\pi$
$114$	13.4195	−	2.30430i	1.25685	−	0.215818i
$115$	2.50725	+	4.34269i	0.233802	+	0.404958i
$116$	−7.31439			−0.679124
$117$	2.18351	+	6.17058i	0.201866	+	0.570470i
$118$			13.9854i			1.28746i
$119$	−5.36094	+	3.09514i	−0.491437	+	0.283731i
$120$	1.10739	+	1.33180i	0.101090	+	0.121576i
$121$	−9.54884	+	5.46073i	−0.868077	+	0.496430i
$122$	−7.93110	−	4.57903i	−0.718048	−	0.414565i
$123$	7.77626	−	6.46593i	0.701162	−	0.583013i
$124$	2.78313	+	4.82052i	0.249932	+	0.432895i
$125$		−	1.00000i		−	0.0894427i
$126$	3.67965	+	10.3987i	0.327810	+	0.926386i
$127$		−	16.4881i		−	1.46308i	−0.681797	−	0.731541i	$-0.738801\pi$
$127$		−	16.4881i		−	1.46308i	0.681797	−	0.731541i	$-0.261199\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	5.70362	−	0.979384i	0.502176	−	0.0862299i
$130$	−1.09092	+	1.88953i	−0.0956800	+	0.165723i
$131$	2.63052	−	4.55620i	0.229830	−	0.398077i	−0.727928	−	0.685654i	$-0.759516\pi$
$131$	2.63052	−	4.55620i	0.229830	−	0.398077i	0.957758	+	0.287577i	$0.0928497\pi$
$132$	4.68403	+	3.32564i	0.407692	+	0.289460i
$133$	14.4521	+	25.0317i	1.25315	+	2.17053i
$134$	−13.7578			−1.18849
$135$	−0.0698151	+	5.19568i	−0.00600873	+	0.447173i
$136$	1.68359			0.144367
$137$	1.72788	−	0.997591i	0.147623	−	0.0852300i	−0.424369	−	0.905489i	$-0.639504\pi$
$137$	1.72788	−	0.997591i	0.147623	−	0.0852300i	0.571992	+	0.820259i	$0.306171\pi$
$138$	3.00710	−	8.14819i	0.255981	−	0.693620i
$139$	−13.3236	−	7.69241i	−1.13010	−	0.652462i	−0.186137	−	0.982524i	$-0.559597\pi$
$139$	−13.3236	−	7.69241i	−1.13010	−	0.652462i	−0.943959	+	0.330062i	$0.892930\pi$
$140$	−1.83842	+	3.18423i	−0.155375	+	0.269117i
$141$	−8.80077	+	1.51120i	−0.741158	+	0.127266i
$142$	6.87439	−	3.96893i	0.576886	−	0.333065i
$143$	−1.88729	+	6.98590i	−0.157823	+	0.584190i
$144$	0.547388	−	2.94964i	0.0456156	−	0.245803i
$145$		−	7.31439i		−	0.607427i
$146$	4.15936	−	2.40141i	0.344231	−	0.198742i
$147$	−8.68214	+	7.21916i	−0.716091	+	0.595426i
$148$	4.92145	−	8.52419i	0.404540	−	0.700684i
$149$	10.8574	−	18.8056i	0.889476	−	1.54062i	0.0489799	−	0.998800i	$-0.484403\pi$
$149$	10.8574	−	18.8056i	0.889476	−	1.54062i	0.840496	−	0.541818i	$-0.182264\pi$
$150$	−1.33180	+	1.10739i	−0.108741	+	0.0904178i
$151$	0.961201	−	0.554950i	0.0782214	−	0.0451612i	−0.460379	−	0.887722i	$-0.652287\pi$
$151$	0.961201	−	0.554950i	0.0782214	−	0.0451612i	0.538601	+	0.842561i	$0.318953\pi$
$152$		−	7.86116i		−	0.637624i
$153$	3.83988	+	3.28110i	0.310436	+	0.265261i
$154$	−3.18046	+	11.7726i	−0.256288	+	0.948665i
$155$	−4.82052	+	2.78313i	−0.387193	+	0.223546i
$156$	3.72455	−	0.639551i	0.298202	−	0.0512051i
$157$	11.6455	−	20.1706i	0.929411	−	1.60979i	0.145102	−	0.989417i	$-0.453649\pi$
$157$	11.6455	−	20.1706i	0.929411	−	1.60979i	0.784309	−	0.620371i	$-0.213018\pi$
$158$	−12.4035	−	7.16118i	−0.986771	−	0.569713i
$159$	−2.79982	+	7.58655i	−0.222040	+	0.601652i
$160$	0.866025	−	0.500000i	0.0684653	−	0.0395285i
$161$	18.4375			1.45308
$162$	6.99693	−	5.66065i	0.549731	−	0.444743i
$163$	8.91357			0.698165			0.349082	−	0.937092i	$-0.386493\pi$
$163$	8.91357			0.698165			0.349082	+	0.937092i	$0.386493\pi$
$164$	−2.91945	−	5.05664i	−0.227971	−	0.394857i
$165$	−3.32564	+	4.68403i	−0.258901	+	0.364651i
$166$	−2.79143	+	4.83489i	−0.216657	+	0.375260i
$167$	−5.12001	+	8.86811i	−0.396198	+	0.686235i	−0.993253	−	0.115965i	$-0.963004\pi$
$167$	−5.12001	+	8.86811i	−0.396198	+	0.686235i	0.597055	+	0.802200i	$0.296337\pi$
$168$	6.27660	−	1.07777i	0.484250	−	0.0831518i
$169$	−4.11979	−	7.13568i	−0.316907	−	0.548899i
$170$			1.68359i			0.129126i
$171$	15.3204	−	17.9295i	1.17158	−	1.37110i
$172$		−	3.34118i		−	0.254763i
$173$	6.65243	+	11.5223i	0.505775	+	0.876027i	0.999978	+	0.00668085i	$0.00212660\pi$
$173$	6.65243	+	11.5223i	0.505775	+	0.876027i	−0.494203	+	0.869346i	$0.664540\pi$
$174$	−9.74131	+	8.09986i	−0.738486	+	0.614048i
$175$	−3.18423	−	1.83842i	−0.240705	−	0.138971i
$176$	2.35003	−	2.34038i	0.177140	−	0.176412i
$177$	15.4872	+	18.6257i	1.16409	+	1.40000i
$178$	−11.2445	+	6.49203i	−0.842812	+	0.486598i
$179$			21.7749i			1.62753i	0.581194	+	0.813765i	$0.302586\pi$
$179$			21.7749i			1.62753i	−0.581194	+	0.813765i	$0.697414\pi$
$180$	2.94964	+	0.547388i	0.219853	+	0.0407999i
$181$	17.9379			1.33331			0.666655	−	0.745366i	$-0.267725\pi$
$181$	17.9379			1.33331			0.666655	+	0.745366i	$0.267725\pi$
$182$	4.01113	+	6.94748i	0.297325	+	0.514981i
$183$	−15.6334	+	2.68445i	−1.15565	+	0.198440i
$184$	−4.34269	−	2.50725i	−0.320147	−	0.184837i
$185$	8.52419	+	4.92145i	0.626711	+	0.361832i
$186$	9.04475	+	3.33797i	0.663193	+	0.244752i
$187$	1.43410	+	5.39654i	0.104872	+	0.394634i
$188$			5.15549i			0.376003i
$189$	16.4159	+	9.77414i	1.19408	+	0.710964i
$190$	7.86116			0.570309
$191$	−4.55854	+	2.63187i	−0.329844	+	0.190436i	−0.655772	−	0.754959i	$-0.727657\pi$
$191$	−4.55854	+	2.63187i	−0.329844	+	0.190436i	0.325928	+	0.945395i	$0.394323\pi$
$192$	−1.62493	−	0.599680i	−0.117269	−	0.0432782i
$193$	−2.26126	−	1.30554i	−0.162769	−	0.0939748i	0.416403	−	0.909180i	$-0.363291\pi$
$193$	−2.26126	−	1.30554i	−0.162769	−	0.0939748i	−0.579172	+	0.815205i	$0.696624\pi$
$194$	−7.38202	+	12.7860i	−0.529998	+	0.917984i
$195$	0.639551	+	3.72455i	0.0457992	+	0.266720i
$196$	3.25955	+	5.64570i	0.232825	+	0.403264i
$197$	12.7694			0.909780			0.454890	−	0.890548i	$-0.349679\pi$
$197$	12.7694			0.909780			0.454890	+	0.890548i	$0.349679\pi$
$198$	9.92096	−	0.757946i	0.705052	−	0.0538649i
$199$	−2.16043			−0.153149			−0.0765744	−	0.997064i	$-0.524398\pi$
$199$	−2.16043			−0.153149			−0.0765744	+	0.997064i	$0.524398\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$	−18.3227	+	15.2352i	−1.29238	+	1.07461i
$202$	0.670430	−	1.16122i	0.0471713	−	0.0817031i
$203$	−23.2907	−	13.4469i	−1.63469	−	0.943786i
$204$	2.24221	−	1.86439i	0.156986	−	0.130533i
$205$	5.05664	−	2.91945i	0.353171	−	0.203904i
$206$	0.340812			0.0237455
$207$	−5.01835	−	14.1818i	−0.348800	−	0.985703i
$208$		−	2.18184i		−	0.151283i
$209$	25.1980	−	6.69621i	1.74298	−	0.463186i
$210$	1.07777	+	6.27660i	0.0743733	+	0.433126i
$211$	2.37810	+	1.37300i	0.163715	+	0.0945209i	0.579619	−	0.814888i	$-0.303201\pi$
$211$	2.37810	+	1.37300i	0.163715	+	0.0945209i	−0.415904	+	0.909409i	$0.636535\pi$
$212$	4.04335	+	2.33443i	0.277698	+	0.160329i
$213$	4.76017	−	12.8984i	0.326162	−	0.883786i
$214$	3.09075	+	5.35334i	0.211279	+	0.365947i
$215$	3.34118			0.227867
$216$	−2.53738	−	4.53450i	−0.172647	−	0.308534i
$217$			20.4662i			1.38933i
$218$	−5.42565	+	3.13250i	−0.367471	+	0.212160i
$219$	2.88015	−	7.80422i	0.194623	−	0.527360i
$220$	2.34038	+	2.35003i	0.157788	+	0.158439i
$221$	3.18119	+	1.83666i	0.213990	+	0.123547i
$222$	−2.88520	−	16.8025i	−0.193642	−	1.12771i
$223$	8.12070	+	14.0655i	0.543802	+	0.941893i	0.998681	+	0.0513397i	$0.0163491\pi$
$223$	8.12070	+	14.0655i	0.543802	+	0.941893i	−0.454879	+	0.890553i	$0.650318\pi$
$224$		−	3.67683i		−	0.245669i
$225$	−0.547388	+	2.94964i	−0.0364925	+	0.196643i
$226$		−	2.00131i		−	0.133125i
$227$	−0.0573427	−	0.0993205i	−0.00380597	−	0.00659213i	0.864116	−	0.503292i	$-0.167878\pi$
$227$	−0.0573427	−	0.0993205i	−0.00380597	−	0.00659213i	−0.867922	+	0.496700i	$0.834545\pi$
$228$	−8.70535	−	10.4695i	−0.576526	−	0.693360i
$229$	6.68658	−	11.5815i	0.441862	−	0.765327i	−0.555966	−	0.831205i	$-0.687651\pi$
$229$	6.68658	−	11.5815i	0.441862	−	0.765327i	0.997828	+	0.0658780i	$0.0209848\pi$
