LMFDB - Embedded newform 390.2.x.b.199.5

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			199.5
Root			$1.75374 - 1.62986i$ of defining polynomial
Character	$\chi$	$=$	390.199
Dual form			390.2.x.b.49.5

$q$-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} +(-0.809179 - 2.08452i) q^{10} +(-1.14057 - 0.658509i) q^{11} -1.00000i q^{12} +(2.41225 - 2.67975i) q^{13} -1.52767 q^{14} +(2.08452 - 0.809179i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.35904 - 0.784645i) q^{17} +1.00000 q^{18} +(-4.18063 + 2.41369i) q^{19} +(-2.20984 - 0.341491i) 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} +(0.341491 - 2.20984i) q^{30} +1.62745i q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.658509 - 1.14057i) q^{33} -1.56929i q^{34} +(-3.37591 - 0.521687i) 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} +(2.20984 + 0.341491i) q^{45} +(7.31172 - 4.22143i) q^{46} -4.94552 q^{47} +(-0.866025 + 0.500000i) q^{48} +(2.33310 - 4.04106i) q^{49} +(-4.76677 - 1.50928i) q^{50} +1.56929 q^{51} +(-3.52686 - 0.749192i) q^{52} +13.9161i q^{53} +(0.866025 + 0.500000i) q^{54} +(-2.74535 + 1.06570i) 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} +(-1.29215 - 7.95804i) 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} +(1.50928 - 4.76677i) q^{75} +(4.18063 + 2.41369i) q^{76} +2.01198i q^{77} +(0.749192 - 3.52686i) q^{78} +4.87632 q^{79} +(0.809179 + 2.08452i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.35904 - 0.784645i) q^{82} +6.39020 q^{83} +(-1.32301 + 0.763837i) q^{84} +(0.535898 - 3.46788i) 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} +(-1.64851 + 10.6677i) 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} + 4 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} + 2 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} - 22 q^{35} + 6 q^{36} + 12 q^{37} - 2 q^{39} - 2 q^{40} - 18 q^{41} + 12 q^{42} + 36 q^{43} - 2 q^{45} - 6 q^{46} - 16 q^{47} + 8 q^{49} - 20 q^{50} + 16 q^{51} - 10 q^{52} + 8 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} - 44 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} + 16 q^{75} + 6 q^{76} + 2 q^{78} + 4 q^{79} - 4 q^{80} - 6 q^{81} - 18 q^{82} - 72 q^{83} + 12 q^{84} + 48 q^{85} - 6 q^{87} - 6 q^{88} + 18 q^{89} + 2 q^{90} + 2 q^{91} + 16 q^{93} - 8 q^{94} + 18 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 + 4 * 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 + 2 * 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 - 22 * q^35 + 6 * q^36 + 12 * q^37 - 2 * q^39 - 2 * q^40 - 18 * q^41 + 12 * q^42 + 36 * q^43 - 2 * q^45 - 6 * q^46 - 16 * q^47 + 8 * q^49 - 20 * q^50 + 16 * q^51 - 10 * q^52 + 8 * 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 - 44 * 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 + 16 * q^75 + 6 * q^76 + 2 * q^78 + 4 * q^79 - 4 * q^80 - 6 * q^81 - 18 * q^82 - 72 * q^83 + 12 * q^84 + 48 * q^85 - 6 * q^87 - 6 * q^88 + 18 * q^89 + 2 * q^90 + 2 * q^91 + 16 * q^93 - 8 * q^94 + 18 * 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	0.684797	−	0.728734i	$-0.259891\pi$
$7$	−0.763837	−	1.32301i	−0.288703	−	0.500049i	−0.973501	+	0.228685i	$0.926557\pi$
$8$	−1.00000			−0.353553
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−0.809179	−	2.08452i	−0.255885	−	0.659184i
$11$	−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
$15$	2.08452	−	0.809179i	0.538221	−	0.208929i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.35904	−	0.784645i	0.329617	−	0.190304i	−0.326054	−	0.945351i	$-0.605719\pi$
$17$	1.35904	−	0.784645i	0.329617	−	0.190304i	0.655671	+	0.755047i	$0.272386\pi$
$18$	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	$0.520132\pi$
$20$	−2.20984	−	0.341491i	−0.494135	−	0.0763597i
$21$		−	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	$0.00927724\pi$
$23$	7.31172	+	4.22143i	1.52460	+	0.880228i	0.525025	+	0.851087i	$0.324056\pi$
$24$	−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	$0.301557\pi$
$30$	0.341491	−	2.20984i	0.0623475	−	0.403459i
$31$			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
$35$	−3.37591	−	0.521687i	−0.570634	−	0.0881813i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	1.40148	−	2.42743i	0.230402	−	0.399067i	−0.727525	−	0.686081i	$-0.759329\pi$
$37$	1.40148	−	2.42743i	0.230402	−	0.399067i	0.957926	+	0.287014i	$0.0926627\pi$
$38$			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	−0.108318	−	0.994116i	$-0.534547\pi$
$43$	4.58006	−	2.64430i	0.698452	−	0.403252i	0.806771	+	0.590865i	$0.201213\pi$
$44$			1.31702i			0.198548i
$45$	2.20984	+	0.341491i	0.329423	+	0.0509065i
