LMFDB - Embedded newform 390.2.x.a.199.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(49,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("390.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.x (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 8 x^{10} + 34 x^{9} + 8 x^{8} - 134 x^{7} + 98 x^{6} + 154 x^{5} + 104 x^{4} + \cdots + 2197 $ x^12 - 2x^11 - 8x^10 + 34x^9 + 8x^8 - 134x^7 + 98x^6 + 154x^5 + 104x^4 + 190x^3 - 1196x^2 - 338*x + 2197
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.2
Root			$1.75374 - 1.62986i$ of defining polynomial
Character	$\chi$	$=$	390.199
Dual form			390.2.x.a.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.40066 - 1.74303i) q^{5} +(0.866025 - 0.500000i) q^{6} +(0.763837 + 1.32301i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.40066 - 1.74303i) q^{5} +(0.866025 - 0.500000i) q^{6} +(0.763837 + 1.32301i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(2.20984 - 0.341491i) q^{10} +(-1.14057 - 0.658509i) q^{11} +1.00000i q^{12} +(-2.41225 + 2.67975i) q^{13} -1.52767 q^{14} +(0.341491 + 2.20984i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.35904 + 0.784645i) q^{17} -1.00000 q^{18} +(-4.18063 + 2.41369i) q^{19} +(-0.809179 + 2.08452i) q^{20} -1.52767i q^{21} +(1.14057 - 0.658509i) q^{22} +(-7.31172 - 4.22143i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(-1.07631 + 4.88278i) q^{25} +(-1.11461 - 3.42894i) q^{26} -1.00000i q^{27} +(0.763837 - 1.32301i) q^{28} +(-2.21438 + 3.83543i) q^{29} +(-2.08452 - 0.809179i) q^{30} +1.62745i q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.658509 + 1.14057i) q^{33} -1.56929i q^{34} +(1.23616 - 3.18447i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-1.40148 + 2.42743i) q^{37} -4.82738i q^{38} +(3.42894 - 1.11461i) q^{39} +(-1.40066 - 1.74303i) q^{40} +(1.35904 + 0.784645i) q^{41} +(1.32301 + 0.763837i) q^{42} +(-4.58006 + 2.64430i) q^{43} +1.31702i q^{44} +(0.809179 - 2.08452i) q^{45} +(7.31172 - 4.22143i) q^{46} +4.94552 q^{47} +(0.866025 - 0.500000i) q^{48} +(2.33310 - 4.04106i) q^{49} +(-3.69046 - 3.37350i) q^{50} +1.56929 q^{51} +(3.52686 + 0.749192i) q^{52} -13.9161i q^{53} +(0.866025 + 0.500000i) q^{54} +(0.449750 + 2.91040i) q^{55} +(0.763837 + 1.32301i) q^{56} +4.82738 q^{57} +(-2.21438 - 3.83543i) q^{58} +(-9.07005 + 5.23660i) q^{59} +(1.74303 - 1.40066i) q^{60} +(2.49134 + 4.31513i) q^{61} +(-1.40941 - 0.813725i) q^{62} +(-0.763837 + 1.32301i) q^{63} +1.00000 q^{64} +(8.04962 + 0.451203i) q^{65} -1.31702 q^{66} +(1.38628 - 2.40112i) q^{67} +(1.35904 + 0.784645i) q^{68} +(4.22143 + 7.31172i) q^{69} +(2.13975 + 2.66278i) q^{70} +(-12.8513 + 7.41968i) q^{71} +(0.500000 + 0.866025i) q^{72} +5.98944 q^{73} +(-1.40148 - 2.42743i) q^{74} +(3.37350 - 3.69046i) q^{75} +(4.18063 + 2.41369i) q^{76} -2.01198i q^{77} +(-0.749192 + 3.52686i) q^{78} +4.87632 q^{79} +(2.20984 - 0.341491i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.35904 + 0.784645i) q^{82} -6.39020 q^{83} +(-1.32301 + 0.763837i) q^{84} +(3.27122 + 1.26984i) q^{85} -5.28860i q^{86} +(3.83543 - 2.21438i) q^{87} +(-1.14057 - 0.658509i) q^{88} +(15.9738 + 9.22251i) q^{89} +(1.40066 + 1.74303i) q^{90} +(-5.38789 - 1.14452i) q^{91} +8.44285i q^{92} +(0.813725 - 1.40941i) q^{93} +(-2.47276 + 4.28295i) q^{94} +(10.0628 + 3.90621i) q^{95} +1.00000i q^{96} +(0.963028 + 1.66801i) q^{97} +(2.33310 + 4.04106i) q^{98} -1.31702i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} - 6 q^{4} - 2 q^{5} - 2 q^{7} + 12 q^{8} + 6 q^{9}+O(q^{10}) $ 12 * q - 6 * q^2 - 6 * q^4 - 2 * q^5 - 2 * q^7 + 12 * q^8 + 6 * q^9	$ 12 q - 6 q^{2} - 6 q^{4} - 2 q^{5} - 2 q^{7} + 12 q^{8} + 6 q^{9} - 2 q^{10} + 6 q^{11} - 8 q^{13} + 4 q^{14} + 6 q^{15} - 6 q^{16} + 18 q^{17} - 12 q^{18} - 6 q^{19} + 4 q^{20} - 6 q^{22} + 6 q^{23} - 10 q^{25} - 2 q^{26} - 2 q^{28} + 14 q^{29} - 6 q^{30} - 6 q^{32} + 6 q^{33} + 26 q^{35} + 6 q^{36} - 12 q^{37} - 2 q^{39} - 2 q^{40} - 18 q^{41} - 12 q^{42} - 36 q^{43} - 4 q^{45} - 6 q^{46} + 16 q^{47} + 8 q^{49} - 10 q^{50} + 16 q^{51} + 10 q^{52} - 28 q^{55} - 2 q^{56} - 8 q^{57} + 14 q^{58} - 36 q^{59} + 10 q^{61} + 6 q^{62} + 2 q^{63} + 12 q^{64} + 6 q^{65} - 12 q^{66} + 4 q^{67} - 18 q^{68} + 16 q^{69} - 4 q^{70} - 12 q^{71} + 6 q^{72} + 28 q^{73} - 12 q^{74} - 8 q^{75} + 6 q^{76} - 2 q^{78} + 4 q^{79} - 2 q^{80} - 6 q^{81} + 18 q^{82} + 72 q^{83} + 12 q^{84} + 18 q^{85} + 6 q^{87} + 6 q^{88} + 18 q^{89} + 2 q^{90} + 2 q^{91} - 16 q^{93} - 8 q^{94} - 42 q^{95} - 48 q^{97} + 8 q^{98}+O(q^{100}) $ 12 * q - 6 * q^2 - 6 * q^4 - 2 * q^5 - 2 * q^7 + 12 * q^8 + 6 * q^9 - 2 * q^10 + 6 * q^11 - 8 * q^13 + 4 * q^14 + 6 * q^15 - 6 * q^16 + 18 * q^17 - 12 * q^18 - 6 * q^19 + 4 * q^20 - 6 * q^22 + 6 * q^23 - 10 * q^25 - 2 * q^26 - 2 * q^28 + 14 * q^29 - 6 * q^30 - 6 * q^32 + 6 * q^33 + 26 * q^35 + 6 * q^36 - 12 * q^37 - 2 * q^39 - 2 * q^40 - 18 * q^41 - 12 * q^42 - 36 * q^43 - 4 * q^45 - 6 * q^46 + 16 * q^47 + 8 * q^49 - 10 * q^50 + 16 * q^51 + 10 * q^52 - 28 * q^55 - 2 * q^56 - 8 * q^57 + 14 * q^58 - 36 * q^59 + 10 * q^61 + 6 * q^62 + 2 * q^63 + 12 * q^64 + 6 * q^65 - 12 * q^66 + 4 * q^67 - 18 * q^68 + 16 * q^69 - 4 * q^70 - 12 * q^71 + 6 * q^72 + 28 * q^73 - 12 * q^74 - 8 * q^75 + 6 * q^76 - 2 * q^78 + 4 * q^79 - 2 * q^80 - 6 * q^81 + 18 * q^82 + 72 * q^83 + 12 * q^84 + 18 * q^85 + 6 * q^87 + 6 * q^88 + 18 * q^89 + 2 * q^90 + 2 * q^91 - 16 * q^93 - 8 * q^94 - 42 * q^95 - 48 * q^97 + 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.40066	−	1.74303i	−0.626394	−	0.779507i
$5$	−1.40066	−	1.74303i	−0.626394	−	0.779507i
$6$	0.866025	−	0.500000i	0.353553	−	0.204124i
$7$	0.763837	+	1.32301i	0.288703	+	0.500049i	0.973501	−	0.228685i	$-0.0734425\pi$
$7$	0.763837	+	1.32301i	0.288703	+	0.500049i	−0.684797	+	0.728734i	$0.740109\pi$
$8$	1.00000			0.353553
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	2.20984	−	0.341491i	0.698812	−	0.107989i
$11$	−1.14057	−	0.658509i	−0.343895	−	0.198548i	0.318098	−	0.948058i	$-0.396956\pi$
$11$	−1.14057	−	0.658509i	−0.343895	−	0.198548i	−0.661993	+	0.749510i	$0.730289\pi$
$12$			1.00000i			0.288675i
$13$	−2.41225	+	2.67975i	−0.669037	+	0.743229i
$13$	−2.41225	+	2.67975i	−0.669037	+	0.743229i
$14$	−1.52767			−0.408288
$15$	0.341491	+	2.20984i	0.0881726	+	0.570578i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.35904	+	0.784645i	−0.329617	+	0.190304i	−0.655671	−	0.755047i	$-0.727614\pi$
$17$	−1.35904	+	0.784645i	−0.329617	+	0.190304i	0.326054	+	0.945351i	$0.394281\pi$
$18$	−1.00000			−0.235702
$19$	−4.18063	+	2.41369i	−0.959103	+	0.553738i	−0.895897	−	0.444262i	$-0.853466\pi$
$19$	−4.18063	+	2.41369i	−0.959103	+	0.553738i	−0.0632058	+	0.998001i	$0.520132\pi$
$20$	−0.809179	+	2.08452i	−0.180938	+	0.466113i
$21$		−	1.52767i		−	0.333366i
$22$	1.14057	−	0.658509i	0.243171	−	0.140395i
$23$	−7.31172	−	4.22143i	−1.52460	−	0.880228i	−0.999575	−	0.0291412i	$-0.990723\pi$
$23$	−7.31172	−	4.22143i	−1.52460	−	0.880228i	−0.525025	−	0.851087i	$-0.675944\pi$
$24$	−0.866025	−	0.500000i	−0.176777	−	0.102062i
$25$	−1.07631	+	4.88278i	−0.215262	+	0.976556i
$26$	−1.11461	−	3.42894i	−0.218593	−	0.672471i
$27$		−	1.00000i		−	0.192450i
$28$	0.763837	−	1.32301i	0.144352	−	0.250025i
$29$	−2.21438	+	3.83543i	−0.411201	+	0.712221i	−0.995021	−	0.0996620i	$-0.968224\pi$
$29$	−2.21438	+	3.83543i	−0.411201	+	0.712221i	0.583821	+	0.811883i	$0.301557\pi$
$30$	−2.08452	−	0.809179i	−0.380580	−	0.147735i
$31$			1.62745i			0.292299i	0.989263	+	0.146149i	$0.0466880\pi$
$31$			1.62745i			0.292299i	−0.989263	+	0.146149i	$0.953312\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	0.658509	+	1.14057i	0.114632	+	0.198548i
$34$		−	1.56929i		−	0.269131i
$35$	1.23616	−	3.18447i	0.208950	−	0.538274i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	−1.40148	+	2.42743i	−0.230402	+	0.399067i	−0.957926	−	0.287014i	$-0.907337\pi$
$37$	−1.40148	+	2.42743i	−0.230402	+	0.399067i	0.727525	+	0.686081i	$0.240671\pi$
$38$		−	4.82738i		−	0.783104i
$39$	3.42894	−	1.11461i	0.549070	−	0.178480i
$40$	−1.40066	−	1.74303i	−0.221464	−	0.275597i
$41$	1.35904	+	0.784645i	0.212247	+	0.122541i	0.602355	−	0.798228i	$-0.294229\pi$
$41$	1.35904	+	0.784645i	0.212247	+	0.122541i	−0.390108	+	0.920769i	$0.627562\pi$
$42$	1.32301	+	0.763837i	0.204144	+	0.117863i
$43$	−4.58006	+	2.64430i	−0.698452	+	0.403252i	−0.806771	−	0.590865i	$-0.798787\pi$
$43$	−4.58006	+	2.64430i	−0.698452	+	0.403252i	0.108318	+	0.994116i	$0.465453\pi$
$44$			1.31702i			0.198548i
$45$	0.809179	−	2.08452i	0.120625	−	0.310742i
$46$	7.31172	−	4.22143i	1.07805	−	0.622415i
$47$	4.94552			0.721378			0.360689	−	0.932686i	$-0.382542\pi$
$47$	4.94552			0.721378			0.360689	+	0.932686i	$0.382542\pi$
$48$	0.866025	−	0.500000i	0.125000	−	0.0721688i
$49$	2.33310	−	4.04106i	0.333301	−	0.577294i
$50$	−3.69046	−	3.37350i	−0.521910	−	0.477085i
$51$	1.56929			0.219744
$52$	3.52686	+	0.749192i	0.489087	+	0.103894i
$53$		−	13.9161i		−	1.91152i	−0.294148	−	0.955760i	$-0.595036\pi$
$53$		−	13.9161i		−	1.91152i	0.294148	−	0.955760i	$-0.404964\pi$
$54$	0.866025	+	0.500000i	0.117851	+	0.0680414i
$55$	0.449750	+	2.91040i	0.0606443	+	0.392438i
$56$	0.763837	+	1.32301i	0.102072	+	0.176794i