$230$	2.50725	−	4.34269i	0.165323	−	0.286348i
$231$	8.80112	+	19.2008i	0.579071	+	1.26332i
$232$	3.65719	+	6.33444i	0.240106	+	0.415877i
$233$	−5.42880			−0.355652			−0.177826	−	0.984062i	$-0.556906\pi$
$233$	−5.42880			−0.355652			−0.177826	+	0.984062i	$0.556906\pi$
$234$	4.25212	−	4.97627i	0.277970	−	0.325309i
$235$	−5.15549			−0.336307
$236$	12.1117	−	6.99268i	0.788403	−	0.455185i
$237$	−24.4492	+	4.19824i	−1.58815	+	0.272705i
$238$	5.36094	+	3.09514i	0.347498	+	0.200628i
$239$	2.95156	−	5.11225i	0.190921	−	0.330684i	−0.754635	−	0.656145i	$-0.772186\pi$
$239$	2.95156	−	5.11225i	0.190921	−	0.330684i	0.945556	+	0.325461i	$0.105519\pi$
$240$	0.599680	−	1.62493i	0.0387092	−	0.104889i
$241$	−25.7690	+	14.8778i	−1.65993	+	0.958361i	−0.687184	+	0.726483i	$0.741154\pi$
$241$	−25.7690	+	14.8778i	−1.65993	+	0.958361i	−0.972745	+	0.231878i	$0.925513\pi$
$242$	9.50355	+	5.53917i	0.610912	+	0.356072i
$243$	3.04998	−	15.2872i	0.195656	−	0.980672i
$244$			9.15805i			0.586284i
$245$	−5.64570	+	3.25955i	−0.360691	+	0.208245i
$246$	−9.48779	−	3.50148i	−0.604920	−	0.223246i
$247$	8.57589	−	14.8539i	0.545671	−	0.945130i
$248$	2.78313	−	4.82052i	0.176729	−	0.306103i
$249$	1.63647	+	9.53030i	0.103707	+	0.603958i
$250$	−0.866025	+	0.500000i	−0.0547723	+	0.0316228i
$251$			2.25143i			0.142109i	0.997472	+	0.0710545i	$0.0226364\pi$
$251$			2.25143i			0.142109i	−0.997472	+	0.0710545i	$0.977364\pi$
$252$	7.16567	−	8.38600i	0.451395	−	0.528268i
$253$	4.33754	−	16.0556i	0.272699	−	1.00941i
$254$	−14.2791	+	8.24405i	−0.895952	+	0.517278i
$255$	1.86439	+	2.24221i	0.116753	+	0.140413i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	18.5247	+	10.6952i	1.15554	+	0.667151i	0.950231	−	0.311546i	$-0.100847\pi$
$257$	18.5247	+	10.6952i	1.15554	+	0.667151i	0.205308	+	0.978697i	$0.434180\pi$
$258$	−3.69998	−	4.44979i	−0.230351	−	0.277032i
$259$	31.3420	−	18.0953i	1.94750	−	1.12439i
$260$	2.18184			0.135312
$261$	−4.00380	+	21.5748i	−0.247829	+	1.33545i
$262$	−5.26104			−0.325028
$263$	3.76673	+	6.52416i	0.232266	+	0.402297i	0.958475	−	0.285178i	$-0.0920526\pi$
$263$	3.76673	+	6.52416i	0.232266	+	0.402297i	−0.726208	+	0.687475i	$0.758719\pi$
$264$	0.538072	−	5.71931i	0.0331160	−	0.351999i
$265$	−2.33443	+	4.04335i	−0.143403	+	0.248381i
$266$	14.4521	−	25.0317i	0.886114	−	1.53479i
$267$	−7.78627	+	21.0981i	−0.476512	+	1.29118i
$268$	6.87891	+	11.9146i	0.420196	+	0.727801i
$269$		−	16.3429i		−	0.996446i	−0.867049	−	0.498223i	$-0.833986\pi$
$269$		−	16.3429i		−	0.996446i	0.867049	−	0.498223i	$-0.166014\pi$
$270$	4.53450	−	2.53738i	0.275961	−	0.154420i
$271$			0.605209i			0.0367638i	0.999831	+	0.0183819i	$0.00585148\pi$
$271$			0.605209i			0.0367638i	−0.999831	+	0.0183819i	$0.994149\pi$
$272$	−0.841796	−	1.45803i	−0.0510414	−	0.0884063i
$273$	13.0356	+	4.81079i	0.788949	+	0.291162i
$274$	−1.72788	−	0.997591i	−0.104385	−	0.0602667i
$275$	−2.35003	+	2.34038i	−0.141712	+	0.141130i
$276$	−8.56009	+	1.46988i	−0.515257	+	0.0884761i
$277$	−10.2745	+	5.93197i	−0.617333	+	0.356418i	−0.775830	−	0.630942i	$-0.782669\pi$
$277$	−10.2745	+	5.93197i	−0.617333	+	0.356418i	0.158497	+	0.987360i	$0.449335\pi$
$278$			15.3848i			0.922720i
$279$	15.7422	−	5.57053i	0.942463	−	0.333499i
$280$	3.67683			0.219733
$281$	4.36042	+	7.55247i	0.260121	+	0.450543i	0.966274	−	0.257517i	$-0.0829042\pi$
$281$	4.36042	+	7.55247i	0.260121	+	0.450543i	−0.706153	+	0.708059i	$0.749571\pi$
$282$	5.70912	+	6.86609i	0.339973	+	0.408870i
$283$	−8.87392	−	5.12336i	−0.527500	−	0.304552i	0.212498	−	0.977162i	$-0.431840\pi$
$283$	−8.87392	−	5.12336i	−0.527500	−	0.304552i	−0.739998	+	0.672609i	$0.765174\pi$
$284$	−6.87439	−	3.96893i	−0.407920	−	0.235513i
$285$	10.4695	−	8.70535i	0.620160	−	0.515660i
$286$	6.99361	−	1.85851i	0.413541	−	0.109896i
$287$		−	21.4687i		−	1.26726i
$288$	−2.82816	+	1.00077i	−0.166651	+	0.0589708i
$289$	−14.1655			−0.833266
$290$	−6.33444	+	3.65719i	−0.371971	+	0.214758i
$291$	4.32771	+	25.2032i	0.253695	+	1.47744i
$292$	−4.15936	−	2.40141i	−0.243408	−	0.140532i
$293$	7.99621	−	13.8498i	0.467143	−	0.809116i	−0.532152	−	0.846649i	$-0.678617\pi$
$293$	7.99621	−	13.8498i	0.467143	−	0.809116i	0.999295	+	0.0375328i	$0.0119499\pi$
$294$	10.5930	+	3.90937i	0.617799	+	0.227999i
$295$	6.99268	+	12.1117i	0.407130	+	0.705169i
$296$	−9.84289			−0.572106
$297$	12.3734	−	11.9958i	0.717978	−	0.696066i
$298$	−21.7149			−1.25791
$299$	−5.47042	−	9.47504i	−0.316362	−	0.547956i
$300$	1.62493	+	0.599680i	0.0938151	+	0.0346225i
$301$	6.14248	−	10.6391i	0.354047	−	0.613227i
$302$	−0.961201	−	0.554950i	−0.0553109	−	0.0319338i
$303$	−0.393039	−	2.28894i	−0.0225795	−	0.131496i
$304$	−6.80796	+	3.93058i	−0.390464	+	0.225434i
$305$	−9.15805			−0.524388
$306$	0.921577	−	4.96599i	0.0526831	−	0.283887i
$307$			16.8203i			0.959986i	0.877272	+	0.479993i	$0.159361\pi$
$307$			16.8203i			0.959986i	−0.877272	+	0.479993i	$0.840639\pi$
$308$	11.7856	−	3.13196i	0.671548	−	0.178460i
$309$	0.453894	−	0.377411i	0.0258211	−	0.0214701i
$310$	4.82052	+	2.78313i	0.273787	+	0.158071i
$311$	6.39007	+	3.68931i	0.362348	+	0.209202i	0.670110	−	0.742262i	$-0.266247\pi$
$311$	6.39007	+	3.68931i	0.362348	+	0.209202i	−0.307762	+	0.951463i	$0.599580\pi$
$312$	−2.41614	−	2.90578i	−0.136787	−	0.164507i
$313$	−12.2973	−	21.2995i	−0.695082	−	1.20392i	−0.970153	−	0.242493i	$-0.922035\pi$
$313$	−12.2973	−	21.2995i	−0.695082	−	1.20392i	0.275071	−	0.961424i	$-0.411299\pi$
$314$	−23.2910			−1.31439
$315$	8.38600	+	7.16567i	0.472498	+	0.403740i
$316$			14.3224i			0.805695i
$317$	−0.940567	+	0.543036i	−0.0528275	+	0.0305000i	−0.526181	−	0.850373i	$-0.676377\pi$
$317$	−0.940567	+	0.543036i	−0.0528275	+	0.0305000i	0.473354	+	0.880872i	$0.343043\pi$
$318$	7.97005	−	1.36856i	0.446938	−	0.0767449i
$319$	−17.1890	+	17.1184i	−0.962401	+	0.958447i
$320$	−0.866025	−	0.500000i	−0.0484123	−	0.0279508i
$321$	10.0445	+	3.70692i	0.560628	+	0.206900i
$322$	−9.21874	−	15.9673i	−0.513740	−	0.889824i
$323$		−	13.2350i		−	0.736414i
$324$	−8.40073	−	3.22919i	−0.466707	−	0.179400i
$325$			2.18184i			0.121027i
$326$	−4.45679	−	7.71938i	−0.246839	−	0.427537i
$327$	−3.75699	+	10.1802i	−0.207762	+	0.562964i
$328$	−2.91945	+	5.05664i	−0.161200	+	0.279206i
$329$	−9.47794	+	16.4163i	−0.522536	+	0.905058i
$330$	5.71931	+	0.538072i	0.314838	+	0.0296199i
$331$	−2.48198	−	4.29891i	−0.136422	−	0.236290i	0.789718	−	0.613470i	$-0.210227\pi$
$331$	−2.48198	−	4.29891i	−0.136422	−	0.236290i	−0.926140	+	0.377181i	$0.876894\pi$
$332$	5.58285			0.306399
$333$	−22.4494	−	19.1825i	−1.23022	−	1.05120i
$334$	10.2400			0.560309
$335$	−11.9146	+	6.87891i	−0.650965	+	0.375835i
$336$	−4.07168	−	4.89681i	−0.222128	−	0.267143i
$337$	−15.0511	−	8.68976i	−0.819886	−	0.473361i	0.0304911	−	0.999535i	$-0.490293\pi$
$337$	−15.0511	−	8.68976i	−0.819886	−	0.473361i	−0.850377	+	0.526174i	$0.823626\pi$
$338$	−4.11979	+	7.13568i	−0.224087	+	0.388130i
$339$	−2.21622	−	2.66534i	−0.120369	−	0.144762i
$340$	1.45803	−	0.841796i	0.0790730	−	0.0456528i
$341$	17.8223	+	4.81480i	0.965129	+	0.260736i
$342$	−23.1876	−	4.30310i	−1.25384	−	0.232685i
$343$		−	1.76821i		−	0.0954742i
$344$	−2.89355	+	1.67059i	−0.156010	+	0.0900722i
$345$	−1.46988	−	8.56009i	−0.0791354	−	0.460860i
$346$	6.65243	−	11.5223i	0.357637	−	0.619445i
$347$	5.68546	−	9.84750i	0.305211	−	0.528641i	−0.672097	−	0.740463i	$-0.734606\pi$
$347$	5.68546	−	9.84750i	0.305211	−	0.528641i	0.977308	+	0.211822i	$0.0679396\pi$