$46$	7.31172	−	4.22143i	1.07805	−	0.622415i
$47$	−4.94552			−0.721378			−0.360689	−	0.932686i	$-0.617458\pi$
$47$	−4.94552			−0.721378			−0.360689	+	0.932686i	$0.617458\pi$
$48$	−0.866025	+	0.500000i	−0.125000	+	0.0721688i
$49$	2.33310	−	4.04106i	0.333301	−	0.577294i
$50$	−4.76677	−	1.50928i	−0.674123	−	0.213444i
$51$	1.56929			0.219744
$52$	−3.52686	−	0.749192i	−0.489087	−	0.103894i
$53$			13.9161i			1.91152i	0.294148	+	0.955760i	$0.404964\pi$
$53$			13.9161i			1.91152i	−0.294148	+	0.955760i	$0.595036\pi$
$54$	0.866025	+	0.500000i	0.117851	+	0.0680414i
$55$	−2.74535	+	1.06570i	−0.370183	+	0.143699i
$56$	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
$65$	−1.29215	−	7.95804i	−0.160272	−	0.987073i
$66$	−1.31702			−0.162114
$67$	−1.38628	+	2.40112i	−0.169362	+	0.293343i	−0.938196	−	0.346105i	$-0.887504\pi$
$67$	−1.38628	+	2.40112i	−0.169362	+	0.293343i	0.768834	+	0.639448i	$0.220837\pi$
$68$	−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	$-0.613990\pi$
$73$	−5.98944			−0.701011			−0.350505	+	0.936561i	$0.613990\pi$
$74$	−1.40148	−	2.42743i	−0.162919	−	0.282183i
$75$	1.50928	−	4.76677i	0.174277	−	0.550419i
$76$	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	$0.411549\pi$
$80$	0.809179	+	2.08452i	0.0904690	+	0.233057i
$81$	−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	$-0.385941\pi$
$83$	6.39020			0.701416			0.350708	+	0.936485i	$0.385941\pi$
$84$	−1.32301	+	0.763837i	−0.144352	+	0.0833415i
$85$	0.535898	−	3.46788i	0.0581263	−	0.376144i
$86$		−	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
$95$	−1.64851	+	10.6677i	−0.169133	+	1.09449i
$96$			1.00000i			0.102062i
$97$	−0.963028	−	1.66801i	−0.0977807	−	0.169361i	0.812985	−	0.582285i	$-0.197841\pi$
$97$	−0.963028	−	1.66801i	−0.0977807	−	0.169361i	−0.910766	+	0.412923i	$0.864508\pi$
$98$	−2.33310	−	4.04106i	−0.235679	−	0.408208i
$99$		−	1.31702i		−	0.132365i
$100$	−3.69046	+	3.37350i	−0.369046	+	0.337350i
$101$	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	$0.209789\pi$
$103$			12.4300i			1.22477i	−0.790561	+	0.612383i	$0.790211\pi$
$104$	−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	0.869708	−	0.493566i	$-0.164307\pi$
$107$	9.07302	+	5.23831i	0.877122	+	0.506407i	0.00741349	+	0.999973i	$0.497640\pi$
$108$	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	$-0.307571\pi$
$110$	−0.449750	+	2.91040i	−0.0428820	+	0.277495i
$111$	2.42743	−	1.40148i	0.230402	−	0.133022i
$112$	1.52767			0.144352
$113$	−2.25151	+	1.29991i	−0.211805	+	0.122285i	−0.602150	−	0.798383i	$-0.705689\pi$
$113$	−2.25151	+	1.29991i	−0.211805	+	0.122285i	0.390345	+	0.920669i	$0.372356\pi$
$114$	−2.41369	+	4.18063i	−0.226063	+	0.391552i
$115$	17.5993	−	6.83178i	1.64114	−	0.637067i
$116$	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
$120$	−2.08452	+	0.809179i	−0.190290	+	0.0738676i
$121$	−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	0.155325	−	0.987863i	$-0.450357\pi$
$127$	−7.01552	−	4.05041i	−0.622527	−	0.359416i	−0.777852	+	0.628447i	$0.783691\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	5.28860			0.465635
$130$	−7.53794	−	2.85998i	−0.661121	−	0.250837i
$131$	−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	$-0.990829\pi$
$137$	−6.14192	−	10.6381i	−0.524740	−	0.908876i	0.474845	−	0.880069i	$-0.342504\pi$
$138$	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	$0.924440\pi$
$140$	1.23616	+	3.18447i	0.104475	+	0.269137i
$141$	−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
$145$	3.58367	+	9.23186i	0.297607	+	0.766664i
$146$	−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	$0.372694\pi$
$150$	−3.37350	−	3.69046i	−0.275445	−	0.301325i
$151$			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	$-0.961604\pi$
$157$		−	3.01556i		−	0.240668i	0.992733	−	0.120334i	$-0.0383965\pi$
$158$	2.43816	−	4.22302i	0.193970	−	0.335965i
$159$	−6.95804	+	12.0517i	−0.551808	+	0.955760i
$160$	2.20984	+	0.341491i	0.174703	+	0.0269972i
$161$		−	12.8979i		−	1.01650i
$162$	0.500000	+	0.866025i	0.0392837	+	0.0680414i
$163$	4.95812	+	8.58772i	0.388350	+	0.672642i	0.992228	−	0.124435i	$-0.0397119\pi$
$163$	4.95812	+	8.58772i	0.388350	+	0.672642i	−0.603878	+	0.797077i	$0.706379\pi$
$164$		−	1.56929i		−	0.122541i
$165$	−2.91040	−	0.449750i	−0.226574	−	0.0350130i
$166$	3.19510	−	5.53408i	0.247988	−	0.429528i
$167$	6.49472	−	11.2492i	0.502576	−	0.870488i	−0.497419	−	0.867510i	$-0.665719\pi$
$167$	6.49472	−	11.2492i	0.502576	−	0.870488i	0.999996	−	0.00297754i	$-0.000947782\pi$
$168$			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	−0.622175	−	0.782878i	$-0.713751\pi$