$57$	4.82738			0.639402
$58$	−2.21438	−	3.83543i	−0.290763	−	0.503616i
$59$	−9.07005	+	5.23660i	−1.18082	+	0.681747i	−0.956204	−	0.292700i	$-0.905446\pi$
$59$	−9.07005	+	5.23660i	−1.18082	+	0.681747i	−0.224616	+	0.974447i	$0.572113\pi$
$60$	1.74303	−	1.40066i	0.225024	−	0.180824i
$61$	2.49134	+	4.31513i	0.318984	+	0.552496i	0.980276	−	0.197632i	$-0.0633252\pi$
$61$	2.49134	+	4.31513i	0.318984	+	0.552496i	−0.661293	+	0.750128i	$0.729992\pi$
$62$	−1.40941	−	0.813725i	−0.178996	−	0.103343i
$63$	−0.763837	+	1.32301i	−0.0962345	+	0.166683i
$64$	1.00000			0.125000
$65$	8.04962	+	0.451203i	0.998433	+	0.0559648i
$66$	−1.31702			−0.162114
$67$	1.38628	−	2.40112i	0.169362	−	0.293343i	−0.768834	−	0.639448i	$-0.779163\pi$
$67$	1.38628	−	2.40112i	0.169362	−	0.293343i	0.938196	+	0.346105i	$0.112496\pi$
$68$	1.35904	+	0.784645i	0.164808	+	0.0951521i
$69$	4.22143	+	7.31172i	0.508200	+	0.880228i
$70$	2.13975	+	2.66278i	0.255749	+	0.318264i
$71$	−12.8513	+	7.41968i	−1.52516	+	0.880554i	−0.525608	+	0.850727i	$0.676162\pi$
$71$	−12.8513	+	7.41968i	−1.52516	+	0.880554i	−0.999555	+	0.0298269i	$0.990504\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	5.98944			0.701011			0.350505	−	0.936561i	$-0.386010\pi$
$73$	5.98944			0.701011			0.350505	+	0.936561i	$0.386010\pi$
$74$	−1.40148	−	2.42743i	−0.162919	−	0.282183i
$75$	3.37350	−	3.69046i	0.389538	−	0.426137i
$76$	4.18063	+	2.41369i	0.479551	+	0.276869i
$77$		−	2.01198i		−	0.229286i
$78$	−0.749192	+	3.52686i	−0.0848293	+	0.399338i
$79$	4.87632			0.548629			0.274315	−	0.961640i	$-0.411549\pi$
$79$	4.87632			0.548629			0.274315	+	0.961640i	$0.411549\pi$
$80$	2.20984	−	0.341491i	0.247067	−	0.0381799i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−1.35904	+	0.784645i	−0.150081	+	0.0866495i
$83$	−6.39020			−0.701416			−0.350708	−	0.936485i	$-0.614059\pi$
$83$	−6.39020			−0.701416			−0.350708	+	0.936485i	$0.614059\pi$
$84$	−1.32301	+	0.763837i	−0.144352	+	0.0833415i
$85$	3.27122	+	1.26984i	0.354813	+	0.137733i
$86$		−	5.28860i		−	0.570284i
$87$	3.83543	−	2.21438i	0.411201	−	0.237407i
$88$	−1.14057	−	0.658509i	−0.121585	−	0.0701973i
$89$	15.9738	+	9.22251i	1.69322	+	0.977584i	0.951886	+	0.306452i	$0.0991419\pi$
$89$	15.9738	+	9.22251i	1.69322	+	0.977584i	0.741338	+	0.671131i	$0.234191\pi$
$90$	1.40066	+	1.74303i	0.147642	+	0.183732i
$91$	−5.38789	−	1.14452i	−0.564804	−	0.119978i
$92$			8.44285i			0.880228i
$93$	0.813725	−	1.40941i	0.0843794	−	0.146149i
$94$	−2.47276	+	4.28295i	−0.255046	+	0.441752i
$95$	10.0628	+	3.90621i	1.03242	+	0.400769i
$96$			1.00000i			0.102062i
$97$	0.963028	+	1.66801i	0.0977807	+	0.169361i	0.910766	−	0.412923i	$-0.135492\pi$
$97$	0.963028	+	1.66801i	0.0977807	+	0.169361i	−0.812985	+	0.582285i	$0.802159\pi$
$98$	2.33310	+	4.04106i	0.235679	+	0.408208i
$99$		−	1.31702i		−	0.132365i
$100$	4.76677	−	1.50928i	0.476677	−	0.150928i
$101$	1.21929	−	2.11188i	0.121324	−	0.210140i	−0.798966	−	0.601376i	$-0.794619\pi$
$101$	1.21929	−	2.11188i	0.121324	−	0.210140i	0.920290	+	0.391237i	$0.127953\pi$
$102$	−0.784645	+	1.35904i	−0.0776914	+	0.134565i
$103$		−	12.4300i		−	1.22477i	−0.790561	−	0.612383i	$-0.790211\pi$
$103$		−	12.4300i		−	1.22477i	0.790561	−	0.612383i	$-0.209789\pi$
$104$	−2.41225	+	2.67975i	−0.236540	+	0.262771i
$105$	−2.66278	+	2.13975i	−0.259861	+	0.208818i
$106$	12.0517	+	6.95804i	1.17056	+	0.675824i
$107$	−9.07302	−	5.23831i	−0.877122	−	0.506407i	−0.00741349	−	0.999973i	$-0.502360\pi$
$107$	−9.07302	−	5.23831i	−0.877122	−	0.506407i	−0.869708	+	0.493566i	$0.835693\pi$
$108$	−0.866025	+	0.500000i	−0.0833333	+	0.0481125i
$109$		−	17.1799i		−	1.64553i	−0.568379	−	0.822767i	$-0.692429\pi$
$109$		−	17.1799i		−	1.64553i	0.568379	−	0.822767i	$-0.307571\pi$
$110$	−2.74535	−	1.06570i	−0.261759	−	0.101611i
$111$	2.42743	−	1.40148i	0.230402	−	0.133022i
$112$	−1.52767			−0.144352
$113$	2.25151	−	1.29991i	0.211805	−	0.122285i	−0.390345	−	0.920669i	$-0.627644\pi$
$113$	2.25151	−	1.29991i	0.211805	−	0.122285i	0.602150	+	0.798383i	$0.294311\pi$
$114$	−2.41369	+	4.18063i	−0.226063	+	0.391552i
$115$	2.88316	+	18.6573i	0.268856	+	1.73981i
$116$	4.42877			0.411201
$117$	−3.52686	−	0.749192i	−0.326058	−	0.0692628i
$118$		−	10.4732i		−	0.964136i
$119$	−2.07618	−	1.19868i	−0.190323	−	0.109883i
$120$	0.341491	+	2.20984i	0.0311737	+	0.201730i
$121$	−4.63273	−	8.02413i	−0.421157	−	0.729466i
$122$	−4.98268			−0.451111
$123$	−0.784645	−	1.35904i	−0.0707490	−	0.122541i
$124$	1.40941	−	0.813725i	0.126569	−	0.0730747i
$125$	10.0184	−	4.96307i	0.896071	−	0.443911i
$126$	−0.763837	−	1.32301i	−0.0680481	−	0.117863i
$127$	7.01552	+	4.05041i	0.622527	+	0.359416i	0.777852	−	0.628447i	$-0.216309\pi$
$127$	7.01552	+	4.05041i	0.622527	+	0.359416i	−0.155325	+	0.987863i	$0.549643\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	5.28860			0.465635
$130$	−4.41556	+	6.74558i	−0.387271	+	0.591626i
$131$	−2.32506			−0.203141			−0.101571	−	0.994828i	$-0.532387\pi$
$131$	−2.32506			−0.203141			−0.101571	+	0.994828i	$0.532387\pi$
$132$	0.658509	−	1.14057i	0.0573158	−	0.0992740i
$133$	−6.38665	−	3.68733i	−0.553792	−	0.319732i
$134$	1.38628	+	2.40112i	0.119757	+	0.207425i
$135$	−1.74303	+	1.40066i	−0.150016	+	0.120550i
$136$	−1.35904	+	0.784645i	−0.116537	+	0.0672827i
$137$	6.14192	+	10.6381i	0.524740	+	0.908876i	0.999585	+	0.0288066i	$0.00917069\pi$
$137$	6.14192	+	10.6381i	0.524740	+	0.908876i	−0.474845	+	0.880069i	$0.657496\pi$
$138$	−8.44285			−0.718703
$139$	−3.32861	−	5.76531i	−0.282329	−	0.489008i	0.689629	−	0.724163i	$-0.257774\pi$
$139$	−3.32861	−	5.76531i	−0.282329	−	0.489008i	−0.971958	+	0.235155i	$0.924440\pi$
$140$	−3.37591	+	0.521687i	−0.285317	+	0.0440906i
$141$	−4.28295	−	2.47276i	−0.360689	−	0.208244i
$142$		−	14.8394i		−	1.24529i
$143$	4.51598	−	1.46796i	0.377645	−	0.122757i
$144$	−1.00000			−0.0833333
$145$	9.78686	−	1.51239i	0.812755	−	0.125597i
$146$	−2.99472	+	5.18700i	−0.247845	+	0.429280i
$147$	−4.04106	+	2.33310i	−0.333301	+	0.192431i
$148$	2.80296			0.230402
$149$	−2.60768	+	1.50554i	−0.213629	+	0.123339i	−0.602997	−	0.797744i	$-0.706027\pi$
$149$	−2.60768	+	1.50554i	−0.213629	+	0.123339i	0.389368	+	0.921082i	$0.372694\pi$
$150$	1.50928	+	4.76677i	0.123232	+	0.389205i
$151$			12.0149i			0.977759i	0.872351	+	0.488880i	$0.162594\pi$
$151$			12.0149i			0.977759i	−0.872351	+	0.488880i	$0.837406\pi$
$152$	−4.18063	+	2.41369i	−0.339094	+	0.195776i
$153$	−1.35904	−	0.784645i	−0.109872	−	0.0634348i
$154$	1.74242	+	1.00599i	0.140408	+	0.0810648i
$155$	2.83670	−	2.27950i	0.227849	−	0.183094i
$156$	−2.67975	−	2.41225i	−0.214552	−	0.193134i
$157$			3.01556i			0.240668i	0.992733	+	0.120334i	$0.0383965\pi$
$157$			3.01556i			0.240668i	−0.992733	+	0.120334i	$0.961604\pi$
$158$	−2.43816	+	4.22302i	−0.193970	+	0.335965i
$159$	−6.95804	+	12.0517i	−0.551808	+	0.955760i
$160$	−0.809179	+	2.08452i	−0.0639712	+	0.164796i
$161$		−	12.8979i		−	1.01650i
$162$	−0.500000	−	0.866025i	−0.0392837	−	0.0680414i
$163$	−4.95812	−	8.58772i	−0.388350	−	0.672642i	0.603878	−	0.797077i	$-0.293621\pi$
$163$	−4.95812	−	8.58772i	−0.388350	−	0.672642i	−0.992228	+	0.124435i	$0.960288\pi$
$164$		−	1.56929i		−	0.122541i
$165$	1.06570	−	2.74535i	0.0829649	−	0.213725i
$166$	3.19510	−	5.53408i	0.247988	−	0.429528i
$167$	−6.49472	+	11.2492i	−0.502576	+	0.870488i	0.497419	+	0.867510i	$0.334281\pi$
$167$	−6.49472	+	11.2492i	−0.502576	+	0.870488i	−0.999996	+	0.00297754i	$0.999052\pi$
$168$		−	1.52767i		−	0.117863i
$169$	−1.36213	−	12.9284i	−0.104779	−	0.994496i
$170$	−2.73532	+	2.19804i	−0.209789	+	0.168582i
$171$	−4.18063	−	2.41369i	−0.319701	−	0.184579i
$172$	4.58006	+	2.64430i	0.349226	+	0.201626i
$173$	3.35755	−	1.93848i	0.255270	−	0.147380i	−0.366905	−	0.930258i	$-0.619583\pi$
$173$	3.35755	−	1.93848i	0.255270	−	0.147380i	0.622175	+	0.782878i	$0.286249\pi$
$174$			4.42877i			0.335744i
$175$	−7.28207	+	2.30569i	−0.550473	+	0.174294i
$176$	1.14057	−	0.658509i	0.0859738	−	0.0496370i
$177$	10.4732			0.787213
$178$	−15.9738	+	9.22251i	−1.19729	+	0.691256i
$179$	7.05325	−	12.2166i	0.527185	−	0.913111i	−0.472313	−	0.881431i	$-0.656581\pi$
$179$	7.05325	−	12.2166i	0.527185	−	0.913111i	0.999498	−	0.0316802i	$-0.0100858\pi$
$180$	−2.20984	+	0.341491i	−0.164712	+	0.0254532i
$181$	−26.1472			−1.94351			−0.971753	−	0.236001i	$-0.924163\pi$
$181$	−26.1472			−1.94351			−0.971753	+	0.236001i	$0.924163\pi$
$182$	3.68513	−	4.09379i	0.273160	−	0.303452i
$183$		−	4.98268i		−	0.368331i
$184$	−7.31172	−	4.22143i	−0.539027	−	0.311208i
$185$	6.19408	−	0.957185i	0.455398	−	0.0703736i
$186$	0.813725	+	1.40941i	0.0596652	+	0.103343i
$187$	2.06678			0.151138
$188$	−2.47276	−	4.28295i	−0.180345	−	0.312366i
$189$	1.32301	−	0.763837i	0.0962345	−	0.0555610i
$190$	−8.41426	+	6.76151i	−0.610435	+	0.490531i
$191$	−9.42713	−	16.3283i	−0.682123	−	1.18147i	−0.974332	−	0.225117i	$-0.927723\pi$
$191$	−9.42713	−	16.3283i	−0.682123	−	1.18147i	0.292208	−	0.956355i	$-0.405610\pi$
$192$	−0.866025	−	0.500000i	−0.0625000	−	0.0360844i
$193$	−8.94600	+	15.4949i	−0.643947	+	1.11535i	0.340596	+	0.940210i	$0.389371\pi$
$193$	−8.94600	+	15.4949i	−0.643947	+	1.11535i	−0.984544	+	0.175140i	$0.943962\pi$
$194$	−1.92606			−0.138283
$195$	−6.74558	−	4.41556i	−0.483061	−	0.316205i