$348$	11.8853	+	4.38629i	0.637121	+	0.235130i
$349$	5.30746	−	3.06426i	0.284102	−	0.164026i	−0.351177	−	0.936309i	$-0.614218\pi$
$349$	5.30746	−	3.06426i	0.284102	−	0.164026i	0.635279	+	0.772283i	$0.280885\pi$
$350$			3.67683i			0.196535i
$351$	0.152325	−	11.3361i	0.00813052	−	0.605079i
$352$	−3.20184	−	0.864999i	−0.170659	−	0.0461046i
$353$	−24.2020	+	13.9730i	−1.28814	+	0.743708i	−0.978322	−	0.207088i	$-0.933601\pi$
$353$	−24.2020	+	13.9730i	−1.28814	+	0.743708i	−0.309818	+	0.950796i	$0.600268\pi$
$354$	8.38674	−	22.7252i	0.445750	−	1.20783i
$355$	3.96893	−	6.87439i	0.210649	−	0.364855i
$356$	11.2445	+	6.49203i	0.595958	+	0.344077i
$357$	10.5672	−	1.81453i	0.559277	−	0.0960349i
$358$	18.8576	−	10.8874i	0.996654	−	0.575419i
$359$	−32.1274			−1.69562			−0.847809	−	0.530301i	$-0.822079\pi$
$359$	−32.1274			−1.69562			−0.847809	+	0.530301i	$0.822079\pi$
$360$	−1.00077	−	2.82816i	−0.0527451	−	0.149057i
$361$	−42.7978			−2.25252
$362$	−8.96893	−	15.5346i	−0.471396	−	0.816483i
$363$	18.7909	−	3.14704i	0.986264	−	0.165177i
$364$	4.01113	−	6.94748i	0.210240	−	0.364147i
$365$	2.40141	−	4.15936i	0.125695	−	0.217711i
$366$	10.1415	+	12.1967i	0.530105	+	0.637532i
$367$	7.97900	+	13.8200i	0.416500	+	0.721400i	0.995585	−	0.0938681i	$-0.0299232\pi$
$367$	7.97900	+	13.8200i	0.416500	+	0.721400i	−0.579084	+	0.815268i	$0.696590\pi$
$368$			5.01450i			0.261399i
$369$	−16.5133	+	5.84339i	−0.859650	+	0.304195i
$370$		−	9.84289i		−	0.511708i
$371$	8.58330	+	14.8667i	0.445623	+	0.771842i
$372$	−1.63161	−	9.50197i	−0.0845949	−	0.492654i
$373$	18.1064	+	10.4537i	0.937513	+	0.541273i	0.889180	−	0.457558i	$-0.151276\pi$
$373$	18.1064	+	10.4537i	0.937513	+	0.541273i	0.0483331	+	0.998831i	$0.484609\pi$
$374$	3.95649	−	3.94024i	0.204585	−	0.203745i
$375$	−0.599680	+	1.62493i	−0.0309673	+	0.0839108i
$376$	4.46479	−	2.57775i	0.230254	−	0.132937i
$377$			15.9588i			0.821921i
$378$	0.256698	−	19.1037i	0.0132031	−	0.982586i
$379$	−15.3751			−0.789767			−0.394884	−	0.918731i	$-0.629215\pi$
$379$	−15.3751			−0.789767			−0.394884	+	0.918731i	$0.629215\pi$
$380$	−3.93058	−	6.80796i	−0.201635	−	0.349241i
$381$	−9.88759	+	26.7920i	−0.506556	+	1.37259i
$382$	4.55854	+	2.63187i	0.233235	+	0.134658i
$383$	−2.05066	−	1.18395i	−0.104784	−	0.0604971i	0.446692	−	0.894688i	$-0.352602\pi$
$383$	−2.05066	−	1.18395i	−0.104784	−	0.0604971i	−0.551476	+	0.834191i	$0.685935\pi$
$384$	0.293125	+	1.70707i	0.0149585	+	0.0871134i
$385$	3.13196	+	11.7856i	0.159619	+	0.600651i
$386$			2.61108i			0.132900i
$387$	−9.85528	−	1.82892i	−0.500972	−	0.0929693i
$388$	14.7640			0.749531
$389$	−30.7171	+	17.7345i	−1.55742	+	0.899176i	−0.559916	+	0.828549i	$0.689167\pi$
$389$	−30.7171	+	17.7345i	−1.55742	+	0.899176i	−0.997503	+	0.0706272i	$0.977500\pi$
$390$	2.90578	−	2.41614i	0.147140	−	0.122346i
$391$	−7.31131	−	4.22119i	−0.369749	−	0.213475i
$392$	3.25955	−	5.64570i	0.164632	−	0.285151i
$393$	−7.00666	+	5.82601i	−0.353439	+	0.293883i
$394$	−6.38468	−	11.0586i	−0.321656	−	0.557124i
$395$	−14.3224			−0.720636
$396$	−5.61688	−	8.21283i	−0.282259	−	0.412710i
$397$	13.9573			0.700495			0.350248	−	0.936657i	$-0.386097\pi$
$397$	13.9573			0.700495			0.350248	+	0.936657i	$0.386097\pi$
$398$	1.08022	+	1.87099i	0.0541463	+	0.0937842i
$399$	−8.47253	−	49.3414i	−0.424157	−	2.47016i
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$	5.40421	+	3.12012i	0.269873	+	0.155811i	0.628830	−	0.777543i	$-0.283534\pi$
$401$	5.40421	+	3.12012i	0.269873	+	0.155811i	−0.358957	+	0.933354i	$0.616867\pi$
$402$	22.3554	+	8.25029i	1.11499	+	0.411487i
$403$	10.5176	−	6.07234i	0.523919	−	0.302485i
$404$	−1.34086			−0.0667103
$405$	3.22919	−	8.40073i	0.160460	−	0.417436i
$406$			26.8938i			1.33472i
$407$	−8.38426	−	31.5501i	−0.415593	−	1.56388i
$408$	−2.73571	−	1.00962i	−0.135438	−	0.0499835i
$409$	12.7021	+	7.33357i	0.628079	+	0.362622i	0.780008	−	0.625770i	$-0.215215\pi$
$409$	12.7021	+	7.33357i	0.628079	+	0.362622i	−0.151929	+	0.988391i	$0.548548\pi$
$410$	−5.05664	−	2.91945i	−0.249730	−	0.144182i
$411$	−3.40591	+	0.584837i	−0.168001	+	0.0288479i
$412$	−0.170406	−	0.295152i	−0.00839530	−	0.0145411i
$413$	51.4218			2.53030
$414$	−9.77262	+	11.4369i	−0.480298	+	0.562094i
$415$			5.58285i			0.274051i
$416$	−1.88953	+	1.09092i	−0.0926417	+	0.0534867i
$417$	17.0369	+	20.4895i	0.834303	+	1.00338i
$418$	−18.3981	−	18.4740i	−0.899879	−	0.903591i
$419$	26.1506	+	15.0981i	1.27754	+	0.737588i	0.976396	−	0.215990i	$-0.0692979\pi$
$419$	26.1506	+	15.0981i	1.27754	+	0.737588i	0.301145	+	0.953578i	$0.402631\pi$
$420$	4.89681	−	4.07168i	0.238940	−	0.198677i
$421$	4.66929	+	8.08745i	0.227567	+	0.394158i	0.957087	−	0.289802i	$-0.0935895\pi$
$421$	4.66929	+	8.08745i	0.227567	+	0.394158i	−0.729519	+	0.683960i	$0.760256\pi$
$422$		−	2.74599i		−	0.133673i
$423$	15.2068	+	2.82205i	0.739382	+	0.137213i
$424$		−	4.66886i		−	0.226740i
$425$	0.841796	+	1.45803i	0.0408331	+	0.0707250i
$426$	−13.5505	+	2.32678i	−0.656522	+	0.112733i
$427$	−16.8363	+	29.1613i	−0.814766	+	1.41122i
$428$	3.09075	−	5.35334i	0.149397	−	0.258763i
$429$	7.25601	−	10.2198i	0.350323	−	0.493417i
$430$	−1.67059	−	2.89355i	−0.0805631	−	0.139539i
$431$	−24.4410			−1.17728			−0.588641	−	0.808394i	$-0.700337\pi$
$431$	−24.4410			−1.17728			−0.588641	+	0.808394i	$0.700337\pi$
$432$	−2.65830	+	4.46469i	−0.127898	+	0.214807i
$433$	25.3732			1.21936			0.609680	−	0.792648i	$-0.291298\pi$
$433$	25.3732			1.21936			0.609680	+	0.792648i	$0.291298\pi$
$434$	17.7242	−	10.2331i	0.850790	−	0.491204i
$435$	−4.38629	+	11.8853i	−0.210307	+	0.569858i
$436$	5.42565	+	3.13250i	0.259841	+	0.150020i
$437$	−19.7099	+	34.1386i	−0.942853	+	1.63307i
$438$	−8.19872	+	1.40782i	−0.391750	+	0.0672684i
$439$	−17.5588	+	10.1376i	−0.838034	+	0.483839i	−0.856596	−	0.515988i	$-0.827425\pi$
$439$	−17.5588	+	10.1376i	−0.838034	+	0.483839i	0.0185613	+	0.999828i	$0.494091\pi$
$440$	0.864999	−	3.20184i	0.0412372	−	0.152642i
$441$	18.4370	−	6.52410i	0.877953	−	0.310671i
$442$		−	3.67333i		−	0.174722i
$443$	17.8653	−	10.3145i	0.848804	−	0.490057i	−0.0114429	−	0.999935i	$-0.503642\pi$
$443$	17.8653	−	10.3145i	0.848804	−	0.490057i	0.860247	+	0.509877i	$0.170309\pi$
$444$	−13.1088	+	10.8999i	−0.622115	+	0.517286i
$445$	−6.49203	+	11.2445i	−0.307752	+	0.533041i
$446$	8.12070	−	14.0655i	0.384526	−	0.666019i
$447$	−28.9199	+	24.0468i	−1.36786	+	1.13737i
$448$	−3.18423	+	1.83842i	−0.150441	+	0.0868570i
$449$		−	29.2409i		−	1.37996i	−0.723826	−	0.689982i	$-0.757618\pi$
$449$		−	29.2409i		−	1.37996i	0.723826	−	0.689982i	$-0.242382\pi$
$450$	2.82816	−	1.00077i	0.133321	−	0.0471766i
$451$	−18.6952	−	5.05065i	−0.880325	−	0.237826i
$452$	−1.73318	+	1.00065i	−0.0815221	+	0.0470668i
$453$	−1.89467	+	0.325339i	−0.0890195	+	0.0152858i
$454$	−0.0573427	+	0.0993205i	−0.00269123	+	0.00466134i
$455$	6.94748	+	4.01113i	0.325703	+	0.188045i
$456$	−4.71418	+	12.7738i	−0.220762	+	0.598188i
$457$	−26.9068	+	15.5347i	−1.25865	+	0.726681i	−0.972812	−	0.231597i	$-0.925605\pi$
$457$	−26.9068	+	15.5347i	−1.25865	+	0.726681i	−0.285837	+	0.958278i	$0.592272\pi$
$458$	−13.3732			−0.624887
$459$	−4.27191	−	7.63425i	−0.199396	−	0.356336i
$460$	−5.01450			−0.233802
$461$	−14.4654	−	25.0548i	−0.673722	−	1.16692i	−0.976841	−	0.213968i	$-0.931361\pi$
$461$	−14.4654	−	25.0548i	−0.673722	−	1.16692i	0.303119	−	0.952953i	$-0.401972\pi$
$462$	12.2278	−	17.2224i	0.568889	−	0.801258i
$463$	1.25707	−	2.17732i	0.0584212	−	0.101188i	−0.835336	−	0.549740i	$-0.814727\pi$