$173$	−3.35755	+	1.93848i	−0.255270	+	0.147380i	0.366905	+	0.930258i	$0.380417\pi$
$174$			4.42877i			0.335744i
$175$	−5.63782	+	5.15361i	−0.426179	+	0.389577i
$176$	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	$-0.0100858\pi$
$180$	−0.809179	−	2.08452i	−0.0603126	−	0.155371i
$181$	−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
$185$	−2.26809	−	5.84282i	−0.166754	−	0.429573i
$186$	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	$-0.610629\pi$
$193$	8.94600	−	15.4949i	0.643947	−	1.11535i	0.984544	−	0.175140i	$-0.0560378\pi$
$194$	−1.92606			−0.138283
$195$	2.85998	−	7.53794i	0.204808	−	0.539803i
$196$	−4.66621			−0.333301
$197$	−0.312928	+	0.542008i	−0.0222952	+	0.0386165i	−0.876958	−	0.480567i	$-0.840431\pi$
$197$	−0.312928	+	0.542008i	−0.0222952	+	0.0386165i	0.854663	+	0.519184i	$0.173764\pi$
$198$	−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
$205$	3.27122	−	1.26984i	0.228472	−	0.0886892i
$206$	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
$210$	−3.18447	+	1.23616i	−0.219749	+	0.0853033i
$211$	−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
$215$	1.80601	−	11.6869i	0.123169	−	0.797043i
$216$		−	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	−0.772320	−	0.635234i	$-0.780904\pi$
$223$	2.44858	−	4.24107i	0.163969	−	0.284003i	0.936289	+	0.351231i	$0.114237\pi$
$224$	0.763837	−	1.32301i	0.0510360	−	0.0883970i
$225$	3.69046	−	3.37350i	0.246031	−	0.224900i
$226$			2.59982i			0.172938i
$227$	−5.07567	−	8.79132i	−0.336884	−	0.583500i	0.646961	−	0.762523i	$-0.276040\pi$
$227$	−5.07567	−	8.79132i	−0.336884	−	0.583500i	−0.983845	+	0.179023i	$0.942706\pi$
$228$	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	$-0.169871\pi$
$230$	2.88316	−	18.6573i	0.190110	−	1.23023i
$231$	−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	$-0.894697\pi$
$233$		−	9.91624i		−	0.649634i	0.945777	−	0.324817i	$-0.105303\pi$
$234$	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	$-0.0989948\pi$
$240$	−0.341491	+	2.20984i	−0.0220432	+	0.142644i
$241$	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
$245$	−3.77580	−	9.72681i	−0.241227	−	0.621423i
$246$	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
$250$	−9.30734	+	6.19463i	−0.588648	+	0.391783i
$251$	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	0.392566	−	0.919724i	$-0.371587\pi$
$257$	−3.32895	−	1.92197i	−0.207654	−	0.119889i	−0.600221	+	0.799834i	$0.704921\pi$
$258$	2.64430	−	4.58006i	0.164627	−	0.285142i
$259$	−4.28201			−0.266071
$260$	−6.24579	+	5.09805i	−0.387347	+	0.316168i
$261$	−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	$0.0592880\pi$
$263$	26.5060	+	15.3032i	1.63443	+	0.943638i	0.651726	+	0.758455i	$0.274045\pi$
$264$	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	$0.647426\pi$
$270$	2.08452	−	0.809179i	0.126860	−	0.0492451i
$271$	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
$275$	−1.98775	+	6.27792i	−0.119866	+	0.378573i
$276$	4.22143	−	7.31172i	0.254100	−	0.440114i
$277$	14.5855	−	8.42097i	0.876360	−	0.505967i	0.00690380	−	0.999976i	$-0.497802\pi$
$277$	14.5855	−	8.42097i	0.876360	−	0.505967i	0.869457	+	0.494009i	$0.164469\pi$
$278$	−6.65721			−0.399273
$279$	−1.40941	+	0.813725i	−0.0843794	+	0.0487165i
$280$	3.37591	+	0.521687i	0.201749	+	0.0311768i
$281$			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	−0.425392	−	0.905009i	$-0.639864\pi$
$283$	−23.9192	−	13.8098i	−1.42185	−	0.820905i	−0.996457	+	0.0841040i	$0.973197\pi$
$284$	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
$290$	9.78686	+	1.51239i	0.574704	+	0.0888103i
$291$		−	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	$-0.821770\pi$
$293$	−15.1250	−	26.1973i	−0.883614	−	1.53046i	−0.0363205	−	0.999340i	$-0.511564\pi$
$294$		−	4.66621i		−	0.272139i
$295$	−3.57650	+	23.1441i	−0.208232	+	1.34750i
$296$	−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
$305$	11.0109	+	1.70154i	0.630484	+	0.0974300i
$306$	1.35904	−	0.784645i	0.0776914	−	0.0448552i
$307$	−14.1392			−0.806966			−0.403483	−	0.914987i	$-0.632201\pi$
$307$	−14.1392			−0.806966			−0.403483	+	0.914987i	$0.632201\pi$
$308$	1.74242	−	1.00599i	0.0992837	−	0.0573215i
$309$	−6.21501	+	10.7647i	−0.353559	+	0.612383i
$310$	3.39246	−	1.31690i	0.192679	−	0.0747948i
$311$	−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	$-0.972216\pi$
$313$		−	3.08460i		−	0.174352i	0.996193	−	0.0871760i	$-0.0277843\pi$
$314$	−2.61155	−	1.50778i	−0.147378	−	0.0850888i
$315$	−1.23616	−	3.18447i	−0.0696499	−	0.179425i
$316$	−2.43816	−	4.22302i	−0.137157	−	0.237563i