$196$	−4.66621			−0.333301
$197$	0.312928	−	0.542008i	0.0222952	−	0.0386165i	−0.854663	−	0.519184i	$-0.826236\pi$
$197$	0.312928	−	0.542008i	0.0222952	−	0.0386165i	0.876958	+	0.480567i	$0.159569\pi$
$198$	1.14057	+	0.658509i	0.0810568	+	0.0467982i
$199$	−8.84057	−	15.3123i	−0.626691	−	1.08546i	−0.988211	−	0.153097i	$-0.951075\pi$
$199$	−8.84057	−	15.3123i	−0.626691	−	1.08546i	0.361520	−	0.932364i	$-0.382258\pi$
$200$	−1.07631	+	4.88278i	−0.0761065	+	0.345265i
$201$	−2.40112	+	1.38628i	−0.169362	+	0.0977810i
$202$	1.21929	+	2.11188i	0.0857891	+	0.148591i
$203$	−6.76572			−0.474860
$204$	−0.784645	−	1.35904i	−0.0549361	−	0.0951521i
$205$	−0.535898	−	3.46788i	−0.0374288	−	0.242207i
$206$	10.7647	+	6.21501i	0.750013	+	0.433020i
$207$		−	8.44285i		−	0.586819i
$208$	−1.11461	−	3.42894i	−0.0772842	−	0.237754i
$209$	6.35774			0.439774
$210$	−0.521687	−	3.37591i	−0.0359999	−	0.232960i
$211$	−8.62227	+	14.9342i	−0.593581	+	1.02811i	0.400164	+	0.916443i	$0.368953\pi$
$211$	−8.62227	+	14.9342i	−0.593581	+	1.02811i	−0.993745	+	0.111669i	$0.964380\pi$
$212$	−12.0517	+	6.95804i	−0.827712	+	0.477880i
$213$	14.8394			1.01678
$214$	9.07302	−	5.23831i	0.620219	−	0.358083i
$215$	11.0242	+	4.27942i	0.751844	+	0.291854i
$216$		−	1.00000i		−	0.0680414i
$217$	−2.15313	+	1.24311i	−0.146164	+	0.0843877i
$218$	14.8782	+	8.58994i	1.00768	+	0.581784i
$219$	−5.18700	−	2.99472i	−0.350505	−	0.202364i
$220$	2.29560	−	1.84469i	0.154769	−	0.124369i
$221$	1.17570	−	5.53466i	0.0790861	−	0.372301i
$222$			2.80296i			0.188122i
$223$	−2.44858	+	4.24107i	−0.163969	+	0.284003i	−0.936289	−	0.351231i	$-0.885763\pi$
$223$	−2.44858	+	4.24107i	−0.163969	+	0.284003i	0.772320	+	0.635234i	$0.219096\pi$
$224$	0.763837	−	1.32301i	0.0510360	−	0.0883970i
$225$	−4.76677	+	1.50928i	−0.317785	+	0.100619i
$226$			2.59982i			0.172938i
$227$	5.07567	+	8.79132i	0.336884	+	0.583500i	0.983845	−	0.179023i	$-0.0572936\pi$
$227$	5.07567	+	8.79132i	0.336884	+	0.583500i	−0.646961	+	0.762523i	$0.723960\pi$
$228$	−2.41369	−	4.18063i	−0.159850	−	0.276869i
$229$		−	15.3959i		−	1.01739i	−0.860947	−	0.508694i	$-0.830129\pi$
$229$		−	15.3959i		−	1.01739i	0.860947	−	0.508694i	$-0.169871\pi$
$230$	−17.5993	−	6.83178i	−1.16046	−	0.450474i
$231$	−1.00599	+	1.74242i	−0.0661891	+	0.114643i
$232$	−2.21438	+	3.83543i	−0.145381	+	0.251808i
$233$			9.91624i			0.649634i	0.945777	+	0.324817i	$0.105303\pi$
$233$			9.91624i			0.649634i	−0.945777	+	0.324817i	$0.894697\pi$
$234$	2.41225	−	2.67975i	0.157694	−	0.175181i
$235$	−6.92699	−	8.62019i	−0.451867	−	0.562319i
$236$	9.07005	+	5.23660i	0.590410	+	0.340873i
$237$	−4.22302	−	2.43816i	−0.274315	−	0.158376i
$238$	2.07618	−	1.19868i	0.134579	−	0.0776990i
$239$		−	9.46167i		−	0.612024i	−0.952028	−	0.306012i	$-0.901005\pi$
$239$		−	9.46167i		−	0.612024i	0.952028	−	0.306012i	$-0.0989948\pi$
$240$	−2.08452	−	0.809179i	−0.134555	−	0.0522323i
$241$	11.3482	−	6.55189i	0.731002	−	0.422044i	−0.0877865	−	0.996139i	$-0.527979\pi$
$241$	11.3482	−	6.55189i	0.731002	−	0.422044i	0.818789	+	0.574095i	$0.194646\pi$
$242$	9.26546			0.595607
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	2.49134	−	4.31513i	0.159492	−	0.276248i
$245$	−10.3116	+	1.59347i	−0.658782	+	0.101803i
$246$	1.56929			0.100054
$247$	3.61663	−	17.0255i	0.230121	−	1.08330i
$248$			1.62745i			0.103343i
$249$	5.53408	+	3.19510i	0.350708	+	0.202481i
$250$	−0.711042	+	11.1577i	−0.0449702	+	0.705675i
$251$	11.5822	+	20.0610i	0.731062	+	1.26624i	0.956430	+	0.291963i	$0.0943085\pi$
$251$	11.5822	+	20.0610i	0.731062	+	1.26624i	−0.225367	+	0.974274i	$0.572358\pi$
$252$	1.52767			0.0962345
$253$	5.55969	+	9.62967i	0.349535	+	0.605412i
$254$	−7.01552	+	4.05041i	−0.440193	+	0.254146i
$255$	−2.19804	−	2.73532i	−0.137647	−	0.171292i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.32895	+	1.92197i	0.207654	+	0.119889i	0.600221	−	0.799834i	$-0.295079\pi$
$257$	3.32895	+	1.92197i	0.207654	+	0.119889i	−0.392566	+	0.919724i	$0.628413\pi$
$258$	−2.64430	+	4.58006i	−0.164627	+	0.285142i
$259$	−4.28201			−0.266071
$260$	−3.63406	−	7.19678i	−0.225375	−	0.446325i
$261$	−4.42877			−0.274134
$262$	1.16253	−	2.01356i	0.0718213	−	0.124398i
$263$	−26.5060	−	15.3032i	−1.63443	−	0.943638i	−0.982704	−	0.185184i	$-0.940712\pi$
$263$	−26.5060	−	15.3032i	−1.63443	−	0.943638i	−0.651726	−	0.758455i	$-0.725955\pi$
$264$	0.658509	+	1.14057i	0.0405284	+	0.0701973i
$265$	−24.2561	+	19.4917i	−1.49004	+	1.19736i
$266$	6.38665	−	3.68733i	0.391590	−	0.226085i
$267$	−9.22251	−	15.9738i	−0.564408	−	0.977584i
$268$	−2.77257			−0.169362
$269$	9.04370	+	15.6641i	0.551404	+	0.955060i	0.998174	+	0.0604109i	$0.0192411\pi$
$269$	9.04370	+	15.6641i	0.551404	+	0.955060i	−0.446769	+	0.894649i	$0.647426\pi$
$270$	−0.341491	−	2.20984i	−0.0207825	−	0.134486i
$271$	12.2869	+	7.09382i	0.746373	+	0.430919i	0.824382	−	0.566034i	$-0.191523\pi$
$271$	12.2869	+	7.09382i	0.746373	+	0.430919i	−0.0780089	+	0.996953i	$0.524856\pi$
$272$		−	1.56929i		−	0.0951521i
$273$	4.09379	+	3.68513i	0.247767	+	0.223034i
$274$	−12.2838			−0.742094
$275$	4.44296	−	4.86040i	0.267921	−	0.293093i
$276$	4.22143	−	7.31172i	0.254100	−	0.440114i
$277$	−14.5855	+	8.42097i	−0.876360	+	0.505967i	−0.869457	−	0.494009i	$-0.835531\pi$
$277$	−14.5855	+	8.42097i	−0.876360	+	0.505967i	−0.00690380	+	0.999976i	$0.502198\pi$
$278$	6.65721			0.399273
$279$	−1.40941	+	0.813725i	−0.0843794	+	0.0487165i
$280$	1.23616	−	3.18447i	0.0738748	−	0.190309i
$281$			8.61535i			0.513949i	0.966418	+	0.256974i	$0.0827256\pi$
$281$			8.61535i			0.513949i	−0.966418	+	0.256974i	$0.917274\pi$
$282$	4.28295	−	2.47276i	0.255046	−	0.147251i
$283$	23.9192	+	13.8098i	1.42185	+	0.820905i	0.996457	−	0.0841040i	$-0.0268028\pi$
$283$	23.9192	+	13.8098i	1.42185	+	0.820905i	0.425392	+	0.905009i	$0.360136\pi$
$284$	12.8513	+	7.41968i	0.762582	+	0.440277i
$285$	−6.76151	−	8.41426i	−0.400517	−	0.498418i
$286$	−0.986699	+	4.64493i	−0.0583447	+	0.274661i
$287$			2.39736i			0.141512i
$288$	0.500000	−	0.866025i	0.0294628	−	0.0510310i
$289$	−7.26867	+	12.5897i	−0.427569	+	0.740570i
$290$	−3.58367	+	9.23186i	−0.210440	+	0.542114i
$291$		−	1.92606i		−	0.112907i
$292$	−2.99472	−	5.18700i	−0.175253	−	0.303546i
$293$	15.1250	+	26.1973i	0.883614	+	1.53046i	0.847294	+	0.531125i	$0.178230\pi$
$293$	15.1250	+	26.1973i	0.883614	+	1.53046i	0.0363205	+	0.999340i	$0.488436\pi$
$294$		−	4.66621i		−	0.272139i
$295$	21.8316	+	8.47469i	1.27108	+	0.493415i
$296$	−1.40148	+	2.42743i	−0.0814593	+	0.141092i
$297$	−0.658509	+	1.14057i	−0.0382106	+	0.0661826i
$298$		−	3.01108i		−	0.174427i
$299$	28.9501	−	9.41048i	1.67422	−	0.544222i
$300$	−4.88278	−	1.07631i	−0.281908	−	0.0621407i
$301$	−6.99684	−	4.03963i	−0.403291	−	0.232840i
$302$	−10.4052	−	6.00745i	−0.598753	−	0.345690i
$303$	−2.11188	+	1.21929i	−0.121324	+	0.0700465i
$304$		−	4.82738i		−	0.276869i
$305$	4.03188	−	10.3865i	0.230865	−	0.594730i
$306$	1.35904	−	0.784645i	0.0776914	−	0.0448552i
$307$	14.1392			0.806966			0.403483	−	0.914987i	$-0.367799\pi$
$307$	14.1392			0.806966			0.403483	+	0.914987i	$0.367799\pi$
$308$	−1.74242	+	1.00599i	−0.0992837	+	0.0573215i
$309$	−6.21501	+	10.7647i	−0.353559	+	0.612383i
$310$	0.555760	+	3.59640i	0.0315650	+	0.204262i
$311$	−9.97427			−0.565589			−0.282794	−	0.959181i	$-0.591261\pi$
$311$	−9.97427			−0.565589			−0.282794	+	0.959181i	$0.591261\pi$
$312$	3.42894	−	1.11461i	0.194126	−	0.0631023i
$313$			3.08460i			0.174352i	0.996193	+	0.0871760i	$0.0277843\pi$
$313$			3.08460i			0.174352i	−0.996193	+	0.0871760i	$0.972216\pi$
$314$	−2.61155	−	1.50778i	−0.147378	−	0.0850888i
$315$	3.37591	−	0.521687i	0.190211	−	0.0293938i
$316$	−2.43816	−	4.22302i	−0.137157	−	0.237563i
$317$	−14.2980			−0.803054			−0.401527	−	0.915847i	$-0.631520\pi$
$317$	−14.2980			−0.803054			−0.401527	+	0.915847i	$0.631520\pi$
$318$	−6.95804	−	12.0517i	−0.390187	−	0.675824i
$319$	5.05132	−	2.91638i	0.282820	−	0.163286i
$320$	−1.40066	−	1.74303i	−0.0782992	−	0.0974384i
$321$	5.23831	+	9.07302i	0.292374	+	0.506407i
$322$	11.1699	+	6.44897i	0.622476	+	0.359387i
$323$	3.78778	−	6.56062i	0.210757	−	0.365043i
$324$	1.00000			0.0555556
$325$	−10.4883	−	14.6627i	−0.581787	−	0.813341i
$326$	9.91624			0.549210
$327$	−8.58994	+	14.8782i	−0.475025	+	0.822767i
$328$	1.35904	+	0.784645i	0.0750407	+	0.0433248i
$329$	3.77757	+	6.54295i	0.208264	+	0.360724i
$330$	1.84469	+	2.29560i	0.101547	+	0.126369i
$331$	−9.89017	+	5.71009i	−0.543613	+	0.313855i	−0.746542	−	0.665338i	$-0.768287\pi$
$331$	−9.89017	+	5.71009i	−0.543613	+	0.313855i	0.202929	+	0.979193i	$0.434954\pi$
$332$	3.19510	+	5.53408i	0.175354	+	0.303722i
$333$	−2.80296			−0.153601
$334$	−6.49472	−	11.2492i	−0.355375	−	0.615528i
$335$	−6.12693	+	0.946808i	−0.334750	+	0.0517296i
$336$	1.32301	+	0.763837i	0.0721759	+	0.0416708i
$337$		−	5.53208i		−	0.301352i	−0.988583	−	0.150676i	$-0.951855\pi$
$337$		−	5.53208i		−	0.301352i	0.988583	−	0.150676i	$-0.0481450\pi$
$338$	11.8774	+	5.28458i	0.646047	+	0.287443i
$339$	−2.59982			−0.141203
$340$	−0.535898	−	3.46788i	−0.0290632	−	0.188072i
$341$	1.07169	−	1.85622i	0.0580353	−	0.100520i
$342$	4.18063	−	2.41369i	0.226063	−	0.130517i
$343$	17.8222			0.962307