$463$	1.25707	−	2.17732i	0.0584212	−	0.101188i	0.893757	+	0.448552i	$0.148060\pi$
$464$	3.65719	−	6.33444i	0.169781	−	0.294069i
$465$	9.50197	−	1.63161i	0.440643	−	0.0756640i
$466$	2.71440	+	4.70148i	0.125742	+	0.217792i
$467$			2.01504i			0.0932448i	0.998913	+	0.0466224i	$0.0148457\pi$
$467$			2.01504i			0.0932448i	−0.998913	+	0.0466224i	$0.985154\pi$
$468$	−6.43564	−	1.19431i	−0.297487	−	0.0552071i
$469$			50.5852i			2.33581i
$470$	2.57775	+	4.46479i	0.118903	+	0.205945i
$471$	−31.0189	+	25.7921i	−1.42928	+	1.18844i
$472$	−12.1117	−	6.99268i	−0.557485	−	0.321864i
$473$	−7.81962	−	7.85188i	−0.359547	−	0.361030i
$474$	15.8604	+	19.0745i	0.728492	+	0.876122i
$475$	6.80796	−	3.93058i	0.312371	−	0.180347i
$476$		−	6.19029i		−	0.283731i
$477$	9.09900	−	10.6486i	0.416615	−	0.487565i
$478$	−5.90312			−0.270002
$479$	3.15987	+	5.47305i	0.144378	+	0.250070i	0.929141	−	0.369726i	$-0.120549\pi$
$479$	3.15987	+	5.47305i	0.144378	+	0.250070i	−0.784763	+	0.619796i	$0.787215\pi$
$480$	−1.70707	+	0.293125i	−0.0779166	+	0.0133793i
$481$	−18.5984	−	10.7378i	−0.848015	−	0.489602i
$482$	25.7690	+	14.8778i	1.17375	+	0.677663i
$483$	−29.9595	−	11.0566i	−1.36321	−	0.503092i
$484$	0.0452884	−	10.9999i	0.00205856	−	0.499996i
$485$			14.7640i			0.670401i
$486$	−14.7641	+	5.00222i	−0.669712	+	0.226905i
$487$	−13.1443			−0.595626			−0.297813	−	0.954624i	$-0.596257\pi$
$487$	−13.1443			−0.595626			−0.297813	+	0.954624i	$0.596257\pi$
$488$	7.93110	−	4.57903i	0.359024	−	0.207283i
$489$	−14.4839	−	5.34529i	−0.654984	−	0.241722i
$490$	5.64570	+	3.25955i	0.255047	+	0.147251i
$491$	−7.95737	+	13.7826i	−0.359111	+	0.621999i	−0.987813	−	0.155648i	$-0.950253\pi$
$491$	−7.95737	+	13.7826i	−0.359111	+	0.621999i	0.628702	+	0.777647i	$0.283587\pi$
$492$	1.71153	+	9.96741i	0.0771617	+	0.449365i
$493$	6.15722	+	10.6646i	0.277307	+	0.480310i
$494$	−17.1518			−0.771695
$495$	8.21283	−	5.61688i	0.369139	−	0.252460i
$496$	−5.56625			−0.249932
$497$	−14.5931	−	25.2760i	−0.654589	−	1.13378i
$498$	7.43525	−	6.18238i	0.333181	−	0.277039i
$499$	17.8573	−	30.9298i	0.799403	−	1.38461i	−0.120602	−	0.992701i	$-0.538482\pi$
$499$	17.8573	−	30.9298i	0.799403	−	1.38461i	0.920005	−	0.391906i	$-0.128184\pi$
$500$	0.866025	+	0.500000i	0.0387298	+	0.0223607i
$501$	13.6377	−	11.3397i	0.609286	−	0.506619i
$502$	1.94980	−	1.12571i	0.0870236	−	0.0502431i
$503$	21.6640			0.965951			0.482975	−	0.875634i	$-0.339556\pi$
$503$	21.6640			0.965951			0.482975	+	0.875634i	$0.339556\pi$
$504$	−10.8453	−	2.01265i	−0.483089	−	0.0896507i
$505$		−	1.34086i		−	0.0596675i
$506$	−16.0734	+	4.27140i	−0.714548	+	0.189887i
$507$	2.41523	+	14.0655i	0.107264	+	0.624671i
$508$	14.2791	+	8.24405i	0.633534	+	0.365771i
$509$	−1.67154	−	0.965064i	−0.0740897	−	0.0427757i	0.462498	−	0.886621i	$-0.346953\pi$
$509$	−1.67154	−	0.965064i	−0.0740897	−	0.0427757i	−0.536587	+	0.843845i	$0.680287\pi$
$510$	1.00962	−	2.73571i	0.0447066	−	0.121139i
$511$	−8.82957	−	15.2933i	−0.390597	−	0.676534i
$512$	1.00000			0.0441942
$513$	−35.6464	+	19.9468i	−1.57383	+	0.880671i
$514$		−	21.3905i		−	0.943494i
$515$	0.295152	−	0.170406i	0.0130059	−	0.00750898i
$516$	−2.00364	+	5.42917i	−0.0882053	+	0.239006i
$517$	12.0658	+	12.1156i	0.530653	+	0.532842i
$518$	−31.3420	−	18.0953i	−1.37709	−	0.795063i
$519$	−3.89998	−	22.7123i	−0.171190	−	0.996958i
$520$	−1.09092	−	1.88953i	−0.0478400	−	0.0828613i
$521$		−	12.3020i		−	0.538960i	−0.963006	−	0.269480i	$-0.913148\pi$
$521$		−	12.3020i		−	0.538960i	0.963006	−	0.269480i	$-0.0868518\pi$
$522$	20.6862	−	7.32000i	0.905411	−	0.320388i
$523$			12.3025i			0.537949i	0.963147	+	0.268975i	$0.0866848\pi$
$523$			12.3025i			0.537949i	−0.963147	+	0.268975i	$0.913315\pi$
$524$	2.63052	+	4.55620i	0.114915	+	0.199038i
$525$	4.07168	+	4.89681i	0.177703	+	0.213714i
$526$	3.76673	−	6.52416i	0.164237	−	0.284467i
$527$	4.68565	−	8.11578i	0.204110	−	0.353529i
$528$	−5.22210	+	2.39367i	−0.227263	+	0.104171i
$529$	1.07262	+	1.85783i	0.0466355	+	0.0807750i
$530$	4.66886			0.202802
$531$	−13.9961	−	39.5528i	−0.607379	−	1.71645i
$532$	−28.9042			−1.25315
$533$	−11.0328	+	6.36978i	−0.477883	+	0.275906i
$534$	22.1646	−	3.80595i	0.959158	−	0.164699i
$535$	5.35334	+	3.09075i	0.231445	+	0.133625i
$536$	6.87891	−	11.9146i	0.297124	−	0.514633i
$537$	13.0579	−	35.3825i	0.563492	−	1.52687i
$538$	−14.1534	+	8.17146i	−0.610196	+	0.352297i
$539$	20.8731	+	5.63901i	0.899068	+	0.242889i
$540$	−4.46469	−	2.65830i	−0.192130	−	0.114395i
$541$		−	28.2186i		−	1.21321i	−0.795003	−	0.606606i	$-0.792531\pi$
$541$		−	28.2186i		−	1.21321i	0.795003	−	0.606606i	$-0.207469\pi$
$542$	0.524126	−	0.302605i	0.0225132	−	0.0129980i
$543$	−29.1477	−	10.7570i	−1.25085	−	0.461626i
$544$	−0.841796	+	1.45803i	−0.0360917	+	0.0625127i
$545$	−3.13250	+	5.42565i	−0.134182	+	0.232409i
$546$	−2.35152	−	13.6945i	−0.100636	−	0.586072i
$547$	−8.18909	+	4.72797i	−0.350140	+	0.202154i	−0.664747	−	0.747069i	$-0.731461\pi$
$547$	−8.18909	+	4.72797i	−0.350140	+	0.202154i	0.314607	+	0.949222i	$0.398127\pi$
$548$			1.99518i			0.0852300i
$549$	27.0129	+	5.01300i	1.15288	+	0.213950i
$550$	3.20184	+	0.864999i	0.136527	+	0.0368837i
$551$	49.7961	−	28.7498i	2.12138	−	1.22478i
$552$	5.55299	+	6.67832i	0.236351	+	0.284248i
$553$	−26.3304	+	45.6057i	−1.11968	+	1.93935i
$554$	10.2745	+	5.93197i	0.436521	+	0.252025i
$555$	−10.8999	−	13.1088i	−0.462675	−	0.556436i
$556$	13.3236	−	7.69241i	0.565048	−	0.326231i
$557$	25.6402			1.08641			0.543205	−	0.839600i	$-0.317211\pi$
$557$	25.6402			1.08641			0.543205	+	0.839600i	$0.317211\pi$
$558$	−12.6953	−	10.8479i	−0.537436	−	0.459229i
$559$	−7.28992			−0.308331
$560$	−1.83842	−	3.18423i	−0.0776873	−	0.134558i
$561$	0.905894	−	9.62898i	0.0382469	−	0.406536i
$562$	4.36042	−	7.55247i	0.183933	−	0.318582i
$563$	−9.85158	+	17.0634i	−0.415194	+	0.719138i	−0.995449	−	0.0952975i	$-0.969620\pi$
$563$	−9.85158	+	17.0634i	−0.415194	+	0.719138i	0.580254	+	0.814435i	$0.302953\pi$
$564$	3.09164	−	8.37729i	0.130182	−	0.352748i
$565$	−1.00065	−	1.73318i	−0.0420978	−	0.0729156i
$566$			10.2467i			0.430702i
$567$	−20.8133	−	25.7265i	−0.874075	−	1.08041i
$568$			7.93786i			0.333065i
$569$	−0.958507	−	1.66018i	−0.0401827	−	0.0695985i	0.845235	−	0.534395i	$-0.179461\pi$
$569$	−0.958507	−	1.66018i	−0.0401827	−	0.0695985i	−0.885417	+	0.464797i	$0.846127\pi$
$570$	−12.7738	−	4.71418i	−0.535036	−	0.197455i
$571$	0.599207	+	0.345953i	0.0250760	+	0.0144777i	0.512486	−	0.858696i	$-0.328725\pi$
$571$	0.599207	+	0.345953i	0.0250760	+	0.0144777i	−0.487410	+	0.873173i	$0.662058\pi$
$572$	−5.10632	−	5.12739i	−0.213506	−	0.214387i
$573$	8.98556	−	1.54293i	0.375377	−	0.0644570i
$574$	−18.5924	+	10.7343i	−0.776033	+	0.448043i
$575$		−	5.01450i		−	0.209119i
$576$	2.28077	+	1.94887i	0.0950320	+	0.0812030i
$577$	−34.3382			−1.42952			−0.714760	−	0.699370i	$-0.753464\pi$
$577$	−34.3382			−1.42952			−0.714760	+	0.699370i	$0.753464\pi$
$578$	7.08276	+	12.2677i	0.294604	+	0.510269i
$579$	2.89148	+	3.47744i	0.120166	+	0.144517i
$580$	6.33444	+	3.65719i	0.263023	+	0.151857i
$581$	17.7771	+	10.2636i	0.737518	+	0.425806i
$582$	19.6628	−	16.3495i	0.815048	−	0.677709i
$583$	14.9654	−	3.97698i	0.619805	−	0.164709i
$584$			4.80281i			0.198742i
$585$	1.19431	−	6.43564i	0.0493787	−	0.266081i
$586$	−15.9924			−0.660640
$587$	21.0084	−	12.1292i	0.867108	−	0.500625i	0.000721891	−	1.00000i	$-0.499770\pi$