$317$	14.2980			0.803054			0.401527	−	0.915847i	$-0.368480\pi$
$317$	14.2980			0.803054			0.401527	+	0.915847i	$0.368480\pi$
$318$	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
$325$	−15.6810	−	8.89424i	−0.869823	−	0.493363i
$326$	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
$335$	2.24351	+	5.77948i	0.122576	+	0.315767i
$336$	1.32301	+	0.763837i	0.0721759	+	0.0416708i
$337$			5.53208i			0.301352i	0.988583	+	0.150676i	$0.0481450\pi$
$337$			5.53208i			0.301352i	−0.988583	+	0.150676i	$0.951855\pi$
$338$	−11.8774	−	5.28458i	−0.646047	−	0.287443i
$339$	−2.59982			−0.141203
$340$	−3.27122	+	1.26984i	−0.177407	+	0.0688665i
$341$	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
$345$	18.6573	+	2.88316i	1.00448	+	0.155224i
$346$			3.87696i			0.208427i
$347$	−2.44226	+	1.41004i	−0.131107	+	0.0756949i	−0.564119	−	0.825693i	$-0.690784\pi$
$347$	−2.44226	+	1.41004i	−0.131107	+	0.0756949i	0.433012	+	0.901388i	$0.357451\pi$
$348$	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	−0.634617	−	0.772826i	$-0.718842\pi$
$353$	6.61308	−	11.4542i	0.351979	−	0.609645i	0.986596	+	0.163182i	$0.0521757\pi$
$354$	−5.23660	+	9.07005i	−0.278322	+	0.482068i
$355$	−5.06751	+	32.7926i	−0.268955	+	1.74045i
$356$		−	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	$0.894041\pi$
$360$	−2.20984	−	0.341491i	−0.116469	−	0.0179982i
$361$	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	0.651670	−	0.758502i	$-0.274069\pi$
$367$	6.14226	+	3.54624i	0.320623	+	0.185112i	−0.331047	+	0.943614i	$0.607402\pi$
$368$	−7.31172	+	4.22143i	−0.381150	+	0.220057i
$369$			1.56929i			0.0816939i
$370$	−6.19408	−	0.957185i	−0.322015	−	0.0497617i
$371$	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	$0.740071\pi$
$373$	−32.0259	+	18.4902i	−1.65824	+	0.957384i	−0.973528	+	0.228568i	$0.926596\pi$
$374$	−1.03339	+	1.78989i	−0.0534354	+	0.0925528i
$375$	−6.19463	−	9.30734i	−0.319890	−	0.480629i
$376$	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	$-0.674842\pi$
$380$	10.0628	−	3.90621i	0.516209	−	0.200384i
$381$	−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	$-0.935040\pi$
$383$	−13.0170	−	22.5461i	−0.665137	−	1.15205i	0.314111	−	0.949386i	$-0.398294\pi$
$384$	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	$0.550531\pi$
$390$	−5.09805	−	6.24579i	−0.258150	−	0.316268i
$391$	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	$0.205917\pi$
$397$	18.3498	+	31.7827i	0.920948	+	1.59513i	0.122997	+	0.992407i	$0.460750\pi$
$398$	−17.6811			−0.886275
$399$	3.68733	+	6.38665i	0.184597	+	0.319732i
$400$	4.76677	+	1.50928i	0.238338	+	0.0754640i
$401$	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
$405$	0.809179	+	2.08452i	0.0402084	+	0.103581i
$406$	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	$0.209615\pi$
$410$	0.535898	−	3.46788i	0.0264661	−	0.171266i
$411$		−	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	$0.938064\pi$
$420$	−0.521687	+	3.37591i	−0.0254557	+	0.164728i
$421$			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
$425$	−5.29400	−	5.79140i	−0.256797	−	0.280924i
$426$	−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	−0.205144	−	0.978732i	$-0.565766\pi$
$433$	11.2344	−	6.48619i	0.539891	−	0.311706i	0.745035	+	0.667026i	$0.232433\pi$
$434$		−	2.48622i		−	0.119342i
$435$	−1.51239	+	9.78686i	−0.0725133	+	0.469244i
$436$	−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	$0.182231\pi$
$440$	2.74535	−	1.06570i	0.130880	−	0.0508054i
$441$	4.66621			0.222200
$442$	−4.20530	−	3.78551i	−0.200026	−	0.180059i
$443$			25.7082i			1.22143i	0.791849	+	0.610717i	$0.209119\pi$
$443$			25.7082i			1.22143i	−0.791849	+	0.610717i	$0.790881\pi$
$444$	−2.42743	−	1.40148i	−0.115201	−	0.0665112i
$445$	38.4490	−	14.9253i	1.82266	−	0.707528i
$446$	−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
$455$	−9.54153	+	7.78817i	−0.447314	+	0.365115i
$456$	4.82738			0.226063
$457$	12.3213	−	21.3412i	0.576368	−	0.998299i	−0.419523	−	0.907745i	$-0.637803\pi$
$457$	12.3213	−	21.3412i	0.576368	−	0.998299i	0.995891	−	0.0905546i	$-0.0288640\pi$
$458$	−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	$-0.523566\pi$
$463$	−3.18319			−0.147936			−0.0739678	+	0.997261i	$0.523566\pi$
$464$	−2.21438	−	3.83543i	−0.102800	−	0.178055i
$465$	1.31690	+	3.39246i	0.0610697	+	0.157321i
$466$	−8.58772	−	4.95812i	−0.397818	−	0.229680i
$467$		−	21.6747i		−	1.00298i	−0.865162	−	0.501492i	$-0.832785\pi$
$467$		−	21.6747i		−	1.00298i	0.865162	−	0.501492i	$-0.167215\pi$
$468$	−1.11461	−	3.42894i	−0.0515228	−	0.158503i
$469$	4.23559			0.195581