$344$	−4.58006	+	2.64430i	−0.246940	+	0.142571i
$345$	6.83178	−	17.5993i	0.367811	−	0.947515i
$346$			3.87696i			0.208427i
$347$	2.44226	−	1.41004i	0.131107	−	0.0756949i	−0.433012	−	0.901388i	$-0.642549\pi$
$347$	2.44226	−	1.41004i	0.131107	−	0.0756949i	0.564119	+	0.825693i	$0.309216\pi$
$348$	−3.83543	−	2.21438i	−0.205600	−	0.118703i
$349$	23.0704	+	13.3197i	1.23493	+	0.712986i	0.968053	−	0.250745i	$-0.0806757\pi$
$349$	23.0704	+	13.3197i	1.23493	+	0.712986i	0.266875	+	0.963731i	$0.414009\pi$
$350$	1.64425	−	7.45930i	0.0878889	−	0.398717i
$351$	2.67975	+	2.41225i	0.143035	+	0.128756i
$352$			1.31702i			0.0701973i
$353$	−6.61308	+	11.4542i	−0.351979	+	0.609645i	−0.986596	−	0.163182i	$-0.947824\pi$
$353$	−6.61308	+	11.4542i	−0.351979	+	0.609645i	0.634617	+	0.772826i	$0.281158\pi$
$354$	−5.23660	+	9.07005i	−0.278322	+	0.482068i
$355$	30.9329	+	12.0077i	1.64175	+	0.637302i
$356$		−	18.4450i		−	0.977584i
$357$	1.19868	+	2.07618i	0.0634410	+	0.109883i
$358$	7.05325	+	12.2166i	0.372776	+	0.645667i
$359$			12.3827i			0.653532i	0.945105	+	0.326766i	$0.105959\pi$
$359$			12.3827i			0.653532i	−0.945105	+	0.326766i	$0.894041\pi$
$360$	0.809179	−	2.08452i	0.0426475	−	0.109864i
$361$	2.15178	−	3.72700i	0.113252	−	0.196158i
$362$	13.0736	−	22.6441i	0.687133	−	1.19015i
$363$			9.26546i			0.486311i
$364$	1.70276	+	5.23831i	0.0892489	+	0.274562i
$365$	−8.38916	−	10.4398i	−0.439109	−	0.546443i
$366$	4.31513	+	2.49134i	0.225556	+	0.130225i
$367$	−6.14226	−	3.54624i	−0.320623	−	0.185112i	0.331047	−	0.943614i	$-0.392598\pi$
$367$	−6.14226	−	3.54624i	−0.320623	−	0.185112i	−0.651670	+	0.758502i	$0.725931\pi$
$368$	7.31172	−	4.22143i	0.381150	−	0.220057i
$369$			1.56929i			0.0816939i
$370$	−2.26809	+	5.84282i	−0.117913	+	0.303754i
$371$	18.4110	−	10.6296i	0.955854	−	0.551862i
$372$	−1.62745			−0.0843794
$373$	32.0259	−	18.4902i	1.65824	−	0.957384i	0.684709	−	0.728816i	$-0.259929\pi$
$373$	32.0259	−	18.4902i	1.65824	−	0.957384i	0.973528	−	0.228568i	$-0.0734042\pi$
$374$	−1.03339	+	1.78989i	−0.0534354	+	0.0925528i
$375$	−11.1577	−	0.711042i	−0.576181	−	0.0367180i
$376$	4.94552			0.255046
$377$	−4.93634	−	15.1860i	−0.254235	−	0.782118i
$378$			1.52767i			0.0785751i
$379$	−29.6252	−	17.1041i	−1.52174	−	0.878580i	−0.999670	−	0.0256802i	$-0.991825\pi$
$379$	−29.6252	−	17.1041i	−1.52174	−	0.878580i	−0.522075	−	0.852900i	$-0.674842\pi$
$380$	−1.64851	−	10.6677i	−0.0845666	−	0.547243i
$381$	−4.05041	−	7.01552i	−0.207509	−	0.359416i
$382$	18.8543			0.964668
$383$	13.0170	+	22.5461i	0.665137	+	1.15205i	0.979248	+	0.202665i	$0.0649603\pi$
$383$	13.0170	+	22.5461i	0.665137	+	1.15205i	−0.314111	+	0.949386i	$0.601706\pi$
$384$	0.866025	−	0.500000i	0.0441942	−	0.0255155i
$385$	−3.50693	+	2.81809i	−0.178730	+	0.143623i
$386$	−8.94600	−	15.4949i	−0.455340	−	0.788671i
$387$	−4.58006	−	2.64430i	−0.232817	−	0.134417i
$388$	0.963028	−	1.66801i	0.0488904	−	0.0846806i
$389$	−6.23568			−0.316162			−0.158081	−	0.987426i	$-0.550531\pi$
$389$	−6.23568			−0.316162			−0.158081	+	0.987426i	$0.550531\pi$
$390$	7.19678	−	3.63406i	0.364423	−	0.184018i
$391$	13.2493			0.670045
$392$	2.33310	−	4.04106i	0.117840	−	0.204104i
$393$	2.01356	+	1.16253i	0.101571	+	0.0586419i
$394$	0.312928	+	0.542008i	0.0157651	+	0.0273060i
$395$	−6.83007	−	8.49958i	−0.343658	−	0.427660i
$396$	−1.14057	+	0.658509i	−0.0573158	+	0.0330913i
$397$	−18.3498	−	31.7827i	−0.920948	−	1.59513i	−0.797951	−	0.602722i	$-0.794083\pi$
$397$	−18.3498	−	31.7827i	−0.920948	−	1.59513i	−0.122997	−	0.992407i	$-0.539250\pi$
$398$	17.6811			0.886275
$399$	3.68733	+	6.38665i	0.184597	+	0.319732i
$400$	−3.69046	−	3.37350i	−0.184523	−	0.168675i
$401$	24.5044	+	14.1476i	1.22369	+	0.706498i	0.965703	−	0.259651i	$-0.0836074\pi$
$401$	24.5044	+	14.1476i	1.22369	+	0.706498i	0.257987	+	0.966148i	$0.416941\pi$
$402$		−	2.77257i		−	0.138283i
$403$	−4.36116	−	3.92581i	−0.217245	−	0.195559i
$404$	−2.43859			−0.121324
$405$	2.20984	−	0.341491i	0.109808	−	0.0169688i
$406$	3.38286	−	5.85928i	0.167888	−	0.290791i
$407$	3.19697	−	1.84577i	0.158468	−	0.0914915i
$408$	1.56929			0.0776914
$409$	13.2744	−	7.66400i	0.656379	−	0.378961i	−0.134517	−	0.990911i	$-0.542948\pi$
$409$	13.2744	−	7.66400i	0.656379	−	0.378961i	0.790896	+	0.611951i	$0.209615\pi$
$410$	3.27122	+	1.26984i	0.161554	+	0.0627127i
$411$		−	12.2838i		−	0.605917i
$412$	−10.7647	+	6.21501i	−0.530339	+	0.306191i
$413$	−13.8561	−	7.99982i	−0.681814	−	0.393645i
$414$	7.31172	+	4.22143i	0.359352	+	0.207472i
$415$	8.95050	+	11.1383i	0.439363	+	0.546758i
$416$	3.52686	+	0.749192i	0.172918	+	0.0367322i
$417$			6.65721i			0.326005i
$418$	−3.17887	+	5.50597i	−0.155484	+	0.269306i
$419$	−13.4692	+	23.3293i	−0.658013	+	1.13971i	0.323116	+	0.946359i	$0.395270\pi$
$419$	−13.4692	+	23.3293i	−0.658013	+	1.13971i	−0.981129	+	0.193353i	$0.938064\pi$
$420$	3.18447	+	1.23616i	0.155386	+	0.0603186i
$421$			38.5359i			1.87812i	0.343747	+	0.939062i	$0.388304\pi$
$421$			38.5359i			1.87812i	−0.343747	+	0.939062i	$0.611696\pi$
$422$	−8.62227	−	14.9342i	−0.419725	−	0.726986i
$423$	2.47276	+	4.28295i	0.120230	+	0.208244i
$424$		−	13.9161i		−	0.675824i
$425$	−2.36850	−	7.48044i	−0.114889	−	0.362855i
$426$	−7.41968	+	12.8513i	−0.359484	+	0.622645i
$427$	−3.80596	+	6.59212i	−0.184183	+	0.319015i
$428$			10.4766i			0.506407i
$429$	−4.64493	−	0.986699i	−0.224259	−	0.0476383i
$430$	−9.21818	+	7.40752i	−0.444540	+	0.357222i
$431$	2.48744	+	1.43612i	0.119816	+	0.0691756i	0.558710	−	0.829363i	$-0.311296\pi$
$431$	2.48744	+	1.43612i	0.119816	+	0.0691756i	−0.438894	+	0.898539i	$0.644630\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$	−11.2344	+	6.48619i	−0.539891	+	0.311706i	−0.745035	−	0.667026i	$-0.767567\pi$
$433$	−11.2344	+	6.48619i	−0.539891	+	0.311706i	0.205144	+	0.978732i	$0.434234\pi$
$434$		−	2.48622i		−	0.119342i
$435$	−9.23186	−	3.58367i	−0.442634	−	0.171824i
$436$	−14.8782	+	8.58994i	−0.712537	+	0.411383i
$437$	40.7568			1.94966
$438$	5.18700	−	2.99472i	0.247845	−	0.143093i
$439$	−1.02411	+	1.77380i	−0.0488779	+	0.0846590i	−0.889429	−	0.457073i	$-0.848898\pi$
$439$	−1.02411	+	1.77380i	−0.0488779	+	0.0846590i	0.840551	+	0.541732i	$0.182231\pi$
$440$	0.449750	+	2.91040i	0.0214410	+	0.138748i
$441$	4.66621			0.222200
$442$	4.20530	+	3.78551i	0.200026	+	0.180059i
$443$		−	25.7082i		−	1.22143i	−0.791849	−	0.610717i	$-0.790881\pi$
$443$		−	25.7082i		−	1.22143i	0.791849	−	0.610717i	$-0.209119\pi$
$444$	−2.42743	−	1.40148i	−0.115201	−	0.0665112i
$445$	−6.29881	−	40.7605i	−0.298592	−	1.93223i
$446$	−2.44858	−	4.24107i	−0.115944	−	0.200820i
$447$	3.01108			0.142419
$448$	0.763837	+	1.32301i	0.0360879	+	0.0625061i
$449$	−16.0756	+	9.28127i	−0.758656	+	0.438010i	−0.828813	−	0.559526i	$-0.810983\pi$
$449$	−16.0756	+	9.28127i	−0.758656	+	0.438010i	0.0701571	+	0.997536i	$0.477650\pi$
$450$	1.07631	−	4.88278i	0.0507377	−	0.230177i
$451$	−1.03339	−	1.78989i	−0.0486605	−	0.0842824i
$452$	−2.25151	−	1.29991i	−0.105902	−	0.0611427i
$453$	6.00745	−	10.4052i	0.282255	−	0.488880i
$454$	−10.1513			−0.476426
$455$	5.55166	+	10.9943i	0.260266	+	0.515423i
$456$	4.82738			0.226063
$457$	−12.3213	+	21.3412i	−0.576368	+	0.998299i	0.419523	+	0.907745i	$0.362197\pi$
$457$	−12.3213	+	21.3412i	−0.576368	+	0.998299i	−0.995891	+	0.0905546i	$0.971136\pi$
$458$	13.3332	+	7.69794i	0.623020	+	0.359701i
$459$	0.784645	+	1.35904i	0.0366241	+	0.0634348i
$460$	14.7161	−	11.8256i	0.686144	−	0.551369i
$461$	−27.5693	+	15.9171i	−1.28403	+	0.741334i	−0.977582	−	0.210554i	$-0.932473\pi$
$461$	−27.5693	+	15.9171i	−1.28403	+	0.741334i	−0.306446	+	0.951888i	$0.599140\pi$
$462$	−1.00599	−	1.74242i	−0.0468028	−	0.0810648i
$463$	3.18319			0.147936			0.0739678	−	0.997261i	$-0.476434\pi$
$463$	3.18319			0.147936			0.0739678	+	0.997261i	$0.476434\pi$
$464$	−2.21438	−	3.83543i	−0.102800	−	0.178055i
$465$	−3.59640	+	0.555760i	−0.166779	+	0.0257727i
$466$	−8.58772	−	4.95812i	−0.397818	−	0.229680i
$467$			21.6747i			1.00298i	0.865162	+	0.501492i	$0.167215\pi$
$467$			21.6747i			1.00298i	−0.865162	+	0.501492i	$0.832785\pi$
$468$	1.11461	+	3.42894i	0.0515228	+	0.158503i
$469$	4.23559			0.195581
$470$	10.9288	−	1.68885i	0.504108	−	0.0779009i
$471$	1.50778	−	2.61155i	0.0694747	−	0.120334i
$472$	−9.07005	+	5.23660i	−0.417483	+	0.241034i
$473$	6.96517			0.320259
$474$	4.22302	−	2.43816i	0.193970	−	0.111988i
$475$	−7.28586	−	23.0110i	−0.334298	−	1.05582i
$476$			2.39736i			0.109883i
$477$	12.0517	−	6.95804i	0.551808	−	0.318587i
$478$	8.19404	+	4.73083i	0.374787	+	0.216383i
$479$	−25.3765	−	14.6511i	−1.15948	−	0.669426i	−0.208300	−	0.978065i	$-0.566793\pi$
$479$	−25.3765	−	14.6511i	−1.15948	−	0.669426i	−0.951179	+	0.308639i	$0.900127\pi$
$480$	1.74303	−	1.40066i	0.0795581	−	0.0639310i
$481$	−3.12420	−	9.61118i	−0.142451	−	0.438232i
$482$			13.1038i			0.596861i
$483$	−6.44897	+	11.1699i	−0.293438	+	0.508250i
$484$	−4.63273	+	8.02413i	−0.210579	+	0.364733i
$485$	1.55852	−	4.01491i	0.0707690	−	0.182308i
$486$			1.00000i			0.0453609i
$487$	−21.2643	−	36.8309i	−0.963579	−	1.66897i	−0.713385	−	0.700772i	$-0.752839\pi$
$487$	−21.2643	−	36.8309i	−0.963579	−	1.66897i	−0.250194	−	0.968196i	$-0.580494\pi$
$488$	2.49134	+	4.31513i	0.112778	+	0.195337i