$587$	21.0084	−	12.1292i	0.867108	−	0.500625i	0.866386	+	0.499375i	$0.166437\pi$
$588$	−1.91091	−	11.1285i	−0.0788046	−	0.458933i
$589$	−37.8949	−	21.8786i	−1.56143	−	0.901492i
$590$	6.99268	−	12.1117i	0.287884	−	0.498630i
$591$	−20.7493	−	7.65753i	−0.853511	−	0.314989i
$592$	4.92145	+	8.52419i	0.202270	+	0.350342i
$593$	−4.06153			−0.166787			−0.0833935	−	0.996517i	$-0.526576\pi$
$593$	−4.06153			−0.166787			−0.0833935	+	0.996517i	$0.526576\pi$
$594$	−16.5754	−	4.71780i	−0.680095	−	0.193574i
$595$	6.19029			0.253777
$596$	10.8574	+	18.8056i	0.444738	+	0.770309i
$597$	3.51054	+	1.29557i	0.143677	+	0.0530240i
$598$	−5.47042	+	9.47504i	−0.223702	+	0.387463i
$599$	−5.16281	−	2.98075i	−0.210947	−	0.121790i	0.390805	−	0.920474i	$-0.372197\pi$
$599$	−5.16281	−	2.98075i	−0.210947	−	0.121790i	−0.601751	+	0.798683i	$0.705530\pi$
$600$	−0.293125	−	1.70707i	−0.0119668	−	0.0696907i
$601$	9.95223	−	5.74592i	0.405960	−	0.234381i	−0.283093	−	0.959093i	$-0.591360\pi$
$601$	9.95223	−	5.74592i	0.405960	−	0.234381i	0.689052	+	0.724712i	$0.258027\pi$
$602$	−12.2850			−0.500698
$603$	38.9093	−	13.7684i	1.58451	−	0.560692i
$604$			1.10990i			0.0451612i
$605$	10.9999	+	0.0452884i	0.447210	+	0.00184123i
$606$	−1.78576	+	1.48485i	−0.0725415	+	0.0603180i
$607$	8.52188	+	4.92011i	0.345892	+	0.199701i	0.662875	−	0.748730i	$-0.269336\pi$
$607$	8.52188	+	4.92011i	0.345892	+	0.199701i	−0.316982	+	0.948431i	$0.602670\pi$
$608$	6.80796	+	3.93058i	0.276099	+	0.159406i
$609$	29.7818	+	35.8171i	1.20682	+	1.45138i
$610$	4.57903	+	7.93110i	0.185399	+	0.321121i
$611$	11.2485			0.455064
$612$	−4.76146	+	1.68488i	−0.192471	+	0.0681074i
$613$		−	27.7570i		−	1.12109i	−0.828123	−	0.560547i	$-0.810591\pi$
$613$		−	27.7570i		−	1.12109i	0.828123	−	0.560547i	$-0.189409\pi$
$614$	14.5668	−	8.41015i	0.587869	−	0.339406i
$615$	−9.96741	+	1.71153i	−0.401925	+	0.0690155i
$616$	−8.60517	−	8.64067i	−0.346712	−	0.348142i
$617$	1.27815	+	0.737939i	0.0514563	+	0.0297083i	0.525507	−	0.850789i	$-0.323875\pi$
$617$	1.27815	+	0.737939i	0.0514563	+	0.0297083i	−0.474051	+	0.880497i	$0.657209\pi$
$618$	−0.553794	−	0.204378i	−0.0222769	−	0.00822129i
$619$	−7.86282	−	13.6188i	−0.316034	−	0.547386i	0.663623	−	0.748067i	$-0.269018\pi$
$619$	−7.86282	−	13.6188i	−0.316034	−	0.547386i	−0.979657	+	0.200681i	$0.935685\pi$
$620$		−	5.56625i		−	0.223546i
$621$	−0.350088	+	26.0538i	−0.0140485	+	1.04550i
$622$		−	7.37862i		−	0.295856i
$623$	23.8701	+	41.3442i	0.956335	+	1.65642i
$624$	−1.30841	+	3.54533i	−0.0523781	+	0.141927i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−12.2973	+	21.2995i	−0.491497	+	0.851298i
$627$	−44.9604	−	4.22987i	−1.79555	−	0.168925i
$628$	11.6455	+	20.1706i	0.464706	+	0.804894i
$629$	−16.5714			−0.660746
$630$	2.01265	−	10.8453i	0.0801860	−	0.432088i
$631$	−40.8958			−1.62804			−0.814018	−	0.580840i	$-0.802724\pi$
$631$	−40.8958			−1.62804			−0.814018	+	0.580840i	$0.802724\pi$
$632$	12.4035	−	7.16118i	0.493386	−	0.284856i
$633$	−3.04087	−	3.65711i	−0.120864	−	0.145357i
$634$	0.940567	+	0.543036i	0.0373547	+	0.0215667i
$635$	−8.24405	+	14.2791i	−0.327155	+	0.566650i
$636$	−5.17023	−	6.21799i	−0.205013	−	0.246559i
$637$	12.3180	−	7.11181i	0.488057	−	0.281780i
$638$	23.4195	+	6.32693i	0.927186	+	0.250486i
$639$	−15.4699	+	18.1044i	−0.611978	+	0.716200i
$640$			1.00000i			0.0395285i
$641$	38.6523	−	22.3159i	1.52667	−	0.881426i	0.527176	−	0.849756i	$-0.323251\pi$
$641$	38.6523	−	22.3159i	1.52667	−	0.881426i	0.999498	−	0.0316702i	$-0.0100826\pi$
$642$	−1.81195	−	10.5522i	−0.0715120	−	0.416464i
$643$	0.176902	−	0.306403i	0.00697633	−	0.0120834i	−0.862516	−	0.506030i	$-0.831113\pi$
$643$	0.176902	−	0.306403i	0.00697633	−	0.0120834i	0.869492	+	0.493946i	$0.164446\pi$
$644$	−9.21874	+	15.9673i	−0.363269	+	0.629201i
$645$	−5.42917	−	2.00364i	−0.213773	−	0.0788932i
$646$	−11.4618	+	6.61749i	−0.450960	+	0.260362i
$647$		−	9.75059i		−	0.383335i	−0.981460	−	0.191668i	$-0.938610\pi$
$647$		−	9.75059i		−	0.383335i	0.981460	−	0.191668i	$-0.0613896\pi$
$648$	1.40380	+	8.88984i	0.0551467	+	0.349226i
$649$	12.0973	−	44.7789i	0.474861	−	1.75773i
$650$	1.88953	−	1.09092i	0.0741134	−	0.0427894i
$651$	12.2732	−	33.2560i	0.481023	−	1.30341i
$652$	−4.45679	+	7.71938i	−0.174541	+	0.302314i
$653$	−13.4942	−	7.79085i	−0.528067	−	0.304880i	0.212162	−	0.977235i	$-0.431950\pi$
$653$	−13.4942	−	7.79085i	−0.528067	−	0.304880i	−0.740229	+	0.672355i	$0.765283\pi$
$654$	10.6948	−	1.83643i	0.418199	−	0.0718100i
$655$	−4.55620	+	2.63052i	−0.178025	+	0.102783i
$656$	5.83891			0.227971
$657$	−9.36006	+	10.9541i	−0.365171	+	0.427360i
$658$	18.9559			0.738977
$659$	−20.3980	−	35.3304i	−0.794594	−	1.37628i	−0.923096	−	0.384569i	$-0.874350\pi$
$659$	−20.3980	−	35.3304i	−0.794594	−	1.37628i	0.128502	−	0.991709i	$-0.458983\pi$
$660$	−2.39367	−	5.22210i	−0.0931735	−	0.203270i
$661$	3.63429	−	6.29478i	0.141358	−	0.244839i	−0.786650	−	0.617399i	$-0.788187\pi$
$661$	3.63429	−	6.29478i	0.141358	−	0.244839i	0.928008	+	0.372560i	$0.121520\pi$
$662$	−2.48198	+	4.29891i	−0.0964648	+	0.167082i
$663$	−4.06779	−	4.89214i	−0.157980	−	0.189995i
$664$	−2.79143	−	4.83489i	−0.108328	−	0.187630i
$665$		−	28.9042i		−	1.12086i
$666$	−5.38788	+	29.0330i	−0.208776	+	1.12500i
$667$		−	36.6780i		−	1.42018i
$668$	−5.12001	−	8.86811i	−0.198099	−	0.343117i
$669$	−4.76076	−	27.7252i	−0.184061	−	1.07192i
$670$	11.9146	+	6.87891i	0.460302	+	0.265755i
$671$	21.4333	+	21.5217i	0.827422	+	0.830836i
$672$	−2.20492	+	5.97458i	−0.0850567	+	0.230474i
$673$	−4.12089	+	2.37920i	−0.158849	+	0.0917114i	−0.577317	−	0.816520i	$-0.695900\pi$
$673$	−4.12089	+	2.37920i	−0.158849	+	0.0917114i	0.418468	+	0.908231i	$0.362567\pi$
$674$			17.3795i			0.669434i
$675$	2.65830	−	4.46469i	0.102318	−	0.171846i
$676$	8.23958			0.316907
$677$	22.4648	+	38.9101i	0.863391	+	1.49544i	0.868636	+	0.495451i	$0.164997\pi$
$677$	22.4648	+	38.9101i	0.863391	+	1.49544i	−0.00524449	+	0.999986i	$0.501669\pi$
$678$	−1.20014	+	3.25198i	−0.0460913	+	0.124891i
$679$	47.0121	+	27.1425i	1.80416	+	1.04163i
$680$	−1.45803	−	0.841796i	−0.0559130	−	0.0322814i
$681$	0.0336172	+	0.195776i	0.00128821	+	0.00750214i
$682$	−4.74139	−	17.8419i	−0.181557	−	0.683203i
$683$			5.30492i			0.202987i	0.994836	+	0.101494i	$0.0323621\pi$
$683$			5.30492i			0.202987i	−0.994836	+	0.101494i	$0.967638\pi$
$684$	7.86719	+	22.2326i	0.300810	+	0.850084i
$685$	−1.99518			−0.0762320
$686$	−1.53131	+	0.884103i	−0.0584658	+	0.0337552i
$687$	−17.8104	+	14.8093i	−0.679509	+	0.565009i
$688$	2.89355	+	1.67059i	0.110316	+	0.0636907i
$689$	5.09335	−	8.82194i	0.194041	−	0.336089i
$690$	−6.67832	+	5.55299i	−0.254239	+	0.211399i
$691$	−11.9138	−	20.6354i	−0.453224	−	0.785007i	0.545360	−	0.838202i	$-0.316393\pi$
$691$	−11.9138	−	20.6354i	−0.453224	−	0.785007i	−0.998584	+	0.0531948i	$0.983060\pi$
$692$	−13.3049			−0.505775
$693$	−2.78684	−	36.4777i	−0.105863	−	1.38567i
$694$	−11.3709			−0.431634
$695$	7.69241	+	13.3236i	0.291790	+	0.505395i
$696$	−2.14403	−	12.4861i	−0.0812692	−	0.473286i
$697$	−4.91517	+	8.51332i	−0.186175	+	0.322465i
$698$	−5.30746	−	3.06426i	−0.200890	−	0.115984i
$699$	8.82139	+	3.25554i	0.333656	+	0.123136i
$700$	3.18423	−	1.83842i	0.120353	−	0.0694856i
$701$	−33.8438			−1.27826			−0.639132	−	0.769097i	$-0.720706\pi$
$701$	−33.8438			−1.27826			−0.639132	+	0.769097i	$0.720706\pi$
$702$	−9.89355	+	5.53616i	−0.373408	+	0.208949i
$703$			77.3765i			2.91831i