$470$	4.00181	+	10.3090i	0.184590	+	0.475521i
$471$	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
$475$	16.2852	+	17.8152i	0.747215	+	0.817419i
$476$			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
$485$	−4.25627	−	0.657731i	−0.193267	−	0.0298660i
$486$			1.00000i			0.0453609i
$487$	21.2643	+	36.8309i	0.963579	+	1.66897i	0.713385	+	0.700772i	$0.247161\pi$
$487$	21.2643	+	36.8309i	0.963579	+	1.66897i	0.250194	+	0.968196i	$0.419506\pi$
$488$	−2.49134	−	4.31513i	−0.112778	−	0.195337i
$489$			9.91624i			0.448428i
$490$	−10.3116	−	1.59347i	−0.465829	−	0.0719856i
$491$	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	$0.967597\pi$
$500$	0.711042	+	11.1577i	0.0317988	+	0.498988i
$501$	11.2492	−	6.49472i	0.502576	−	0.290163i
$502$	23.1644			1.03388
$503$	17.2476	−	9.95791i	0.769033	−	0.444001i	−0.0634967	−	0.997982i	$-0.520225\pi$
$503$	17.2476	−	9.95791i	0.769033	−	0.444001i	0.832529	+	0.553981i	$0.186892\pi$
$504$	−0.763837	+	1.32301i	−0.0340240	+	0.0589313i
$505$	−1.97325	−	5.08328i	−0.0878086	−	0.226203i
$506$	−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	$0.741441\pi$
$510$	−1.26984	−	3.27122i	−0.0562293	−	0.144852i
$511$	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
$520$	1.29215	+	7.95804i	0.0566646	+	0.348983i
$521$	−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	−0.0559138	−	0.998436i	$-0.517807\pi$
$523$	−21.6924	−	12.5241i	−0.948541	−	0.547641i	−0.892627	+	0.450795i	$0.851141\pi$
$524$	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
$530$	29.0084	−	11.2606i	1.26004	−	0.489129i
$531$	−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
$535$	21.8387	−	8.47746i	0.944171	−	0.366513i
$536$	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
$540$	0.341491	−	2.20984i	0.0146954	−	0.0950963i
$541$		−	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	$-0.665482\pi$
$547$		−	40.5960i		−	1.73576i	0.496773	−	0.867880i	$-0.334518\pi$
$548$	−6.14192	+	10.6381i	−0.262370	+	0.454438i
$549$	−2.49134	+	4.31513i	−0.106328	+	0.184165i
$550$	4.44296	+	4.86040i	0.189449	+	0.207248i
$551$		−	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
$555$	0.957185	−	6.19408i	0.0406302	−	0.262924i
$556$	−3.32861	+	5.76531i	−0.141164	+	0.244504i
$557$	−20.6032	+	35.6858i	−0.872985	+	1.51205i	−0.0140907	+	0.999901i	$0.504485\pi$
$557$	−20.6032	+	35.6858i	−0.872985	+	1.51205i	−0.858894	+	0.512153i	$0.828848\pi$
$558$			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	−0.198038	−	0.980194i	$-0.563457\pi$
$563$	13.0933	−	7.55940i	0.551815	−	0.318591i	0.749854	+	0.661603i	$0.230124\pi$
$564$			4.94552i			0.208244i
$565$	−0.887817	+	5.74519i	−0.0373507	+	0.241702i
$566$	−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	$0.978411\pi$
$570$	3.90621	+	10.0628i	0.163613	+	0.421483i
$571$	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
$575$	12.7426	−	40.2451i	0.531404	−	1.67834i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	1.20258			0.0500639			0.0250319	−	0.999687i	$-0.492031\pi$
$577$	1.20258			0.0500639			0.0250319	+	0.999687i	$0.492031\pi$
$578$	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
$585$	6.24579	−	5.09805i	0.258231	−	0.210779i
$586$	−30.2501			−1.24962
$587$	9.53243	−	16.5107i	0.393446	−	0.681468i	−0.599456	−	0.800408i	$-0.704616\pi$
$587$	9.53243	−	16.5107i	0.393446	−	0.681468i	0.992901	+	0.118940i	$0.0379496\pi$
$588$	−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	$-0.421769\pi$
$593$	11.8496			0.486606			0.243303	+	0.969950i	$0.421769\pi$
$594$	−0.658509	−	1.14057i	−0.0270189	−	0.0467982i
$595$	−4.99736	+	1.93990i	−0.204872	+	0.0795280i
$596$	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	$0.413574\pi$
$600$	−1.50928	+	4.76677i	−0.0616161	+	0.194602i
$601$	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
$605$	−20.4752	−	3.16407i	−0.832434	−	0.128638i
$606$		−	2.43859i		−	0.0990608i
$607$	4.20075	−	2.42530i	0.170503	−	0.0984400i	−0.412320	−	0.911039i	$-0.635281\pi$
$607$	4.20075	−	2.42530i	0.170503	−	0.0984400i	0.582823	+	0.812599i	$0.301948\pi$
$608$	−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	−0.999531	−	0.0306146i	$-0.990254\pi$
$613$	−11.7172	+	20.2948i	−0.473253	+	0.819698i	0.526279	+	0.850312i	$0.323587\pi$
$614$	−7.06959	+	12.2449i	−0.285306	+	0.494164i
$615$	3.46788	+	0.535898i	0.139838	+	0.0216095i
$616$		−	2.01198i		−	0.0810648i
$617$	7.01830	+	12.1560i	0.282546	+	0.489384i	0.972011	−	0.234935i	$-0.0754877\pi$
$617$	7.01830	+	12.1560i	0.282546	+	0.489384i	−0.689465	+	0.724319i	$0.742154\pi$
$618$	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	$-0.105196\pi$