$489$			9.91624i			0.448428i
$490$	3.77580	−	9.72681i	0.170573	−	0.439413i
$491$	6.32521	−	10.9556i	0.285453	−	0.494418i	−0.687266	−	0.726406i	$-0.741189\pi$
$491$	6.32521	−	10.9556i	0.285453	−	0.494418i	0.972719	+	0.231987i	$0.0745228\pi$
$492$	−0.784645	+	1.35904i	−0.0353745	+	0.0612705i
$493$		−	6.95002i		−	0.313013i
$494$	12.9362	+	11.6448i	0.582026	+	0.523925i
$495$	−2.29560	+	1.84469i	−0.103180	+	0.0829128i
$496$	−1.40941	−	0.813725i	−0.0632845	−	0.0365373i
$497$	−19.6325	−	11.3349i	−0.880640	−	0.508438i
$498$	−5.53408	+	3.19510i	−0.247988	+	0.143176i
$499$			4.54007i			0.203242i	0.994823	+	0.101621i	$0.0324028\pi$
$499$			4.54007i			0.203242i	−0.994823	+	0.101621i	$0.967597\pi$
$500$	−9.30734	−	6.19463i	−0.416237	−	0.277032i
$501$	11.2492	−	6.49472i	0.502576	−	0.290163i
$502$	−23.1644			−1.03388
$503$	−17.2476	+	9.95791i	−0.769033	+	0.444001i	−0.832529	−	0.553981i	$-0.813108\pi$
$503$	−17.2476	+	9.95791i	−0.769033	+	0.444001i	0.0634967	+	0.997982i	$0.479775\pi$
$504$	−0.763837	+	1.32301i	−0.0340240	+	0.0589313i
$505$	−5.38888	+	0.832755i	−0.239802	+	0.0370571i
$506$	−11.1194			−0.494317
$507$	−5.28458	+	11.8774i	−0.234697	+	0.527495i
$508$		−	8.10083i		−	0.359416i
$509$	−9.09532	−	5.25118i	−0.403143	−	0.232755i	0.284696	−	0.958618i	$-0.408107\pi$
$509$	−9.09532	−	5.25118i	−0.403143	−	0.232755i	−0.687839	+	0.725863i	$0.741441\pi$
$510$	3.46788	−	0.535898i	0.153560	−	0.0237300i
$511$	4.57496	+	7.92406i	0.202384	+	0.350540i
$512$	1.00000			0.0441942
$513$	2.41369	+	4.18063i	0.106567	+	0.184579i
$514$	−3.32895	+	1.92197i	−0.146834	+	0.0847746i
$515$	−21.6659	+	17.4102i	−0.954713	+	0.767185i
$516$	−2.64430	−	4.58006i	−0.116409	−	0.201626i
$517$	−5.64072	−	3.25667i	−0.248078	−	0.143228i
$518$	2.14100	−	3.70833i	0.0940703	−	0.162934i
$519$	−3.87696			−0.170180
$520$	8.04962	+	0.451203i	0.352999	+	0.0197866i
$521$	−24.5221			−1.07433			−0.537166	−	0.843477i	$-0.680505\pi$
$521$	−24.5221			−1.07433			−0.537166	+	0.843477i	$0.680505\pi$
$522$	2.21438	−	3.83543i	0.0969210	−	0.167872i
$523$	21.6924	+	12.5241i	0.948541	+	0.547641i	0.892627	−	0.450795i	$-0.148859\pi$
$523$	21.6924	+	12.5241i	0.948541	+	0.547641i	0.0559138	+	0.998436i	$0.482193\pi$
$524$	1.16253	+	2.01356i	0.0507853	+	0.0879628i
$525$	7.45930	+	1.64425i	0.325551	+	0.0717610i
$526$	26.5060	−	15.3032i	1.15572	−	0.667253i
$527$	−1.27697	−	2.21178i	−0.0556257	−	0.0963466i
$528$	−1.31702			−0.0573158
$529$	24.1409	+	41.8132i	1.04960	+	1.81797i
$530$	−4.75222	−	30.7523i	−0.206423	−	1.33579i
$531$	−9.07005	−	5.23660i	−0.393607	−	0.227249i
$532$			7.37466i			0.319732i
$533$	−5.38100	+	1.74914i	−0.233077	+	0.0757638i
$534$	18.4450			0.798194
$535$	3.57767	+	23.1516i	0.154676	+	1.00093i
$536$	1.38628	−	2.40112i	0.0598784	−	0.103712i
$537$	−12.2166	+	7.05325i	−0.527185	+	0.304370i
$538$	−18.0874			−0.779803
$539$	−5.32214	+	3.07274i	−0.229241	+	0.132352i
$540$	2.08452	+	0.809179i	0.0897035	+	0.0348215i
$541$		−	20.6859i		−	0.889356i	−0.895690	−	0.444678i	$-0.853318\pi$
$541$		−	20.6859i		−	0.889356i	0.895690	−	0.444678i	$-0.146682\pi$
$542$	−12.2869	+	7.09382i	−0.527765	+	0.304705i
$543$	22.6441	+	13.0736i	0.971753	+	0.561042i
$544$	1.35904	+	0.784645i	0.0582686	+	0.0336414i
$545$	−29.9450	+	24.0631i	−1.28270	+	1.03075i
$546$	−5.23831	+	1.70276i	−0.224179	+	0.0728714i
$547$			40.5960i			1.73576i	0.496773	+	0.867880i	$0.334518\pi$
$547$			40.5960i			1.73576i	−0.496773	+	0.867880i	$0.665482\pi$
$548$	6.14192	−	10.6381i	0.262370	−	0.454438i
$549$	−2.49134	+	4.31513i	−0.106328	+	0.184165i
$550$	1.98775	+	6.27792i	0.0847579	+	0.267691i
$551$		−	21.3793i		−	0.910790i
$552$	4.22143	+	7.31172i	0.179676	+	0.311208i
$553$	3.72472	+	6.45140i	0.158391	+	0.274342i
$554$		−	16.8419i		−	0.715545i
$555$	−5.84282	−	2.26809i	−0.248014	−	0.0962752i
$556$	−3.32861	+	5.76531i	−0.141164	+	0.244504i
$557$	20.6032	−	35.6858i	0.872985	−	1.51205i	0.0140907	−	0.999901i	$-0.495515\pi$
$557$	20.6032	−	35.6858i	0.872985	−	1.51205i	0.858894	−	0.512153i	$-0.171152\pi$
$558$		−	1.62745i		−	0.0688955i
$559$	3.96217	−	18.6521i	0.167582	−	0.788900i
$560$	2.13975	+	2.66278i	0.0904210	+	0.112523i
$561$	−1.78989	−	1.03339i	−0.0755690	−	0.0436298i
$562$	−7.46112	−	4.30768i	−0.314728	−	0.181708i
$563$	−13.0933	+	7.55940i	−0.551815	+	0.318591i	−0.749854	−	0.661603i	$-0.769876\pi$
$563$	−13.0933	+	7.55940i	−0.551815	+	0.318591i	0.198038	+	0.980194i	$0.436543\pi$
$564$			4.94552i			0.208244i
$565$	−5.41939	−	2.10372i	−0.227995	−	0.0885043i
$566$	−23.9192	+	13.8098i	−1.00540	+	0.580468i
$567$	−1.52767			−0.0641563
$568$	−12.8513	+	7.41968i	−0.539227	+	0.311323i
$569$	−13.2995	+	23.0353i	−0.557542	+	0.965692i	0.440159	+	0.897920i	$0.354922\pi$
$569$	−13.2995	+	23.0353i	−0.557542	+	0.965692i	−0.997701	+	0.0677716i	$0.978411\pi$
$570$	10.6677	−	1.64851i	0.446822	−	0.0690483i
$571$	31.8452			1.33268			0.666340	−	0.745648i	$-0.267860\pi$
$571$	31.8452			1.33268			0.666340	+	0.745648i	$0.267860\pi$
$572$	−3.52928	−	3.17697i	−0.147567	−	0.132836i
$573$			18.8543i			0.787648i
$574$	−2.07618	−	1.19868i	−0.0866580	−	0.0500320i
$575$	28.4820	−	31.1580i	1.18778	−	1.29938i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	−1.20258			−0.0500639			−0.0250319	−	0.999687i	$-0.507969\pi$
$577$	−1.20258			−0.0500639			−0.0250319	+	0.999687i	$0.507969\pi$
$578$	−7.26867	−	12.5897i	−0.302337	−	0.523662i
$579$	15.4949	−	8.94600i	0.643947	−	0.371783i
$580$	−6.20319	−	7.71948i	−0.257574	−	0.320534i
$581$	−4.88108	−	8.45427i	−0.202501	−	0.350742i
$582$	1.66801	+	0.963028i	0.0691414	+	0.0399188i
$583$	−9.16386	+	15.8723i	−0.379528	+	0.657362i
$584$	5.98944			0.247845
$585$	3.63406	+	7.19678i	0.150250	+	0.297550i
$586$	−30.2501			−1.24962
$587$	−9.53243	+	16.5107i	−0.393446	+	0.681468i	−0.992901	−	0.118940i	$-0.962050\pi$
$587$	−9.53243	+	16.5107i	−0.393446	+	0.681468i	0.599456	+	0.800408i	$0.295384\pi$
$588$	4.04106	+	2.33310i	0.166650	+	0.0962156i
$589$	−3.92816	−	6.80377i	−0.161857	−	0.280344i
$590$	−18.2551	+	14.6694i	−0.751550	+	0.603929i
$591$	−0.542008	+	0.312928i	−0.0222952	+	0.0128722i
$592$	−1.40148	−	2.42743i	−0.0576004	−	0.0997668i
$593$	−11.8496			−0.486606			−0.243303	−	0.969950i	$-0.578231\pi$
$593$	−11.8496			−0.486606			−0.243303	+	0.969950i	$0.578231\pi$
$594$	−0.658509	−	1.14057i	−0.0270189	−	0.0467982i
$595$	0.818679	+	5.29779i	0.0335625	+	0.217188i
$596$	2.60768	+	1.50554i	0.106815	+	0.0616694i
$597$			17.6811i			0.723641i
$598$	−6.32532	+	29.7767i	−0.258661	+	1.21766i
$599$	13.1277			0.536382			0.268191	−	0.963366i	$-0.413574\pi$
$599$	13.1277			0.536382			0.268191	+	0.963366i	$0.413574\pi$
$600$	3.37350	−	3.69046i	0.137723	−	0.150662i
$601$	17.8125	−	30.8522i	0.726589	−	1.25849i	−0.231728	−	0.972781i	$-0.574438\pi$
$601$	17.8125	−	30.8522i	0.726589	−	1.25849i	0.958317	−	0.285708i	$-0.0922288\pi$
$602$	6.99684	−	4.03963i	0.285170	−	0.164643i
$603$	2.77257			0.112908
$604$	10.4052	−	6.00745i	0.423382	−	0.244440i
$605$	−7.49742	+	19.3141i	−0.304813	+	0.785228i
$606$		−	2.43859i		−	0.0990608i
$607$	−4.20075	+	2.42530i	−0.170503	+	0.0984400i	−0.582823	−	0.812599i	$-0.698052\pi$
$607$	−4.20075	+	2.42530i	−0.170503	+	0.0984400i	0.412320	+	0.911039i	$0.364719\pi$
$608$	4.18063	+	2.41369i	0.169547	+	0.0978880i
$609$	5.85928	+	3.38286i	0.237430	+	0.137080i
$610$	6.97904	+	8.68497i	0.282573	+	0.351644i
$611$	−11.9298	+	13.2528i	−0.482629	+	0.536149i
$612$			1.56929i			0.0634348i
$613$	11.7172	−	20.2948i	0.473253	−	0.819698i	−0.526279	−	0.850312i	$-0.676413\pi$
$613$	11.7172	−	20.2948i	0.473253	−	0.819698i	0.999531	+	0.0306146i	$0.00974646\pi$
$614$	−7.06959	+	12.2449i	−0.285306	+	0.494164i
$615$	−1.26984	+	3.27122i	−0.0512047	+	0.131908i
$616$		−	2.01198i		−	0.0810648i
$617$	−7.01830	−	12.1560i	−0.282546	−	0.489384i	0.689465	−	0.724319i	$-0.257846\pi$
$617$	−7.01830	−	12.1560i	−0.282546	−	0.489384i	−0.972011	+	0.234935i	$0.924512\pi$
$618$	−6.21501	−	10.7647i	−0.250004	−	0.433020i
$619$		−	16.1470i		−	0.649002i	−0.945885	−	0.324501i	$-0.894804\pi$
$619$		−	16.1470i		−	0.649002i	0.945885	−	0.324501i	$-0.105196\pi$
$620$	−3.39246	−	1.31690i	−0.136244	−	0.0528879i
$621$	−4.22143	+	7.31172i	−0.169400	+	0.293409i
$622$	4.98713	−	8.63797i	0.199966	−	0.346351i
$623$			28.1780i			1.12893i
$624$	−0.749192	+	3.52686i	−0.0299917	+	0.141187i
$625$	−22.6831	−	10.5108i	−0.907325	−	0.420431i
$626$	−2.67134	−	1.54230i	−0.106768	−	0.0616428i
$627$	−5.50597	−	3.17887i	−0.219887	−	0.126952i
$628$	2.61155	−	1.50778i	0.104212	−	0.0601669i
$629$		−	4.39865i		−	0.175386i
$630$	−1.23616	+	3.18447i	−0.0492499	+	0.126872i
$631$	16.3611	−	9.44608i	0.651325	−	0.376043i	−0.137639	−	0.990483i	$-0.543951\pi$
$631$	16.3611	−	9.44608i	0.651325	−	0.376043i	0.788964	+	0.614440i	$0.210618\pi$
$632$	4.87632			0.193970
$633$	14.9342	−	8.62227i	0.593581	−	0.342704i
$634$	7.14899	−	12.3824i	0.283922	−	0.491768i
$635$	−2.76636	−	17.9015i	−0.109780	−	0.710400i
$636$	13.9161			0.551808
$637$	5.20100	+	16.0002i	0.206071	+	0.633950i
$638$			5.83277i			0.230921i
$639$	−12.8513	−	7.41968i	−0.508388	−	0.293518i
$640$	2.20984	−	0.341491i	0.0873515	−	0.0134986i
$641$	3.57648	+	6.19465i	0.141262	+	0.244674i	0.927972	−	0.372649i	$-0.121551\pi$