$704$	0.851809	+	3.20537i	0.0321038	+	0.120807i
$705$	8.37729	+	3.09164i	0.315507	+	0.116438i
$706$	24.2020	+	13.9730i	0.910853	+	0.525881i
$707$	−4.26961	−	2.46506i	−0.160575	−	0.0927081i
$708$	−23.8740	+	4.09946i	−0.897238	+	0.154067i
$709$	15.7982	+	27.3632i	0.593313	+	1.02765i	0.993783	+	0.111338i	$0.0355136\pi$
$709$	15.7982	+	27.3632i	0.593313	+	1.02765i	−0.400470	+	0.916310i	$0.631153\pi$
$710$	−7.93786			−0.297903
$711$	42.2458	+	7.83988i	1.58434	+	0.294018i
$712$		−	12.9841i		−	0.486598i
$713$	−24.1725	+	13.9560i	−0.905267	+	0.522656i
$714$	−6.85504	−	8.24423i	−0.256543	−	0.308532i
$715$	5.12739	−	5.10632i	0.191753	−	0.190966i
$716$	−18.8576	−	10.8874i	−0.704741	−	0.406882i
$717$	−7.86178	+	6.53704i	−0.293604	+	0.244130i
$718$	16.0637	+	27.8231i	0.599492	+	1.03835i
$719$			18.7053i			0.697590i	0.937199	+	0.348795i	$0.113409\pi$
$719$			18.7053i			0.697590i	−0.937199	+	0.348795i	$0.886591\pi$
$720$	−1.94887	+	2.28077i	−0.0726301	+	0.0849992i
$721$		−	1.25311i		−	0.0466682i
$722$	21.3989	+	37.0640i	0.796385	+	1.37938i
$723$	50.7947	−	8.72208i	1.88907	−	0.324378i
$724$	−8.96893	+	15.5346i	−0.333328	+	0.577340i
$725$	−3.65719	+	6.33444i	−0.135825	+	0.235255i
$726$	−12.1208	−	14.6998i	−0.449847	−	0.545562i
$727$	−10.6707	−	18.4822i	−0.395755	−	0.685468i	0.597442	−	0.801912i	$-0.296184\pi$
$727$	−10.6707	−	18.4822i	−0.395755	−	0.685468i	−0.993197	+	0.116444i	$0.962850\pi$
$728$	−8.02226			−0.297325
$729$	−14.1234	+	23.0115i	−0.523089	+	0.852278i
$730$	−4.80281			−0.177760
$731$	−4.87156	+	2.81259i	−0.180181	+	0.104028i
$732$	5.49190	−	14.8812i	0.202986	−	0.550023i
$733$	−16.3704	−	9.45144i	−0.604654	−	0.349097i	0.166216	−	0.986089i	$-0.446845\pi$
$733$	−16.3704	−	9.45144i	−0.604654	−	0.349097i	−0.770870	+	0.636992i	$0.780178\pi$
$734$	7.97900	−	13.8200i	0.294510	−	0.510106i
$735$	11.1285	−	1.91091i	0.410482	−	0.0704849i
$736$	4.34269	−	2.50725i	0.160074	−	0.0924185i
$737$	44.0503	+	11.9005i	1.62261	+	0.438360i
$738$	13.3172	+	11.3793i	0.490213	+	0.418877i
$739$			24.3579i			0.896019i	0.894029	+	0.448009i	$0.147867\pi$
$739$			24.3579i			0.896019i	−0.894029	+	0.448009i	$0.852133\pi$
$740$	−8.52419	+	4.92145i	−0.313356	+	0.180916i
$741$	−22.8428	+	18.9937i	−0.839150	+	0.697750i
$742$	8.58330	−	14.8667i	0.315103	−	0.545774i
$743$	4.94977	−	8.57325i	0.181589	−	0.314522i	−0.760833	−	0.648948i	$-0.775209\pi$
$743$	4.94977	−	8.57325i	0.181589	−	0.314522i	0.942422	+	0.334426i	$0.108543\pi$
$744$	−7.41314	+	6.16400i	−0.271779	+	0.225983i
$745$	−18.8056	+	10.8574i	−0.688985	+	0.397786i
$746$		−	20.9074i		−	0.765476i
$747$	3.05598	−	16.4674i	0.111813	−	0.602510i
$748$	−5.39059	−	1.45630i	−0.197100	−	0.0532478i
$749$	19.6833	−	11.3642i	0.719213	−	0.415238i
$750$	1.70707	−	0.293125i	0.0623333	−	0.0107034i
$751$	4.08010	−	7.06694i	0.148885	−	0.257876i	−0.781931	−	0.623365i	$-0.785765\pi$
$751$	4.08010	−	7.06694i	0.148885	−	0.257876i	0.930816	+	0.365489i	$0.119098\pi$
$752$	−4.46479	−	2.57775i	−0.162814	−	0.0940007i
$753$	1.35014	−	3.65841i	0.0492017	−	0.133320i
$754$	13.8207	−	7.97941i	0.503322	−	0.290593i
$755$	−1.10990			−0.0403934
$756$	−16.6726	+	9.32952i	−0.606377	+	0.339311i
$757$	−22.7954			−0.828515			−0.414257	−	0.910160i	$-0.635959\pi$
$757$	−22.7954			−0.828515			−0.414257	+	0.910160i	$0.635959\pi$
$758$	7.68756	+	13.3152i	0.279225	+	0.483632i
$759$	−16.6764	+	23.4881i	−0.605316	+	0.852563i
$760$	−3.93058	+	6.80796i	−0.142577	+	0.246951i
$761$	25.0265	−	43.3472i	0.907210	−	1.57133i	0.0892860	−	0.996006i	$-0.471541\pi$
$761$	25.0265	−	43.3472i	0.907210	−	1.57133i	0.817924	−	0.575327i	$-0.195125\pi$
$762$	28.1463	−	4.83307i	1.01963	−	0.175084i
$763$	11.5177	+	19.9492i	0.416968	+	0.722210i
$764$		−	5.26374i		−	0.190436i
$765$	−1.68488	−	4.76146i	−0.0609171	−	0.172151i
$766$			2.36790i			0.0855558i
$767$	−15.2569	−	26.4257i	−0.550895	−	0.954178i
$768$	1.33180	−	1.10739i	0.0480572	−	0.0399594i
$769$	8.34447	+	4.81768i	0.300909	+	0.173730i	0.642851	−	0.765991i	$-0.277751\pi$
$769$	8.34447	+	4.81768i	0.300909	+	0.173730i	−0.341942	+	0.939721i	$0.611085\pi$
$770$	8.64067	−	8.60517i	0.311388	−	0.310109i
$771$	−23.6875	−	28.4879i	−0.853086	−	1.02597i
$772$	2.26126	−	1.30554i	0.0813846	−	0.0469874i
$773$		−	2.06723i		−	0.0743530i	−0.999309	−	0.0371765i	$-0.988164\pi$
$773$		−	2.06723i		−	0.0743530i	0.999309	−	0.0371765i	$-0.0118364\pi$
$774$	3.34375	+	9.44938i	0.120189	+	0.339651i
$775$	5.56625			0.199946
$776$	−7.38202	−	12.7860i	−0.264999	−	0.458992i
$777$	−61.7799	+	10.6084i	−2.21634	+	0.380574i
$778$	30.7171	+	17.7345i	1.10126	+	0.635814i
$779$	39.7511	+	22.9503i	1.42423	+	0.822280i
$780$	−3.54533	−	1.30841i	−0.126943	−	0.0468484i
$781$	−25.4438	+	6.76154i	−0.910451	+	0.241947i
$782$			8.44238i			0.301899i
$783$	19.4439	−	32.6564i	0.694867	−	1.16705i
$784$	−6.51910			−0.232825
$785$	−20.1706	+	11.6455i	−0.719919	+	0.415645i
$786$	8.54881	+	3.15494i	0.304926	+	0.112533i
$787$	37.8141	+	21.8320i	1.34793	+	0.778225i	0.987955	−	0.154739i	$-0.0494536\pi$
$787$	37.8141	+	21.8320i	1.34793	+	0.778225i	0.359970	+	0.932964i	$0.382787\pi$
$788$	−6.38468	+	11.0586i	−0.227445	+	0.393946i
$789$	−2.20824	−	12.8601i	−0.0786155	−	0.457832i
$790$	7.16118	+	12.4035i	0.254783	+	0.441298i
$791$	−7.35847			−0.261637
$792$	−4.30408	+	8.97078i	−0.152939	+	0.318763i
$793$	19.9814			0.709560
$794$	−6.97864	−	12.0874i	−0.247663	−	0.428964i
$795$	6.21799	−	5.17023i	0.220529	−	0.183369i
$796$	1.08022	−	1.87099i	0.0382872	−	0.0663154i
$797$	−16.2279	−	9.36918i	−0.574822	−	0.331873i	0.184251	−	0.982879i	$-0.441014\pi$
$797$	−16.2279	−	9.36918i	−0.574822	−	0.331873i	−0.759073	+	0.651006i	$0.774347\pi$
$798$	−38.4946	+	32.0081i	−1.36269	+	1.13307i
$799$	7.51688	−	4.33987i	0.265928	−	0.153534i
$800$	−1.00000			−0.0353553
$801$	25.3042	−	29.6136i	0.894081	−	1.04635i
$802$		−	6.24024i		−	0.220351i
$803$	−15.3948	+	4.09108i	−0.543271	+	0.144371i
$804$	−4.03276	−	23.4855i	−0.142224	−	0.828270i
$805$	−15.9673	−	9.21874i	−0.562774	−	0.324918i
$806$	−10.5176	−	6.07234i	−0.370466	−	0.213889i
$807$	−9.80052	+	26.5560i	−0.344995	+	0.934817i
$808$	0.670430	+	1.16122i	0.0235856	+	0.0408515i
$809$	14.1963			0.499117			0.249558	−	0.968360i	$-0.419715\pi$
$809$	14.1963			0.499117			0.249558	+	0.968360i	$0.419715\pi$
$810$	−8.88984	+	1.40380i	−0.312357	+	0.0493247i
$811$			19.6216i			0.689008i	0.938785	+	0.344504i	$0.111953\pi$
$811$			19.6216i			0.689008i	−0.938785	+	0.344504i	$0.888047\pi$
$812$	23.2907	−	13.4469i	0.817343	−	0.471893i
$813$	0.362932	−	0.983420i	0.0127286	−	0.0344900i
$814$	−23.1311	+	23.0361i	−0.810745	+	0.807413i
$815$	−7.71938	−	4.45679i	−0.270398	−	0.156114i
$816$	0.493503	+	2.87400i	0.0172760	+	0.100610i
$817$	13.1328	+	22.7467i	0.459458	+	0.795805i
$818$		−	14.6671i		−	0.512824i
$819$	−18.2969	−	15.6343i	−0.639346	−	0.546308i
$820$			5.83891i			0.203904i
$821$	5.30945	+	9.19623i	0.185301	+	0.320951i	0.943678	−	0.330866i	$-0.107341\pi$
$821$	5.30945	+	9.19623i	0.185301	+	0.320951i	−0.758377	+	0.651816i	$0.774007\pi$
$822$	2.20944	+	2.65719i	0.0770630	+	0.0926800i
$823$	−1.08143	+	1.87309i	−0.0376962	+	0.0652917i	−0.884258	−	0.466999i	$-0.845335\pi$
$823$	−1.08143	+	1.87309i	−0.0376962	+	0.0652917i	0.846562	+	0.532290i	$0.178669\pi$
$824$	−0.170406	+	0.295152i	−0.00593637	+	0.0102821i
$825$	5.22210	−	2.39367i	0.181810	−	0.0833369i
$826$	−25.7109	−	44.5326i	−0.894597	−	1.54949i
$827$	−14.4361			−0.501992			−0.250996	−	0.967988i	$-0.580758\pi$