$620$	0.555760	−	3.59640i	0.0223199	−	0.144435i
$621$	−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
$630$	−3.37591	−	0.521687i	−0.134500	−	0.0207845i
$631$	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
$635$	−16.8863	+	6.55502i	−0.670114	+	0.260128i
$636$	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
$640$	−0.809179	−	2.08452i	−0.0319856	−	0.0823979i
$641$	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	$-0.878179\pi$
$643$	−19.9623	−	34.5756i	−0.787235	−	1.36353i	0.140420	−	0.990092i	$-0.455155\pi$
$644$	−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	0.243710	−	0.969848i	$-0.421635\pi$
$647$	−12.0656	−	6.96608i	−0.474348	−	0.273865i	−0.718058	+	0.695983i	$0.754969\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	13.7934			0.541438
$650$	−15.5431	+	9.13299i	−0.609651	+	0.358225i
$651$	2.48622			0.0974425
$652$	4.95812	−	8.58772i	0.194175	−	0.336321i
$653$	25.7670	+	14.8766i	1.00834	+	0.582165i	0.910705	−	0.413058i	$-0.135539\pi$
$653$	25.7670	+	14.8766i	1.00834	+	0.582165i	0.0976340	+	0.995222i	$0.468873\pi$
$654$	−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	$-0.359714\pi$
$660$	1.06570	+	2.74535i	0.0414824	+	0.106863i
$661$	−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
$665$	15.3726	−	5.96742i	0.596125	−	0.231407i
$666$	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
$670$	6.12693	+	0.946808i	0.236704	+	0.0365784i
$671$		−	6.56228i		−	0.253334i
$672$	1.32301	−	0.763837i	0.0510360	−	0.0294657i
$673$	28.1953	+	16.2786i	1.08685	+	0.627492i	0.932736	−	0.360561i	$-0.117415\pi$
$673$	28.1953	+	16.2786i	1.08685	+	0.627492i	0.154113	+	0.988053i	$0.450748\pi$
$674$	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	$0.212372\pi$
$677$			32.2002i			1.23756i	−0.785566	+	0.618778i	$0.787628\pi$
$678$	−1.29991	+	2.25151i	−0.0499228	+	0.0864689i
$679$	−1.47119	+	2.54818i	−0.0564593	+	0.0977903i
$680$	−0.535898	+	3.46788i	−0.0205508	+	0.132987i
$681$		−	10.1513i		−	0.389000i
$682$	−1.07169	−	1.85622i	−0.0410372	−	0.0710784i
$683$	−3.19280	−	5.53009i	−0.122169	−	0.211603i	0.798454	−	0.602056i	$-0.205652\pi$
$683$	−3.19280	−	5.53009i	−0.122169	−	0.211603i	−0.920623	+	0.390453i	$0.872318\pi$
$684$			4.82738i			0.184579i
$685$	−27.1453	−	4.19482i	−1.03717	−	0.160276i
$686$	−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
$695$	−14.7114	−	2.27338i	−0.558034	−	0.0862342i
$696$	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
$700$	7.28207	+	2.30569i	0.275236	+	0.0871469i
$701$	−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
$705$	−10.3090	+	4.00181i	−0.388261	+	0.150717i
$706$	−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
$715$	−3.76665	+	9.92760i	−0.140865	+	0.371271i
$716$	−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
$725$	21.1109	+	6.68425i	0.784040	+	0.248247i
$726$	−8.02413	−	4.63273i	−0.297803	−	0.171937i
$727$			17.2599i			0.640136i	0.947395	+	0.320068i	$0.103706\pi$
$727$			17.2599i			0.640136i	−0.947395	+	0.320068i	$0.896294\pi$
$728$	5.38789	+	1.14452i	0.199688	+	0.0424188i
$729$	−1.00000			−0.0370370
$730$	4.84653	+	12.4851i	0.179378	+	0.462095i
$731$	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	$-0.498208\pi$
$733$	0.304799			0.0112580			0.00562900	+	0.999984i	$0.498208\pi$
$734$	6.14226	−	3.54624i	0.226715	−	0.130894i
$735$	1.59347	−	10.3116i	0.0587760	−	0.380348i
$736$			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	$0.353764\pi$
$743$	−15.1150	+	26.1800i	−0.554517	+	0.960451i	−0.997941	+	0.0641394i	$0.979570\pi$
$744$	0.813725	−	1.40941i	0.0298326	−	0.0516716i
$745$	−1.02826	+	6.65401i	−0.0376725	+	0.243784i
$746$			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
$750$	−11.1577	+	0.711042i	−0.407422	+	0.0259636i
$751$	−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	−0.339782	−	0.940504i	$-0.610353\pi$
$757$	−36.4328	−	21.0345i	−1.32417	−	0.764512i	−0.984392	+	0.175992i	$0.943687\pi$
$758$	−29.6252	+	17.1041i	−1.07604	+	0.621250i
$759$		−	11.1194i		−	0.403608i
$760$	1.64851	−	10.6677i	0.0597976	−	0.386959i
$761$	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
$765$	3.27122	−	1.26984i	0.118271	−	0.0459110i
$766$	−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	$0.865748\pi$
$770$	4.19401	−	1.62805i	0.151141	−	0.0586708i
$771$	−1.92197	−	3.32895i	−0.0692182	−	0.119889i
$772$	−17.8920			−0.643947
$773$	4.13819	+	7.16756i	0.148840	+	0.257799i	0.930799	−	0.365531i	$-0.119113\pi$
$773$	4.13819	+	7.16756i	0.148840	+	0.257799i	−0.781959	+	0.623330i	$0.785779\pi$