$641$	3.57648	+	6.19465i	0.141262	+	0.244674i	−0.786710	+	0.617323i	$0.788217\pi$
$642$	−10.4766			−0.413479
$643$	19.9623	+	34.5756i	0.787235	+	1.36353i	0.927655	+	0.373438i	$0.121821\pi$
$643$	19.9623	+	34.5756i	0.787235	+	1.36353i	−0.140420	+	0.990092i	$0.544845\pi$
$644$	−11.1699	+	6.44897i	−0.440157	+	0.254125i
$645$	−7.40752	−	9.21818i	−0.291671	−	0.362966i
$646$	3.78778	+	6.56062i	0.149028	+	0.258124i
$647$	12.0656	+	6.96608i	0.474348	+	0.273865i	0.718058	−	0.695983i	$-0.245031\pi$
$647$	12.0656	+	6.96608i	0.474348	+	0.273865i	−0.243710	+	0.969848i	$0.578365\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	13.7934			0.541438
$650$	17.9424	−	1.75179i	0.703760	−	0.0687108i
$651$	2.48622			0.0974425
$652$	−4.95812	+	8.58772i	−0.194175	+	0.336321i
$653$	−25.7670	−	14.8766i	−1.00834	−	0.582165i	−0.0976340	−	0.995222i	$-0.531127\pi$
$653$	−25.7670	−	14.8766i	−1.00834	−	0.582165i	−0.910705	+	0.413058i	$0.864461\pi$
$654$	−8.58994	−	14.8782i	−0.335893	−	0.581784i
$655$	3.25662	+	4.05265i	0.127246	+	0.158350i
$656$	−1.35904	+	0.784645i	−0.0530618	+	0.0306352i
$657$	2.99472	+	5.18700i	0.116835	+	0.202364i
$658$	−7.55515			−0.294530
$659$	−14.6318	−	25.3431i	−0.569975	−	0.987226i	−0.996568	−	0.0827819i	$-0.973620\pi$
$659$	−14.6318	−	25.3431i	−0.569975	−	0.987226i	0.426593	−	0.904444i	$-0.359714\pi$
$660$	−2.91040	+	0.449750i	−0.113287	+	0.0175065i
$661$	−30.0903	−	17.3726i	−1.17038	−	0.675717i	−0.216608	−	0.976259i	$-0.569499\pi$
$661$	−30.0903	−	17.3726i	−1.17038	−	0.675717i	−0.953769	+	0.300541i	$0.902833\pi$
$662$		−	11.4202i		−	0.443858i
$663$	−3.78551	+	4.20530i	−0.147017	+	0.163320i
$664$	−6.39020			−0.247988
$665$	2.51838	+	16.2968i	0.0976587	+	0.631963i
$666$	1.40148	−	2.42743i	0.0543062	−	0.0940611i
$667$	32.3819	−	18.6957i	1.25383	−	0.723901i
$668$	12.9894			0.502576
$669$	4.24107	−	2.44858i	0.163969	−	0.0946676i
$670$	2.24351	−	5.77948i	0.0866742	−	0.223281i
$671$		−	6.56228i		−	0.253334i
$672$	−1.32301	+	0.763837i	−0.0510360	+	0.0294657i
$673$	−28.1953	−	16.2786i	−1.08685	−	0.627492i	−0.154113	−	0.988053i	$-0.549252\pi$
$673$	−28.1953	−	16.2786i	−1.08685	−	0.627492i	−0.932736	+	0.360561i	$0.882585\pi$
$674$	4.79092	+	2.76604i	0.184539	+	0.106544i
$675$	4.88278	+	1.07631i	0.187938	+	0.0414272i
$676$	−10.5153	+	7.64386i	−0.404434	+	0.293995i
$677$		−	32.2002i		−	1.23756i	−0.785566	−	0.618778i	$-0.787628\pi$
$677$		−	32.2002i		−	1.23756i	0.785566	−	0.618778i	$-0.212372\pi$
$678$	1.29991	−	2.25151i	0.0499228	−	0.0864689i
$679$	−1.47119	+	2.54818i	−0.0564593	+	0.0977903i
$680$	3.27122	+	1.26984i	0.125445	+	0.0486960i
$681$		−	10.1513i		−	0.389000i
$682$	1.07169	+	1.85622i	0.0410372	+	0.0710784i
$683$	3.19280	+	5.53009i	0.122169	+	0.211603i	0.920623	−	0.390453i	$-0.127682\pi$
$683$	3.19280	+	5.53009i	0.122169	+	0.211603i	−0.798454	+	0.602056i	$0.794348\pi$
$684$			4.82738i			0.184579i
$685$	9.93983	−	25.6059i	0.379781	−	0.978352i
$686$	−8.91109	+	15.4345i	−0.340227	+	0.589290i
$687$	−7.69794	+	13.3332i	−0.293695	+	0.508694i
$688$		−	5.28860i		−	0.201626i
$689$	37.2916	+	33.5690i	1.42070	+	1.27888i
$690$	11.8256	+	14.7161i	0.450191	+	0.560234i
$691$	13.6788	+	7.89748i	0.520368	+	0.300434i	0.737085	−	0.675800i	$-0.236202\pi$
$691$	13.6788	+	7.89748i	0.520368	+	0.300434i	−0.216717	+	0.976234i	$0.569535\pi$
$692$	−3.35755	−	1.93848i	−0.127635	−	0.0736900i
$693$	1.74242	−	1.00599i	0.0661891	−	0.0382143i
$694$			2.82008i			0.107049i
$695$	−5.38688	+	13.8771i	−0.204336	+	0.526388i
$696$	3.83543	−	2.21438i	0.145381	−	0.0839360i
$697$	−2.46267			−0.0932803
$698$	−23.0704	+	13.3197i	−0.873226	+	0.504157i
$699$	4.95812	−	8.58772i	0.187533	−	0.324817i
$700$	5.63782	+	5.15361i	0.213090	+	0.194788i
$701$	−43.7481			−1.65234			−0.826171	−	0.563420i	$-0.809485\pi$
$701$	−43.7481			−1.65234			−0.826171	+	0.563420i	$0.809485\pi$
$702$	−3.42894	+	1.11461i	−0.129417	+	0.0420682i
$703$		−	13.5309i		−	0.510329i
$704$	−1.14057	−	0.658509i	−0.0429869	−	0.0248185i
$705$	1.68885	+	10.9288i	0.0636058	+	0.411602i
$706$	−6.61308	−	11.4542i	−0.248886	−	0.431084i
$707$	3.72537			0.140107
$708$	−5.23660	−	9.07005i	−0.196803	−	0.340873i
$709$	−30.0167	+	17.3302i	−1.12730	+	0.650848i	−0.943255	−	0.332070i	$-0.892253\pi$
$709$	−30.0167	+	17.3302i	−1.12730	+	0.650848i	−0.184046	+	0.982918i	$0.558920\pi$
$710$	−25.8654	+	20.7849i	−0.970713	+	0.780042i
$711$	2.43816	+	4.22302i	0.0914382	+	0.158376i
$712$	15.9738	+	9.22251i	0.598645	+	0.345628i
$713$	6.87016	−	11.8995i	0.257290	−	0.445639i
$714$	−2.39736			−0.0897191
$715$	−8.88404	−	5.81538i	−0.332244	−	0.217483i
$716$	−14.1065			−0.527185
$717$	−4.73083	+	8.19404i	−0.176676	+	0.306012i
$718$	−10.7237	−	6.19133i	−0.400205	−	0.231058i
$719$	−21.9251	−	37.9755i	−0.817670	−	1.41625i	−0.907395	−	0.420279i	$-0.861932\pi$
$719$	−21.9251	−	37.9755i	−0.817670	−	1.41625i	0.0897253	−	0.995967i	$-0.471401\pi$
$720$	1.40066	+	1.74303i	0.0521995	+	0.0649589i
$721$	16.4450	−	9.49451i	0.612443	−	0.353594i
$722$	2.15178	+	3.72700i	0.0800811	+	0.138704i
$723$	−13.1038			−0.487335
$724$	13.0736	+	22.6441i	0.485876	+	0.841563i
$725$	−16.3442	−	14.9405i	−0.607008	−	0.554875i
$726$	−8.02413	−	4.63273i	−0.297803	−	0.171937i
$727$		−	17.2599i		−	0.640136i	−0.947395	−	0.320068i	$-0.896294\pi$
$727$		−	17.2599i		−	0.640136i	0.947395	−	0.320068i	$-0.103706\pi$
$728$	−5.38789	−	1.14452i	−0.199688	−	0.0424188i
$729$	−1.00000			−0.0370370
$730$	13.2357	−	2.04534i	0.489875	−	0.0757014i
$731$	4.14967	−	7.18744i	0.153481	−	0.265837i
$732$	−4.31513	+	2.49134i	−0.159492	+	0.0920826i
$733$	−0.304799			−0.0112580			−0.00562900	−	0.999984i	$-0.501792\pi$
$733$	−0.304799			−0.0112580			−0.00562900	+	0.999984i	$0.501792\pi$
$734$	6.14226	−	3.54624i	0.226715	−	0.130894i
$735$	9.72681	+	3.77580i	0.358779	+	0.139272i
$736$			8.44285i			0.311208i
$737$	−3.16231	+	1.82576i	−0.116485	+	0.0672528i
$738$	−1.35904	−	0.784645i	−0.0500271	−	0.0288832i
$739$	3.14941	+	1.81831i	0.115853	+	0.0668877i	0.556807	−	0.830642i	$-0.312026\pi$
$739$	3.14941	+	1.81831i	0.115853	+	0.0668877i	−0.440954	+	0.897530i	$0.645360\pi$
$740$	−3.92599	−	4.88564i	−0.144322	−	0.179600i
$741$	−11.6448	+	12.9362i	−0.427783	+	0.475222i
$742$			21.2592i			0.780451i
$743$	15.1150	−	26.1800i	0.554517	−	0.960451i	−0.443424	−	0.896312i	$-0.646236\pi$
$743$	15.1150	−	26.1800i	0.554517	−	0.960451i	0.997941	−	0.0641394i	$-0.0204302\pi$
$744$	0.813725	−	1.40941i	0.0298326	−	0.0516716i
$745$	6.27667	+	2.43651i	0.229959	+	0.0892667i
$746$			36.9803i			1.35395i
$747$	−3.19510	−	5.53408i	−0.116903	−	0.202481i
$748$	−1.03339	−	1.78989i	−0.0377845	−	0.0654447i
$749$		−	16.0049i		−	0.584805i
$750$	6.19463	−	9.30734i	0.226196	−	0.339856i
$751$	−0.00159080	+	0.00275535i	−5.80493e−5	+	0.000100544i	−0.866054	−	0.499950i	$-0.833352\pi$
$751$	−0.00159080	+	0.00275535i	−5.80493e−5	+	0.000100544i	0.865996	+	0.500050i	$0.166685\pi$
$752$	−2.47276	+	4.28295i	−0.0901723	+	0.156183i
$753$		−	23.1644i		−	0.844158i
$754$	15.6196	+	3.31800i	0.568833	+	0.120834i
$755$	20.9423	−	16.8288i	0.762170	−	0.612462i
$756$	−1.32301	−	0.763837i	−0.0481172	−	0.0277805i
$757$	36.4328	+	21.0345i	1.32417	+	0.764512i	0.984392	−	0.175992i	$-0.0563132\pi$
$757$	36.4328	+	21.0345i	1.32417	+	0.764512i	0.339782	+	0.940504i	$0.389647\pi$
$758$	29.6252	−	17.1041i	1.07604	−	0.621250i
$759$		−	11.1194i		−	0.403608i
$760$	10.0628	+	3.90621i	0.365015	+	0.141693i
$761$	21.1489	−	12.2103i	0.766646	−	0.442623i	−0.0650310	−	0.997883i	$-0.520715\pi$
$761$	21.1489	−	12.2103i	0.766646	−	0.442623i	0.831677	+	0.555260i	$0.187381\pi$
$762$	8.10083			0.293462
$763$	22.7291	−	13.1226i	0.822847	−	0.475071i
$764$	−9.42713	+	16.3283i	−0.341062	+	0.590736i
$765$	0.535898	+	3.46788i	0.0193754	+	0.125381i
$766$	−26.0340			−0.940646
$767$	7.84643	−	36.9374i	0.283318	−	1.33373i
$768$			1.00000i			0.0360844i
$769$	−28.1198	−	16.2350i	−1.01403	−	0.585449i	−0.101659	−	0.994819i	$-0.532415\pi$
$769$	−28.1198	−	16.2350i	−1.01403	−	0.585449i	−0.912368	+	0.409370i	$0.865748\pi$
$770$	−0.687072	−	4.44614i	−0.0247603	−	0.160228i
$771$	−1.92197	−	3.32895i	−0.0692182	−	0.119889i
$772$	17.8920			0.643947
$773$	−4.13819	−	7.16756i	−0.148840	−	0.257799i	0.781959	−	0.623330i	$-0.214221\pi$
$773$	−4.13819	−	7.16756i	−0.148840	−	0.257799i	−0.930799	+	0.365531i	$0.880887\pi$
$774$	4.58006	−	2.64430i	0.164627	−	0.0950473i
$775$	−7.94649	−	1.75164i	−0.285446	−	0.0629208i
$776$	0.963028	+	1.66801i	0.0345707	+	0.0598782i
$777$	3.70833	+	2.14100i	0.133035	+	0.0768081i
$778$	3.11784	−	5.40026i	0.111780	−	0.193609i
$779$	−7.57555			−0.271422
$780$	−0.451203	+	8.04962i	−0.0161557	+	0.288223i
$781$	19.5437			0.699328
$782$	−6.62464	+	11.4742i	−0.236897	+	0.410317i
$783$	3.83543	+	2.21438i	0.137067	+	0.0791356i
$784$	2.33310	+	4.04106i	0.0833252	+	0.144323i
$785$	5.25620	−	4.22376i	0.187602	−	0.150753i
$786$	−2.01356	+	1.16253i	−0.0718213	+	0.0414661i
$787$	−1.61500	−	2.79726i	−0.0575685	−	0.0997115i	0.835805	−	0.549027i	$-0.185001\pi$
$787$	−1.61500	−	2.79726i	−0.0575685	−	0.0997115i	−0.893373	+	0.449315i	$0.851668\pi$
$788$	−0.625857			−0.0222952
$789$	15.3032	+	26.5060i	0.544810	+	0.943638i
$790$	10.7759	−	1.66522i	0.383389	−	0.0592459i