$827$	−14.4361			−0.501992			−0.250996	+	0.967988i	$0.580758\pi$
$828$	14.7910	+	2.74488i	0.514022	+	0.0953911i
$829$	−26.4349			−0.918124			−0.459062	−	0.888404i	$-0.651814\pi$
$829$	−26.4349			−0.918124			−0.459062	+	0.888404i	$0.651814\pi$
$830$	4.83489	−	2.79143i	0.167822	−	0.0968918i
$831$	20.2525	−	3.47762i	0.702553	−	0.120637i
$832$	1.88953	+	1.09092i	0.0655076	+	0.0378208i
$833$	5.48775	−	9.50506i	0.190139	−	0.329331i
$834$	9.22597	−	24.9992i	0.319469	−	0.865651i
$835$	8.86811	−	5.12001i	0.306894	−	0.177185i
$836$	−6.79989	+	25.1702i	−0.235179	+	0.870529i
$837$	−28.9205	−	0.388609i	−0.999639	−	0.0134323i
$838$		−	30.1961i		−	1.04311i
$839$	−23.0961	+	13.3345i	−0.797365	+	0.460359i	−0.842549	−	0.538620i	$-0.818946\pi$
$839$	−23.0961	+	13.3345i	−0.797365	+	0.460359i	0.0451843	+	0.998979i	$0.485613\pi$
$840$	−5.97458	−	2.20492i	−0.206143	−	0.0760771i
$841$	−12.2501	+	21.2178i	−0.422418	+	0.731649i
$842$	4.66929	−	8.08745i	0.160914	−	0.278712i
$843$	−2.55630	−	14.8871i	−0.0880435	−	0.512738i
$844$	−2.37810	+	1.37300i	−0.0818575	+	0.0472605i
$845$			8.23958i			0.283450i
$846$	−5.15945	−	14.5805i	−0.177385	−	0.501289i
$847$	20.3666	−	34.9430i	0.699805	−	1.20065i
$848$	−4.04335	+	2.33443i	−0.138849	+	0.0801646i
$849$	11.3471	+	13.6466i	0.389431	+	0.468350i
$850$	0.841796	−	1.45803i	0.0288734	−	0.0500101i
$851$	42.7446	+	24.6786i	1.46527	+	0.845972i
$852$	8.79028	+	10.5716i	0.301150	+	0.362179i
$853$	40.4073	−	23.3291i	1.38352	−	0.798775i	0.390944	−	0.920414i	$-0.372149\pi$
$853$	40.4073	−	23.3291i	1.38352	−	0.798775i	0.992574	+	0.121640i	$0.0388153\pi$
$854$	33.6726			1.15225
$855$	−22.2326	+	7.86719i	−0.760338	+	0.269052i
$856$	−6.18150			−0.211279
$857$	−20.5060	−	35.5175i	−0.700473	−	1.21325i	−0.968301	−	0.249788i	$-0.919639\pi$
$857$	−20.5060	−	35.5175i	−0.700473	−	1.21325i	0.267828	−	0.963467i	$-0.413694\pi$
$858$	−12.4786	−	1.17399i	−0.426013	−	0.0400792i
$859$	25.7734	−	44.6409i	0.879379	−	1.52313i	0.0273545	−	0.999626i	$-0.491292\pi$
$859$	25.7734	−	44.6409i	0.879379	−	1.52313i	0.852024	−	0.523503i	$-0.175375\pi$
$860$	−1.67059	+	2.89355i	−0.0569667	+	0.0986692i
$861$	−12.8743	+	34.8850i	−0.438756	+	1.18888i
$862$	12.2205	+	21.1665i	0.416232	+	0.720935i
$863$			52.0631i			1.77225i	0.463446	+	0.886125i	$0.346613\pi$
$863$			52.0631i			1.77225i	−0.463446	+	0.886125i	$0.653387\pi$
$864$	5.19568	+	0.0698151i	0.176761	+	0.00237516i
$865$		−	13.3049i		−	0.452379i
$866$	−12.6866	−	21.9739i	−0.431109	−	0.746703i
$867$	23.0179	+	8.49478i	0.781729	+	0.288498i
$868$	−17.7242	−	10.2331i	−0.601600	−	0.347334i
$869$	33.5197	+	33.6580i	1.13708	+	1.14177i
$870$	12.4861	−	2.14403i	0.423320	−	0.0726894i
$871$	25.9958	−	15.0087i	0.880834	−	0.508550i
$872$		−	6.26500i		−	0.212160i
$873$	8.08166	−	43.5486i	0.273523	−	1.47390i
$874$	39.4198			1.33339
$875$	1.83842	+	3.18423i	0.0621498	+	0.107647i
$876$	5.31857	+	6.39639i	0.179698	+	0.216114i
$877$	25.4764	+	14.7088i	0.860278	+	0.496682i	0.864106	−	0.503311i	$-0.167885\pi$
$877$	25.4764	+	14.7088i	0.860278	+	0.496682i	−0.00382706	+	0.999993i	$0.501218\pi$
$878$	17.5588	+	10.1376i	0.592580	+	0.342126i
$879$	−21.2987	+	17.7098i	−0.718388	+	0.597336i
$880$	−3.20537	+	0.851809i	−0.108053	+	0.0287145i
$881$			10.8313i			0.364917i	0.983214	+	0.182459i	$0.0584056\pi$
$881$			10.8313i			0.364917i	−0.983214	+	0.182459i	$0.941594\pi$
$882$	−14.8685	−	12.7049i	−0.500650	−	0.427795i
$883$	−37.0003			−1.24516			−0.622580	−	0.782556i	$-0.713915\pi$
$883$	−37.0003			−1.24516			−0.622580	+	0.782556i	$0.713915\pi$
$884$	−3.18119	+	1.83666i	−0.106995	+	0.0617737i
$885$	−4.09946	−	23.8740i	−0.137802	−	0.802514i
$886$	−17.8653	−	10.3145i	−0.600195	−	0.346523i
$887$	−19.9221	+	34.5061i	−0.668918	+	1.15860i	0.309289	+	0.950968i	$0.399909\pi$
$887$	−19.9221	+	34.5061i	−0.668918	+	1.15860i	−0.978207	+	0.207632i	$0.933424\pi$
$888$	15.9940	+	5.90258i	0.536722	+	0.198078i
$889$	30.3120	+	52.5019i	1.01663	+	1.76086i
$890$	12.9841			0.435226
$891$	−27.2995	+	12.0722i	−0.914568	+	0.404433i
$892$	−16.2414			−0.543802
$893$	−20.2641	−	35.0984i	−0.678111	−	1.17452i
$894$	35.2851	+	13.0220i	1.18011	+	0.435520i
$895$	10.8874	−	18.8576i	0.363927	−	0.630339i
$896$	3.18423	+	1.83842i	0.106378	+	0.0614172i
$897$	3.20703	+	18.6767i	0.107080	+	0.623598i
$898$	−25.3234	+	14.6205i	−0.845052	+	0.487891i
$899$	40.7137			1.35788
$900$	−2.28077	−	1.94887i	−0.0760256	−	0.0649624i
$901$		−	7.86045i		−	0.261870i
$902$	4.97363	+	18.7159i	0.165604	+	0.623171i
$903$	−16.3611	+	13.6042i	−0.544464	+	0.452720i
$904$	1.73318	+	1.00065i	0.0576448	+	0.0332812i
$905$	−15.5346	−	8.96893i	−0.516389	−	0.298137i
$906$	1.22909	+	1.47817i	0.0408337	+	0.0491087i
$907$	2.96024	+	5.12728i	0.0982931	+	0.170249i	0.910978	−	0.412454i	$-0.135328\pi$
$907$	2.96024	+	5.12728i	0.0982931	+	0.170249i	−0.812685	+	0.582703i	$0.801995\pi$
$908$	0.114685			0.00380597
$909$	−0.733970	+	3.95505i	−0.0243443	+	0.131181i
$910$		−	8.02226i		−	0.265935i
$911$	4.43890	−	2.56280i	0.147067	−	0.0849093i	−0.424661	−	0.905353i	$-0.639607\pi$
$911$	4.43890	−	2.56280i	0.147067	−	0.0849093i	0.571728	+	0.820443i	$0.306273\pi$
$912$	13.4195	−	2.30430i	0.444365	−	0.0763031i
$913$	13.1199	−	13.0660i	0.434204	−	0.432420i
$914$	26.9068	+	15.5347i	0.889999	+	0.513841i
$915$	14.8812	+	5.49190i	0.491956	+	0.181557i
$916$	6.68658	+	11.5815i	0.220931	+	0.382664i
$917$			19.3440i			0.638794i
$918$	−4.47550	+	7.51671i	−0.147713	+	0.248088i
$919$		−	44.4077i		−	1.46488i	−0.680834	−	0.732438i	$-0.738383\pi$
$919$		−	44.4077i		−	1.46488i	0.680834	−	0.732438i	$-0.261617\pi$
$920$	2.50725	+	4.34269i	0.0826616	+	0.143174i
$921$	10.0868	−	27.3317i	0.332371	−	0.900612i
$922$	−14.4654	+	25.0548i	−0.476393	+	0.825137i
$923$	−8.65957	+	14.9988i	−0.285033	+	0.493692i
$924$	−21.0289	−	1.97840i	−0.691801	−	0.0650846i
$925$	−4.92145	−	8.52419i	−0.161816	−	0.280274i
$926$	−2.51415			−0.0826200
$927$	−0.963869	+	0.341073i	−0.0316576	+	0.0112023i
$928$	−7.31439			−0.240106
$929$	−38.1637	+	22.0338i	−1.25211	+	0.722906i	−0.971528	−	0.236925i	$-0.923861\pi$
$929$	−38.1637	+	22.0338i	−1.25211	+	0.722906i	−0.280581	+	0.959830i	$0.590527\pi$
$930$	−6.16400	−	7.41314i	−0.202125	−	0.243087i
$931$	−44.3818	−	25.6238i	−1.45455	−	0.839787i
$932$	2.71440	−	4.70148i	0.0889131	−	0.154002i
$933$	−8.17099	−	9.82685i	−0.267506	−	0.321717i
$934$	1.74507	−	1.00752i	0.0571005	−	0.0329670i
$935$	1.45630	−	5.39059i	0.0476263	−	0.176291i
$936$	2.18351	+	6.17058i	0.0713704	+	0.201692i
$937$			43.9178i			1.43473i	0.696697	+	0.717366i	$0.254652\pi$
$937$			43.9178i			1.43473i	−0.696697	+	0.717366i	$0.745348\pi$
$938$	43.8081	−	25.2926i	1.43038	−	0.825833i
$939$	7.20926	+	41.9845i	0.235265	+	1.37011i
$940$	2.57775	−	4.46479i	0.0840768	−	0.145625i
$941$	−15.7681	+	27.3111i	−0.514024	+	0.890316i	0.485843	+	0.874046i	$0.338513\pi$
$941$	−15.7681	+	27.3111i	−0.514024	+	0.890316i	−0.999868	+	0.0162702i	$0.994821\pi$
$942$	37.8461	+	13.9671i	1.23309	+	0.455074i
$943$	25.3565	−	14.6396i	0.825723	−	0.476731i
$944$			13.9854i			0.455185i
$945$	−9.32952	−	16.6726i	−0.303489	−	0.542360i
$946$	−2.89012	+	10.6979i	−0.0939659	+	0.347820i
$947$	14.2410	−	8.22205i	0.462770	−	0.267181i	−0.250438	−	0.968133i	$-0.580575\pi$
$947$	14.2410	−	8.22205i	0.462770	−	0.267181i	0.713208	+	0.700952i	$0.247241\pi$
$948$	8.58883	−	23.2728i	0.278952	−	0.755864i
$949$	−5.23948	+	9.07505i	−0.170081	+	0.294589i