$774$	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
$780$	−7.95804	+	1.29215i	−0.284943	+	0.0462664i
$781$	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	0.893373	−	0.449315i	$-0.148332\pi$
$787$	1.61500	+	2.79726i	0.0575685	+	0.0997115i	−0.835805	+	0.549027i	$0.814999\pi$
$788$	0.625857			0.0222952
$789$	15.3032	+	26.5060i	0.544810	+	0.943638i
$790$	−3.94582	−	10.1648i	−0.140386	−	0.361647i
$791$	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
$795$	11.2606	+	29.0084i	0.399372	+	1.02882i
$796$	−8.84057	+	15.3123i	−0.313346	+	0.542731i
$797$	−35.1612	+	20.3003i	−1.24547	+	0.719075i	−0.970203	−	0.242292i	$-0.922101\pi$
$797$	−35.1612	+	20.3003i	−1.24547	+	0.719075i	−0.275271	+	0.961367i	$0.588768\pi$
$798$	7.37466			0.261060
$799$	−6.72118	+	3.88048i	−0.237778	+	0.137281i
$800$	3.69046	−	3.37350i	0.130477	−	0.119271i
$801$			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	$0.166657\pi$
$810$	2.20984	+	0.341491i	0.0776458	+	0.0119988i
$811$			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
$815$	21.9133	+	3.38631i	0.767589	+	0.118617i
$816$	−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	−0.791878	−	0.610680i	$-0.790896\pi$
$823$	−18.9040	+	10.9142i	−0.658952	+	0.380446i	0.132926	+	0.991126i	$0.457563\pi$
$824$		−	12.4300i		−	0.433020i
$825$	−4.86040	+	4.44296i	−0.169217	+	0.154684i
$826$	13.8561	−	7.99982i	0.482115	−	0.278349i
$827$	−18.9366			−0.658492			−0.329246	−	0.944244i	$-0.606794\pi$
$827$	−18.9366			−0.658492			−0.329246	+	0.944244i	$0.606794\pi$
$828$	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	$0.170031\pi$
$830$	−5.17082	−	13.3205i	−0.179482	−	0.462362i
$831$	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
$835$	−10.5108	−	27.0768i	−0.363741	−	0.937030i
$836$	−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
$845$	−24.4425	−	15.7341i	−0.840849	−	0.541270i
$846$	−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	$-0.249420\pi$
$853$	41.3790			1.41679			0.708394	+	0.705817i	$0.249420\pi$
$854$	−3.80596	−	6.59212i	−0.130237	−	0.225578i
$855$	−10.0628	+	3.90621i	−0.344139	+	0.133590i
$856$	−9.07302	−	5.23831i	−0.310109	−	0.179042i
$857$		−	30.6051i		−	1.04545i	−0.852501	−	0.522726i	$-0.824915\pi$
$857$		−	30.6051i		−	1.04545i	0.852501	−	0.522726i	$-0.175085\pi$
$858$	−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	$0.323016\pi$
$860$	−11.0242	+	4.27942i	−0.375922	+	0.145927i
$861$	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	$-0.417190\pi$
$863$	15.1133			0.514464			0.257232	+	0.966350i	$0.417190\pi$
$864$	−0.866025	+	0.500000i	−0.0294628	+	0.0170103i
$865$	−1.32395	+	8.56746i	−0.0450156	+	0.291302i
$866$		−	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
$875$	1.08624	+	17.0453i	0.0367216	+	0.576238i
$876$			5.98944i			0.202364i
$877$	5.54757	+	9.60868i	0.187328	+	0.324462i	0.944359	−	0.328918i	$-0.106684\pi$
$877$	5.54757	+	9.60868i	0.187328	+	0.324462i	−0.757030	+	0.653380i	$0.773351\pi$
$878$	1.02411	+	1.77380i	0.0345619	+	0.0598629i
$879$		−	30.2501i		−	1.02031i
$880$	0.449750	−	2.91040i	0.0151611	−	0.0981094i
$881$	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	$-0.940863\pi$
$883$		−	10.9779i		−	0.369435i	0.982792	−	0.184718i	$-0.0591371\pi$
$884$	−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	−0.176076	−	0.984377i	$-0.556341\pi$
$887$	−33.2555	−	19.2001i	−1.11661	−	0.644675i	−0.940533	+	0.339702i	$0.889674\pi$
$888$	−2.42743	+	1.40148i	−0.0814593	+	0.0470305i
$889$			12.3754i			0.415059i
$890$	6.29881	−	40.7605i	0.211136	−	1.36629i
$891$	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
$895$	−11.4147	−	29.4053i	−0.381551	−	0.982911i
$896$	−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
$900$	−4.76677	−	1.50928i	−0.158892	−	0.0503093i
$901$	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	−0.195133	−	0.980777i	$-0.562514\pi$
$907$	−34.3953	−	19.8581i	−1.14208	−	0.659378i	−0.946944	+	0.321399i	$0.895847\pi$
$908$	−5.07567	+	8.79132i	−0.168442	+	0.291750i
$909$	2.43859			0.0808828
$910$	1.97399	+	12.1573i	0.0654370	+	0.403010i
$911$	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	$0.726163\pi$
$920$	−17.5993	+	6.83178i	−0.580232	+	0.225237i
$921$	−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
$925$	−13.3610	−	4.23045i	−0.439308	−	0.139096i
$926$	−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	$0.101455\pi$
$930$	3.59640	+	0.555760i	0.117931	+	0.0182241i
$931$			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	$-0.720492\pi$
$937$		−	47.1112i		−	1.53905i	0.638614	−	0.769527i	$-0.279508\pi$
$938$	2.11779	−	3.66812i	0.0691484	−	0.119769i