$791$	3.43958	+	1.98584i	0.122297	+	0.0706085i
$792$		−	1.31702i		−	0.0467982i
$793$	−17.5732	−	3.73299i	−0.624043	−	0.132562i
$794$	36.6995			1.30242
$795$	30.7523	−	4.75222i	1.09067	−	0.168544i
$796$	−8.84057	+	15.3123i	−0.313346	+	0.542731i
$797$	35.1612	−	20.3003i	1.24547	−	0.719075i	0.275271	−	0.961367i	$-0.411232\pi$
$797$	35.1612	−	20.3003i	1.24547	−	0.719075i	0.970203	+	0.242292i	$0.0778990\pi$
$798$	−7.37466			−0.261060
$799$	−6.72118	+	3.88048i	−0.237778	+	0.137281i
$800$	4.76677	−	1.50928i	0.168531	−	0.0533611i
$801$			18.4450i			0.651722i
$802$	−24.5044	+	14.1476i	−0.865279	+	0.499569i
$803$	−6.83138	−	3.94410i	−0.241074	−	0.139184i
$804$	2.40112	+	1.38628i	0.0846808	+	0.0488905i
$805$	−22.4815	+	18.0656i	−0.792368	+	0.636729i
$806$	5.58043	−	1.81397i	0.196562	−	0.0638944i
$807$		−	18.0874i		−	0.636707i
$808$	1.21929	−	2.11188i	0.0428946	−	0.0742956i
$809$	0.000840236	−	0.00145533i	2.95411e−5	−	5.11667e-5i	−0.866011	−	0.500026i	$-0.833324\pi$
$809$	0.000840236	−	0.00145533i	2.95411e−5	−	5.11667e-5i	0.866040	+	0.499974i	$0.166657\pi$
$810$	−0.809179	+	2.08452i	−0.0284317	+	0.0732426i
$811$			34.9476i			1.22718i	0.789626	+	0.613588i	$0.210274\pi$
$811$			34.9476i			1.22718i	−0.789626	+	0.613588i	$0.789726\pi$
$812$	3.38286	+	5.85928i	0.118715	+	0.205621i
$813$	−7.09382	−	12.2869i	−0.248791	−	0.430919i
$814$			3.69154i			0.129389i
$815$	−8.02401	+	20.6706i	−0.281069	+	0.724060i
$816$	−0.784645	+	1.35904i	−0.0274681	+	0.0475761i
$817$	12.7650	−	22.1097i	0.446592	−	0.773519i
$818$			15.3280i			0.535931i
$819$	−1.70276	−	5.23831i	−0.0594992	−	0.183041i
$820$	−2.73532	+	2.19804i	−0.0955215	+	0.0767589i
$821$	22.0044	+	12.7042i	0.767957	+	0.443380i	0.832145	−	0.554557i	$-0.187112\pi$
$821$	22.0044	+	12.7042i	0.767957	+	0.443380i	−0.0641882	+	0.997938i	$0.520446\pi$
$822$	10.6381	+	6.14192i	0.371047	+	0.214224i
$823$	18.9040	−	10.9142i	0.658952	−	0.380446i	−0.132926	−	0.991126i	$-0.542437\pi$
$823$	18.9040	−	10.9142i	0.658952	−	0.380446i	0.791878	+	0.610680i	$0.209104\pi$
$824$		−	12.4300i		−	0.433020i
$825$	−6.27792	+	1.98775i	−0.218569	+	0.0692045i
$826$	13.8561	−	7.99982i	0.482115	−	0.278349i
$827$	18.9366			0.658492			0.329246	−	0.944244i	$-0.393206\pi$
$827$	18.9366			0.658492			0.329246	+	0.944244i	$0.393206\pi$
$828$	−7.31172	+	4.22143i	−0.254100	+	0.146705i
$829$	−0.304309	+	0.527078i	−0.0105691	+	0.0183062i	−0.871262	−	0.490819i	$-0.836698\pi$
$829$	−0.304309	+	0.527078i	−0.0105691	+	0.0183062i	0.860692	+	0.509125i	$0.170031\pi$
$830$	−14.1213	+	2.18220i	−0.490158	+	0.0757452i
$831$	16.8419			0.584240
$832$	−2.41225	+	2.67975i	−0.0836296	+	0.0929036i
$833$			7.32263i			0.253714i
$834$	−5.76531	−	3.32861i	−0.199637	−	0.115260i
$835$	28.7046	−	4.43578i	0.993362	−	0.153506i
$836$	−3.17887	−	5.50597i	−0.109944	−	0.190428i
$837$	1.62745			0.0562529
$838$	−13.4692	−	23.3293i	−0.465286	−	0.805898i
$839$	−23.3215	+	13.4647i	−0.805148	+	0.464853i	−0.845268	−	0.534342i	$-0.820559\pi$
$839$	−23.3215	+	13.4647i	−0.805148	+	0.464853i	0.0401198	+	0.999195i	$0.487226\pi$
$840$	−2.66278	+	2.13975i	−0.0918748	+	0.0738284i
$841$	4.69300	+	8.12852i	0.161828	+	0.280294i
$842$	−33.3731	−	19.2679i	−1.15011	−	0.664017i
$843$	4.30768	−	7.46112i	0.148364	−	0.256974i
$844$	17.2445			0.593581
$845$	−20.6268	+	20.4826i	−0.709583	+	0.704622i
$846$	−4.94552			−0.170030
$847$	7.07731	−	12.2583i	0.243179	−	0.421199i
$848$	12.0517	+	6.95804i	0.413856	+	0.238940i
$849$	−13.8098	−	23.9192i	−0.473950	−	0.820905i
$850$	7.66250	+	1.68904i	0.262822	+	0.0579336i
$851$	20.4944	−	11.8325i	0.702541	−	0.405612i
$852$	−7.41968	−	12.8513i	−0.254194	−	0.440277i
$853$	−41.3790			−1.41679			−0.708394	−	0.705817i	$-0.750580\pi$
$853$	−41.3790			−1.41679			−0.708394	+	0.705817i	$0.750580\pi$
$854$	−3.80596	−	6.59212i	−0.130237	−	0.225578i
$855$	1.64851	+	10.6677i	0.0563777	+	0.364828i
$856$	−9.07302	−	5.23831i	−0.310109	−	0.179042i
$857$			30.6051i			1.04545i	0.852501	+	0.522726i	$0.175085\pi$
$857$			30.6051i			1.04545i	−0.852501	+	0.522726i	$0.824915\pi$
$858$	3.17697	−	3.52928i	0.108460	−	0.120488i
$859$	30.9385			1.05561			0.527803	−	0.849367i	$-0.323016\pi$
$859$	30.9385			1.05561			0.527803	+	0.849367i	$0.323016\pi$
$860$	−1.80601	−	11.6869i	−0.0615844	−	0.398521i
$861$	1.19868	−	2.07618i	0.0408510	−	0.0707560i
$862$	−2.48744	+	1.43612i	−0.0847225	+	0.0489145i
$863$	−15.1133			−0.514464			−0.257232	−	0.966350i	$-0.582810\pi$
$863$	−15.1133			−0.514464			−0.257232	+	0.966350i	$0.582810\pi$
$864$	−0.866025	+	0.500000i	−0.0294628	+	0.0170103i
$865$	−8.08161	−	3.13716i	−0.274783	−	0.106667i
$866$		−	12.9724i		−	0.440819i
$867$	12.5897	−	7.26867i	0.427569	−	0.246857i
$868$	2.15313	+	1.24311i	0.0730819	+	0.0421938i
$869$	−5.56179	−	3.21110i	−0.188671	−	0.108929i
$870$	7.71948	−	6.20319i	0.261715	−	0.210308i
$871$	3.09033	+	9.50698i	0.104712	+	0.322132i
$872$		−	17.1799i		−	0.581784i
$873$	−0.963028	+	1.66801i	−0.0325936	+	0.0564537i
$874$	−20.3784	+	35.2964i	−0.689310	+	1.19392i
$875$	14.2186	+	9.46339i	0.480676	+	0.319921i
$876$			5.98944i			0.202364i
$877$	−5.54757	−	9.60868i	−0.187328	−	0.324462i	0.757030	−	0.653380i	$-0.226649\pi$
$877$	−5.54757	−	9.60868i	−0.187328	−	0.324462i	−0.944359	+	0.328918i	$0.893316\pi$
$878$	−1.02411	−	1.77380i	−0.0345619	−	0.0598629i
$879$		−	30.2501i		−	1.02031i
$880$	−2.74535	−	1.06570i	−0.0925458	−	0.0359248i
$881$	22.3598	−	38.7283i	0.753321	−	1.30479i	−0.192884	−	0.981222i	$-0.561784\pi$
$881$	22.3598	−	38.7283i	0.753321	−	1.30479i	0.946205	−	0.323568i	$-0.104883\pi$
$882$	−2.33310	+	4.04106i	−0.0785597	+	0.136069i
$883$			10.9779i			0.369435i	0.982792	+	0.184718i	$0.0591371\pi$
$883$			10.9779i			0.369435i	−0.982792	+	0.184718i	$0.940863\pi$
$884$	−5.38100	+	1.74914i	−0.180983	+	0.0588301i
$885$	−14.6694	−	18.2551i	−0.493106	−	0.613638i
$886$	22.2640	+	12.8541i	0.747973	+	0.431842i
$887$	33.2555	+	19.2001i	1.11661	+	0.644675i	0.940533	−	0.339702i	$-0.110326\pi$
$887$	33.2555	+	19.2001i	1.11661	+	0.644675i	0.176076	+	0.984377i	$0.443659\pi$
$888$	2.42743	−	1.40148i	0.0814593	−	0.0470305i
$889$			12.3754i			0.415059i
$890$	38.4490	+	14.9253i	1.28881	+	0.500298i
$891$	1.14057	−	0.658509i	0.0382106	−	0.0220609i
$892$	4.89716			0.163969
$893$	−20.6754	+	11.9369i	−0.691876	+	0.399455i
$894$	−1.50554	+	2.60768i	−0.0503529	+	0.0872137i
$895$	−31.1731	+	4.81725i	−1.04200	+	0.161023i
$896$	−1.52767			−0.0510360
$897$	−29.7767	−	6.32532i	−0.994216	−	0.211196i
$898$		−	18.5625i		−	0.619440i
$899$	−6.24197	−	3.60380i	−0.208181	−	0.120193i
$900$	3.69046	+	3.37350i	0.123015	+	0.112450i
$901$	10.9192	+	18.9126i	0.363770	+	0.630069i
$902$	2.06678			0.0688163
$903$	4.03963	+	6.99684i	0.134430	+	0.232840i
$904$	2.25151	−	1.29991i	0.0748842	−	0.0432344i
$905$	36.6233	+	45.5754i	1.21740	+	1.51498i
$906$	6.00745	+	10.4052i	0.199584	+	0.345690i
$907$	34.3953	+	19.8581i	1.14208	+	0.659378i	0.946944	−	0.321399i	$-0.104153\pi$
$907$	34.3953	+	19.8581i	1.14208	+	0.659378i	0.195133	+	0.980777i	$0.437486\pi$
$908$	5.07567	−	8.79132i	0.168442	−	0.291750i
$909$	2.43859			0.0808828
$910$	−12.2972	−	0.689291i	−0.407648	−	0.0228498i
$911$	17.9575			0.594959			0.297479	−	0.954728i	$-0.403854\pi$
$911$	17.9575			0.594959			0.297479	+	0.954728i	$0.403854\pi$
$912$	−2.41369	+	4.18063i	−0.0799252	+	0.138435i
$913$	7.28848	+	4.20801i	0.241213	+	0.139265i
$914$	−12.3213	−	21.3412i	−0.407554	−	0.705904i
$915$	−8.68497	+	6.97904i	−0.287116	+	0.230720i
$916$	−13.3332	+	7.69794i	−0.440542	+	0.254347i
$917$	−1.77597	−	3.07607i	−0.0586476	−	0.101581i
$918$	−1.56929			−0.0517943
$919$	10.0149	+	17.3463i	0.330361	+	0.572203i	0.982583	−	0.185826i	$-0.0594961\pi$
$919$	10.0149	+	17.3463i	0.330361	+	0.572203i	−0.652221	+	0.758029i	$0.726163\pi$
$920$	2.88316	+	18.6573i	0.0950549	+	0.615114i
$921$	−12.2449	−	7.06959i	−0.403483	−	0.232951i
$922$		−	31.8342i		−	1.04840i
$923$	11.1175	−	52.3363i	0.365938	−	1.72267i
$924$	2.01198			0.0661891
$925$	−10.3442	−	9.45578i	−0.340115	−	0.310904i
$926$	−1.59160	+	2.75673i	−0.0523031	+	0.0905916i
$927$	10.7647	−	6.21501i	0.353559	−	0.204128i
$928$	4.42877			0.145381
$929$	35.1451	−	20.2910i	1.15307	−	0.665727i	0.203439	−	0.979088i	$-0.434788\pi$
$929$	35.1451	−	20.2910i	1.15307	−	0.665727i	0.949634	+	0.313361i	$0.101455\pi$
$930$	1.31690	−	3.39246i	0.0431828	−	0.111243i
$931$			22.5255i			0.738245i
$932$	8.58772	−	4.95812i	0.281300	−	0.162409i
$933$	8.63797	+	4.98713i	0.282794	+	0.163271i
$934$	−18.7708	−	10.8373i	−0.614200	−	0.354609i
$935$	−2.89486	−	3.60246i	−0.0946719	−	0.117813i
$936$	−3.52686	−	0.749192i	−0.115279	−	0.0244881i
$937$			47.1112i			1.53905i	0.638614	+	0.769527i	$0.279508\pi$
$937$			47.1112i			1.53905i	−0.638614	+	0.769527i	$0.720492\pi$
$938$	−2.11779	+	3.66812i	−0.0691484	+	0.119769i
$939$	1.54230	−	2.67134i	0.0503311	−	0.0871760i
$940$	−4.00181	+	10.3090i	−0.130525	+	0.336244i
$941$			4.35101i			0.141839i	0.997482	+	0.0709195i	$0.0225933\pi$
$941$			4.35101i			0.141839i	−0.997482	+	0.0709195i	$0.977407\pi$
$942$	1.50778	+	2.61155i	0.0491261	+	0.0850888i
$943$	−6.62464	−	11.4742i	−0.215728	−	0.373652i
$944$		−	10.4732i		−	0.340873i
$945$	−3.18447	−	1.23616i	−0.103591	−	0.0402124i