$950$	−6.80796	−	3.93058i	−0.220880	−	0.127525i
$951$	1.85400	−	0.318355i	0.0601200	−	0.0103234i
$952$	−5.36094	+	3.09514i	−0.173749	+	0.100314i
$953$	15.2230			0.493121			0.246561	−	0.969127i	$-0.420700\pi$
$953$	15.2230			0.493121			0.246561	+	0.969127i	$0.420700\pi$
$954$	−13.7714	−	2.55568i	−0.445867	−	0.0827430i
$955$	5.26374			0.170331
$956$	2.95156	+	5.11225i	0.0954603	+	0.165342i
$957$	38.1965	−	17.5082i	1.23472	−	0.565960i
$958$	3.15987	−	5.47305i	0.102091	−	0.176826i
$959$	−3.66797	+	6.35312i	−0.118445	+	0.205153i
$960$	1.10739	+	1.33180i	0.0357408	+	0.0429837i
$961$	0.00840758	+	0.0145623i	0.000271212	+	0.000469753i
$962$			21.4756i			0.692401i
$963$	−14.0986	−	12.0469i	−0.454320	−	0.388207i
$964$		−	29.7555i		−	0.958361i
$965$	1.30554	+	2.26126i	0.0420268	+	0.0727926i
$966$	5.40448	+	31.4740i	0.173886	+	1.01266i
$967$	32.1737	+	18.5755i	1.03464	+	0.597347i	0.918309	−	0.395864i	$-0.129555\pi$
$967$	32.1737	+	18.5755i	1.03464	+	0.597347i	0.116326	+	0.993211i	$0.462888\pi$
$968$	−9.54884	+	5.46073i	−0.306911	+	0.175515i
$969$	−7.93676	+	21.5059i	−0.254965	+	0.690868i
$970$	12.7860	−	7.38202i	0.410535	−	0.237022i
$971$		−	41.9406i		−	1.34594i	−0.739671	−	0.672969i	$-0.765019\pi$
$971$		−	41.9406i		−	1.34594i	0.739671	−	0.672969i	$-0.234981\pi$
$972$	11.7141	+	10.2849i	0.375730	+	0.329890i
$973$	56.5674			1.81347
$974$	6.57216	+	11.3833i	0.210586	+	0.364745i
$975$	1.30841	−	3.54533i	0.0419025	−	0.113541i
$976$	−7.93110	−	4.57903i	−0.253868	−	0.146571i
$977$	16.4634	+	9.50512i	0.526709	+	0.304096i	0.739675	−	0.672964i	$-0.234979\pi$
$977$	16.4634	+	9.50512i	0.526709	+	0.304096i	−0.212966	+	0.977060i	$0.568312\pi$
$978$	2.61279	+	15.2161i	0.0835478	+	0.486556i
$979$	41.6187	−	11.0599i	1.33014	−	0.353477i
$980$		−	6.51910i		−	0.208245i
$981$	12.2097	−	14.2890i	0.389825	−	0.456213i
$982$	15.9147			0.507860
$983$	−3.18190	+	1.83707i	−0.101487	+	0.0585935i	−0.549884	−	0.835241i	$-0.685328\pi$
$983$	−3.18190	+	1.83707i	−0.101487	+	0.0585935i	0.448397	+	0.893834i	$0.351995\pi$
$984$	7.77626	−	6.46593i	0.247898	−	0.206126i
$985$	−11.0586	−	6.38468i	−0.352356	−	0.203433i
$986$	6.15722	−	10.6646i	0.196086	−	0.339631i
$987$	25.2455	−	20.9915i	0.803572	−	0.668167i
$988$	8.57589	+	14.8539i	0.272836	+	0.472565i
$989$	16.7544			0.532758
$990$	−8.97078	−	4.30408i	−0.285110	−	0.136793i
$991$	28.6189			0.909109			0.454555	−	0.890719i	$-0.349798\pi$
$991$	28.6189			0.909109			0.454555	+	0.890719i	$0.349798\pi$
$992$	2.78313	+	4.82052i	0.0883644	+	0.153052i
$993$	1.45506	+	8.47380i	0.0461749	+	0.268908i
$994$	−14.5931	+	25.2760i	−0.462865	+	0.801705i
$995$	1.87099	+	1.08022i	0.0593143	+	0.0342451i
$996$	−9.07172	−	3.34792i	−0.287448	−	0.106083i
$997$	−6.92740	+	3.99954i	−0.219393	+	0.126667i	−0.605669	−	0.795717i	$-0.707095\pi$
$997$	−6.92740	+	3.99954i	−0.219393	+	0.126667i	0.386276	+	0.922383i	$0.373761\pi$
$998$	−35.7146			−1.13053
$999$	24.9752	+	44.6326i	0.790179	+	1.41211i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.t.a.131.4	✓	48
3.2	odd	2		2970.2.t.b.2771.24		48
9.2	odd	6		990.2.t.b.461.4	yes	48
9.7	even	3		2970.2.t.a.791.24		48
11.10	odd	2		990.2.t.b.131.4	yes	48
33.32	even	2		2970.2.t.a.2771.24		48
99.43	odd	6		2970.2.t.b.791.24		48
99.65	even	6	inner	990.2.t.a.461.4	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.t.a.131.4	✓	48	1.1	even	1	trivial
990.2.t.a.461.4	yes	48	99.65	even	6	inner
990.2.t.b.131.4	yes	48	11.10	odd	2
990.2.t.b.461.4	yes	48	9.2	odd	6
2970.2.t.a.791.24		48	9.7	even	3
2970.2.t.a.2771.24		48	33.32	even	2
2970.2.t.b.791.24		48	99.43	odd	6
2970.2.t.b.2771.24		48	3.2	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.62493 - 0.599680i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(0.293125 + 1.70707i) q^{6} +(-3.18423 + 1.83842i) q^{7} +1.00000 q^{8} +(2.28077 + 1.94887i) q^{9} +1.00000i q^{10} +(0.851809 + 3.20537i) q^{11} +(1.33180 - 1.10739i) q^{12} +(1.88953 + 1.09092i) q^{13} +(3.18423 + 1.83842i) q^{14} +(1.10739 + 1.33180i) q^{15} +(-0.500000 - 0.866025i) q^{16} +1.68359 q^{17} +(0.547388 - 2.94964i) q^{18} -7.86116i q^{19} +(0.866025 - 0.500000i) q^{20} +(6.27660 - 1.07777i) q^{21} +(2.35003 - 2.34038i) q^{22} +(-4.34269 - 2.50725i) q^{23} +(-1.62493 - 0.599680i) q^{24} +(0.500000 + 0.866025i) q^{25} -2.18184i q^{26} +(-2.53738 - 4.53450i) q^{27} -3.67683i q^{28} +(3.65719 + 6.33444i) q^{29} +(0.599680 - 1.62493i) q^{30} +(2.78313 - 4.82052i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.538072 - 5.71931i) q^{33} +(-0.841796 - 1.45803i) q^{34} +3.67683 q^{35} +(-2.82816 + 1.00077i) q^{36} -9.84289 q^{37} +(-6.80796 + 3.93058i) q^{38} +(-2.41614 - 2.90578i) q^{39} +(-0.866025 - 0.500000i) q^{40} +(-2.91945 + 5.05664i) q^{41} +(-4.07168 - 4.89681i) q^{42} +(-2.89355 + 1.67059i) q^{43} +(-3.20184 - 0.864999i) q^{44} +(-1.00077 - 2.82816i) q^{45} +5.01450i q^{46} +(4.46479 - 2.57775i) q^{47} +(0.293125 + 1.70707i) q^{48} +(3.25955 - 5.64570i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-2.73571 - 1.00962i) q^{51} +(-1.88953 + 1.09092i) q^{52} -4.66886i q^{53} +(-2.65830 + 4.46469i) q^{54} +(0.864999 - 3.20184i) q^{55} +(-3.18423 + 1.83842i) q^{56} +(-4.71418 + 12.7738i) q^{57} +(3.65719 - 6.33444i) q^{58} +(-12.1117 - 6.99268i) q^{59} +(-1.70707 + 0.293125i) q^{60} +(7.93110 - 4.57903i) q^{61} -5.56625 q^{62} +(-10.8453 - 2.01265i) q^{63} +1.00000 q^{64} +(-1.09092 - 1.88953i) q^{65} +(-5.22210 + 2.39367i) q^{66} +(6.87891 - 11.9146i) q^{67} +(-0.841796 + 1.45803i) q^{68} +(5.55299 + 6.67832i) q^{69} +(-1.83842 - 3.18423i) q^{70} +7.93786i q^{71} +(2.28077 + 1.94887i) q^{72} +4.80281i q^{73} +(4.92145 + 8.52419i) q^{74} +(-0.293125 - 1.70707i) q^{75} +(6.80796 + 3.93058i) q^{76} +(-8.60517 - 8.64067i) q^{77} +(-1.30841 + 3.54533i) q^{78} +(12.4035 - 7.16118i) q^{79} +1.00000i q^{80} +(1.40380 + 8.88984i) q^{81} +5.83891 q^{82} +(-2.79143 - 4.83489i) q^{83} +(-2.20492 + 5.97458i) q^{84} +(-1.45803 - 0.841796i) q^{85} +(2.89355 + 1.67059i) q^{86} +(-2.14403 - 12.4861i) q^{87} +(0.851809 + 3.20537i) q^{88} -12.9841i q^{89} +(-1.94887 + 2.28077i) q^{90} -8.02226 q^{91} +(4.34269 - 2.50725i) q^{92} +(-7.41314 + 6.16400i) q^{93} +(-4.46479 - 2.57775i) q^{94} +(-3.93058 + 6.80796i) q^{95} +(1.33180 - 1.10739i) q^{96} +(-7.38202 - 12.7860i) q^{97} -6.51910 q^{98} +(-4.30408 + 8.97078i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{2} - 2 q^{3} - 24 q^{4} - 2 q^{6} + 48 q^{8} + 10 q^{9} - 6 q^{11} + 4 q^{12} + 24 q^{13} - 4 q^{15} - 24 q^{16} - 12 q^{17} - 8 q^{18} - 16 q^{21} + 12 q^{22} + 36 q^{23} - 2 q^{24} + 24 q^{25}+ \cdots - 48 q^{99}+O(q^{100}) \) 48 * q - 24 * q^2 - 2 * q^3 - 24 * q^4 - 2 * q^6 + 48 * q^8 + 10 * q^9 - 6 * q^11 + 4 * q^12 + 24 * q^13 - 4 * q^15 - 24 * q^16 - 12 * q^17 - 8 * q^18 - 16 * q^21 + 12 * q^22 + 36 * q^23 - 2 * q^24 + 24 * q^25 - 8 * q^27 + 8 * q^30 - 24 * q^32 + 2 * q^33 + 6 * q^34 - 2 * q^36 - 6 * q^38 - 40 * q^39 - 6 * q^41 + 8 * q^42 + 30 * q^43 - 6 * q^44 - 2 * q^48 + 24 * q^49 + 24 * q^50 + 22 * q^51 - 24 * q^52 + 22 * q^54 + 40 * q^57 - 54 * q^59 - 4 * q^60 - 38 * q^63 + 48 * q^64 + 8 * q^66 - 6 * q^67 + 6 * q^68 + 76 * q^69 + 10 * q^72 + 2 * q^75 + 6 * q^76 + 6 * q^77 + 32 * q^78 + 10 * q^81 + 12 * q^82 + 36 * q^83 + 8 * q^84 - 30 * q^86 - 44 * q^87 - 6 * q^88 + 24 * q^91 - 36 * q^92 - 68 * q^93 + 4 * q^96 + 6 * q^97 - 48 * q^98 - 48 * q^99

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