$946$	−3.48259	+	6.03202i	−0.113229	+	0.196118i
$947$	−17.4580	+	30.2381i	−0.567307	+	0.982605i	0.429524	+	0.903056i	$0.358681\pi$
$947$	−17.4580	+	30.2381i	−0.567307	+	0.982605i	−0.996831	+	0.0795494i	$0.974652\pi$
$948$			4.87632i			0.158376i
$949$	−14.4480	+	16.0502i	−0.469002	+	0.521011i
$950$	23.5710	+	5.19575i	0.764745	+	0.168572i
$951$	12.3824	+	7.14899i	0.401527	+	0.231822i
$952$	−2.07618	−	1.19868i	−0.0672893	−	0.0388495i
$953$	−8.39700	+	4.84801i	−0.272005	+	0.157042i	−0.629799	−	0.776758i	$-0.716863\pi$
$953$	−8.39700	+	4.84801i	−0.272005	+	0.157042i	0.357793	+	0.933801i	$0.383529\pi$
$954$			13.9161i			0.450550i
$955$	−15.2565	+	39.3021i	−0.493688	+	1.27179i
$956$	−8.19404	+	4.73083i	−0.265014	+	0.153006i
$957$	−5.83277			−0.188547
$958$	25.3765	−	14.6511i	0.819876	−	0.473356i
$959$	−9.38286	+	16.2516i	−0.302988	+	0.524791i
$960$	0.341491	+	2.20984i	0.0110216	+	0.0713222i
$961$	28.3514			0.914561
$962$	9.88562	+	2.09995i	0.318725	+	0.0677052i
$963$		−	10.4766i		−	0.337604i
$964$	−11.3482	−	6.55189i	−0.365501	−	0.211022i
$965$	39.5384	−	6.10996i	1.27279	−	0.196687i
$966$	−6.44897	−	11.1699i	−0.207492	−	0.359387i
$967$	−36.1715			−1.16320			−0.581599	−	0.813476i	$-0.697573\pi$
$967$	−36.1715			−1.16320			−0.581599	+	0.813476i	$0.697573\pi$
$968$	−4.63273	−	8.02413i	−0.148902	−	0.257905i
$969$	−6.56062	+	3.78778i	−0.210757	+	0.121681i
$970$	2.69775	+	3.35718i	0.0866195	+	0.107792i
$971$	0.194688	+	0.337209i	0.00624783	+	0.0108216i	0.869132	−	0.494579i	$-0.164678\pi$
$971$	0.194688	+	0.337209i	0.00624783	+	0.0108216i	−0.862885	+	0.505401i	$0.831345\pi$
$972$	−0.866025	−	0.500000i	−0.0277778	−	0.0160375i
$973$	5.08503	−	8.80753i	0.163019	−	0.282356i
$974$	42.5287			1.36271
$975$	1.75179	+	17.9424i	0.0561022	+	0.574618i
$976$	−4.98268			−0.159492
$977$	2.70086	−	4.67802i	0.0864080	−	0.149663i	−0.819582	−	0.572961i	$-0.805794\pi$
$977$	2.70086	−	4.67802i	0.0864080	−	0.149663i	0.905990	+	0.423298i	$0.139128\pi$
$978$	−8.58772	−	4.95812i	−0.274605	−	0.158543i
$979$	−12.1462	−	21.0378i	−0.388194	−	0.672372i
$980$	6.53577	+	8.13334i	0.208777	+	0.259810i
$981$	14.8782	−	8.58994i	0.475025	−	0.274256i
$982$	6.32521	+	10.9556i	0.201845	+	0.349607i
$983$	−43.6819			−1.39324			−0.696618	−	0.717442i	$-0.745313\pi$
$983$	−43.6819			−1.39324			−0.696618	+	0.717442i	$0.745313\pi$
$984$	−0.784645	−	1.35904i	−0.0250136	−	0.0433248i
$985$	−1.38304	+	0.213725i	−0.0440674	+	0.00680983i
$986$	6.01889	+	3.47501i	0.191681	+	0.110667i
$987$		−	7.55515i		−	0.240483i
$988$	−16.5528	+	5.38064i	−0.526615	+	0.171181i
$989$	44.6508			1.41981
$990$	−0.449750	−	2.91040i	−0.0142940	−	0.0924985i
$991$	27.9427	−	48.3981i	0.887628	−	1.53742i	0.0449569	−	0.998989i	$-0.485685\pi$
$991$	27.9427	−	48.3981i	0.887628	−	1.53742i	0.842671	−	0.538428i	$-0.180982\pi$
$992$	1.40941	−	0.813725i	0.0447489	−	0.0258358i
$993$	11.4202			0.362409
$994$	19.6325	−	11.3349i	0.622706	−	0.359520i
$995$	−14.3072	+	36.8567i	−0.453569	+	1.16844i
$996$		−	6.39020i		−	0.202481i
$997$	−30.9866	+	17.8901i	−0.981357	+	0.566587i	−0.902680	−	0.430314i	$-0.858403\pi$
$997$	−30.9866	+	17.8901i	−0.981357	+	0.566587i	−0.0786773	+	0.996900i	$0.525070\pi$
$998$	−3.93182	−	2.27004i	−0.124460	−	0.0718567i
$999$	2.42743	+	1.40148i	0.0768005	+	0.0443408i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.x.a.199.2	yes	12
3.2	odd	2		1170.2.bj.d.199.5		12
5.2	odd	4		1950.2.bc.i.901.1		12
5.3	odd	4		1950.2.bc.j.901.6		12
5.4	even	2		390.2.x.b.199.5	yes	12
13.10	even	6		390.2.x.b.49.5	yes	12
15.14	odd	2		1170.2.bj.c.199.2		12
39.23	odd	6		1170.2.bj.c.829.2		12
65.23	odd	12		1950.2.bc.j.751.6		12
65.49	even	6	inner	390.2.x.a.49.2	✓	12
65.62	odd	12		1950.2.bc.i.751.1		12
195.179	odd	6		1170.2.bj.d.829.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.x.a.49.2	✓	12	65.49	even	6	inner
390.2.x.a.199.2	yes	12	1.1	even	1	trivial
390.2.x.b.49.5	yes	12	13.10	even	6
390.2.x.b.199.5	yes	12	5.4	even	2
1170.2.bj.c.199.2		12	15.14	odd	2
1170.2.bj.c.829.2		12	39.23	odd	6
1170.2.bj.d.199.5		12	3.2	odd	2
1170.2.bj.d.829.5		12	195.179	odd	6
1950.2.bc.i.751.1		12	65.62	odd	12
1950.2.bc.i.901.1		12	5.2	odd	4
1950.2.bc.j.751.6		12	65.23	odd	12
1950.2.bc.j.901.6		12	5.3	odd	4

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:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.x (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.40066 - 1.74303i) q^{5} +(0.866025 - 0.500000i) q^{6} +(0.763837 + 1.32301i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.40066 - 1.74303i) q^{5} +(0.866025 - 0.500000i) q^{6} +(0.763837 + 1.32301i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(2.20984 - 0.341491i) q^{10} +(-1.14057 - 0.658509i) q^{11} +1.00000i q^{12} +(-2.41225 + 2.67975i) q^{13} -1.52767 q^{14} +(0.341491 + 2.20984i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.35904 + 0.784645i) q^{17} -1.00000 q^{18} +(-4.18063 + 2.41369i) q^{19} +(-0.809179 + 2.08452i) q^{20} -1.52767i q^{21} +(1.14057 - 0.658509i) q^{22} +(-7.31172 - 4.22143i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(-1.07631 + 4.88278i) q^{25} +(-1.11461 - 3.42894i) q^{26} -1.00000i q^{27} +(0.763837 - 1.32301i) q^{28} +(-2.21438 + 3.83543i) q^{29} +(-2.08452 - 0.809179i) q^{30} +1.62745i q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.658509 + 1.14057i) q^{33} -1.56929i q^{34} +(1.23616 - 3.18447i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-1.40148 + 2.42743i) q^{37} -4.82738i q^{38} +(3.42894 - 1.11461i) q^{39} +(-1.40066 - 1.74303i) q^{40} +(1.35904 + 0.784645i) q^{41} +(1.32301 + 0.763837i) q^{42} +(-4.58006 + 2.64430i) q^{43} +1.31702i q^{44} +(0.809179 - 2.08452i) q^{45} +(7.31172 - 4.22143i) q^{46} +4.94552 q^{47} +(0.866025 - 0.500000i) q^{48} +(2.33310 - 4.04106i) q^{49} +(-3.69046 - 3.37350i) q^{50} +1.56929 q^{51} +(3.52686 + 0.749192i) q^{52} -13.9161i q^{53} +(0.866025 + 0.500000i) q^{54} +(0.449750 + 2.91040i) q^{55} +(0.763837 + 1.32301i) q^{56} +4.82738 q^{57} +(-2.21438 - 3.83543i) q^{58} +(-9.07005 + 5.23660i) q^{59} +(1.74303 - 1.40066i) q^{60} +(2.49134 + 4.31513i) q^{61} +(-1.40941 - 0.813725i) q^{62} +(-0.763837 + 1.32301i) q^{63} +1.00000 q^{64} +(8.04962 + 0.451203i) q^{65} -1.31702 q^{66} +(1.38628 - 2.40112i) q^{67} +(1.35904 + 0.784645i) q^{68} +(4.22143 + 7.31172i) q^{69} +(2.13975 + 2.66278i) q^{70} +(-12.8513 + 7.41968i) q^{71} +(0.500000 + 0.866025i) q^{72} +5.98944 q^{73} +(-1.40148 - 2.42743i) q^{74} +(3.37350 - 3.69046i) q^{75} +(4.18063 + 2.41369i) q^{76} -2.01198i q^{77} +(-0.749192 + 3.52686i) q^{78} +4.87632 q^{79} +(2.20984 - 0.341491i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.35904 + 0.784645i) q^{82} -6.39020 q^{83} +(-1.32301 + 0.763837i) q^{84} +(3.27122 + 1.26984i) q^{85} -5.28860i q^{86} +(3.83543 - 2.21438i) q^{87} +(-1.14057 - 0.658509i) q^{88} +(15.9738 + 9.22251i) q^{89} +(1.40066 + 1.74303i) q^{90} +(-5.38789 - 1.14452i) q^{91} +8.44285i q^{92} +(0.813725 - 1.40941i) q^{93} +(-2.47276 + 4.28295i) q^{94} +(10.0628 + 3.90621i) q^{95} +1.00000i q^{96} +(0.963028 + 1.66801i) q^{97} +(2.33310 + 4.04106i) q^{98} -1.31702i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} - 6 q^{4} - 2 q^{5} - 2 q^{7} + 12 q^{8} + 6 q^{9}+O(q^{10}) \) 12 * q - 6 * q^2 - 6 * q^4 - 2 * q^5 - 2 * q^7 + 12 * q^8 + 6 * q^9	\( 12 q - 6 q^{2} - 6 q^{4} - 2 q^{5} - 2 q^{7} + 12 q^{8} + 6 q^{9} - 2 q^{10} + 6 q^{11} - 8 q^{13} + 4 q^{14} + 6 q^{15} - 6 q^{16} + 18 q^{17} - 12 q^{18} - 6 q^{19} + 4 q^{20} - 6 q^{22} + 6 q^{23} - 10 q^{25} - 2 q^{26} - 2 q^{28} + 14 q^{29} - 6 q^{30} - 6 q^{32} + 6 q^{33} + 26 q^{35} + 6 q^{36} - 12 q^{37} - 2 q^{39} - 2 q^{40} - 18 q^{41} - 12 q^{42} - 36 q^{43} - 4 q^{45} - 6 q^{46} + 16 q^{47} + 8 q^{49} - 10 q^{50} + 16 q^{51} + 10 q^{52} - 28 q^{55} - 2 q^{56} - 8 q^{57} + 14 q^{58} - 36 q^{59} + 10 q^{61} + 6 q^{62} + 2 q^{63} + 12 q^{64} + 6 q^{65} - 12 q^{66} + 4 q^{67} - 18 q^{68} + 16 q^{69} - 4 q^{70} - 12 q^{71} + 6 q^{72} + 28 q^{73} - 12 q^{74} - 8 q^{75} + 6 q^{76} - 2 q^{78} + 4 q^{79} - 2 q^{80} - 6 q^{81} + 18 q^{82} + 72 q^{83} + 12 q^{84} + 18 q^{85} + 6 q^{87} + 6 q^{88} + 18 q^{89} + 2 q^{90} + 2 q^{91} - 16 q^{93} - 8 q^{94} - 42 q^{95} - 48 q^{97} + 8 q^{98}+O(q^{100}) \) 12 * q - 6 * q^2 - 6 * q^4 - 2 * q^5 - 2 * q^7 + 12 * q^8 + 6 * q^9 - 2 * q^10 + 6 * q^11 - 8 * q^13 + 4 * q^14 + 6 * q^15 - 6 * q^16 + 18 * q^17 - 12 * q^18 - 6 * q^19 + 4 * q^20 - 6 * q^22 + 6 * q^23 - 10 * q^25 - 2 * q^26 - 2 * q^28 + 14 * q^29 - 6 * q^30 - 6 * q^32 + 6 * q^33 + 26 * q^35 + 6 * q^36 - 12 * q^37 - 2 * q^39 - 2 * q^40 - 18 * q^41 - 12 * q^42 - 36 * q^43 - 4 * q^45 - 6 * q^46 + 16 * q^47 + 8 * q^49 - 10 * q^50 + 16 * q^51 + 10 * q^52 - 28 * q^55 - 2 * q^56 - 8 * q^57 + 14 * q^58 - 36 * q^59 + 10 * q^61 + 6 * q^62 + 2 * q^63 + 12 * q^64 + 6 * q^65 - 12 * q^66 + 4 * q^67 - 18 * q^68 + 16 * q^69 - 4 * q^70 - 12 * q^71 + 6 * q^72 + 28 * q^73 - 12 * q^74 - 8 * q^75 + 6 * q^76 - 2 * q^78 + 4 * q^79 - 2 * q^80 - 6 * q^81 + 18 * q^82 + 72 * q^83 + 12 * q^84 + 18 * q^85 + 6 * q^87 + 6 * q^88 + 18 * q^89 + 2 * q^90 + 2 * q^91 - 16 * q^93 - 8 * q^94 - 42 * q^95 - 48 * q^97 + 8 * q^98

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