$939$	1.54230	−	2.67134i	0.0503311	−	0.0871760i
$940$	10.9288	+	1.68885i	0.356458	+	0.0550842i
$941$			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
$945$	0.521687	−	3.37591i	0.0169705	−	0.109818i
$946$	−3.48259	+	6.03202i	−0.113229	+	0.196118i
$947$	17.4580	−	30.2381i	0.567307	−	0.982605i	−0.429524	−	0.903056i	$-0.641319\pi$
$947$	17.4580	−	30.2381i	0.567307	−	0.982605i	0.996831	−	0.0795494i	$-0.0253481\pi$
$948$		−	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	−0.357793	−	0.933801i	$-0.616471\pi$
$953$	8.39700	−	4.84801i	0.272005	−	0.157042i	0.629799	+	0.776758i	$0.283137\pi$
$954$			13.9161i			0.450550i
$955$	−41.6649	−	6.43856i	−1.34824	−	0.208347i
$956$	−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
$960$	2.08452	−	0.809179i	0.0672776	−	0.0261161i
$961$	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
$965$	−14.4778	−	37.2963i	−0.466058	−	1.20061i
$966$	−6.44897	−	11.1699i	−0.207492	−	0.359387i
$967$	36.1715			1.16320			0.581599	−	0.813476i	$-0.302427\pi$
$967$	36.1715			1.16320			0.581599	+	0.813476i	$0.302427\pi$
$968$	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
$975$	−9.13299	−	15.5431i	−0.292490	−	0.497778i
$976$	−4.98268			−0.159492
$977$	−2.70086	+	4.67802i	−0.0864080	+	0.149663i	−0.905990	−	0.423298i	$-0.860872\pi$
$977$	−2.70086	+	4.67802i	−0.0864080	+	0.149663i	0.819582	+	0.572961i	$0.194206\pi$
$978$	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	$-0.254687\pi$
$983$	43.6819			1.39324			0.696618	+	0.717442i	$0.254687\pi$
$984$	−0.784645	−	1.35904i	−0.0250136	−	0.0433248i
$985$	0.506430	+	1.30461i	0.0161362	+	0.0415684i
$986$	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
$990$	−2.74535	+	1.06570i	−0.0872530	+	0.0338703i
$991$	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
$995$	−39.0725	−	6.03795i	−1.23868	−	0.191416i
$996$		−	6.39020i		−	0.202481i
$997$	30.9866	−	17.8901i	0.981357	−	0.566587i	0.0786773	−	0.996900i	$-0.474930\pi$
$997$	30.9866	−	17.8901i	0.981357	−	0.566587i	0.902680	+	0.430314i	$0.141597\pi$
$998$	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.b.199.5	yes	12
3.2	odd	2		1170.2.bj.c.199.2		12
5.2	odd	4		1950.2.bc.j.901.6		12
5.3	odd	4		1950.2.bc.i.901.1		12
5.4	even	2		390.2.x.a.199.2	yes	12
13.10	even	6		390.2.x.a.49.2	✓	12
15.14	odd	2		1170.2.bj.d.199.5		12
39.23	odd	6		1170.2.bj.d.829.5		12
65.23	odd	12		1950.2.bc.i.751.1		12
65.49	even	6	inner	390.2.x.b.49.5	yes	12
65.62	odd	12		1950.2.bc.j.751.6		12
195.179	odd	6		1170.2.bj.c.829.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.x.a.49.2	✓	12	13.10	even	6
390.2.x.a.199.2	yes	12	5.4	even	2
390.2.x.b.49.5	yes	12	65.49	even	6	inner
390.2.x.b.199.5	yes	12	1.1	even	1	trivial
1170.2.bj.c.199.2		12	3.2	odd	2
1170.2.bj.c.829.2		12	195.179	odd	6
1170.2.bj.d.199.5		12	15.14	odd	2
1170.2.bj.d.829.5		12	39.23	odd	6
1950.2.bc.i.751.1		12	65.23	odd	12
1950.2.bc.i.901.1		12	5.3	odd	4
1950.2.bc.j.751.6		12	65.62	odd	12
1950.2.bc.j.901.6		12	5.2	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} +(-0.809179 - 2.08452i) q^{10} +(-1.14057 - 0.658509i) q^{11} -1.00000i q^{12} +(2.41225 - 2.67975i) q^{13} -1.52767 q^{14} +(2.08452 - 0.809179i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.35904 - 0.784645i) q^{17} +1.00000 q^{18} +(-4.18063 + 2.41369i) q^{19} +(-2.20984 - 0.341491i) 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} +(0.341491 - 2.20984i) q^{30} +1.62745i q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.658509 - 1.14057i) q^{33} -1.56929i q^{34} +(-3.37591 - 0.521687i) 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} +(2.20984 + 0.341491i) q^{45} +(7.31172 - 4.22143i) q^{46} -4.94552 q^{47} +(-0.866025 + 0.500000i) q^{48} +(2.33310 - 4.04106i) q^{49} +(-4.76677 - 1.50928i) q^{50} +1.56929 q^{51} +(-3.52686 - 0.749192i) q^{52} +13.9161i q^{53} +(0.866025 + 0.500000i) q^{54} +(-2.74535 + 1.06570i) 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} +(-1.29215 - 7.95804i) 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} +(1.50928 - 4.76677i) q^{75} +(4.18063 + 2.41369i) q^{76} +2.01198i q^{77} +(0.749192 - 3.52686i) q^{78} +4.87632 q^{79} +(0.809179 + 2.08452i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.35904 - 0.784645i) q^{82} +6.39020 q^{83} +(-1.32301 + 0.763837i) q^{84} +(0.535898 - 3.46788i) 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} +(-1.64851 + 10.6677i) 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	\( 12 q + 6 q^{2} - 6 q^{4} + 2 q^{5} + 2 q^{7} - 12 q^{8} + 6 q^{9} + 4 q^{10} + 6 q^{11} + 8 q^{13} + 4 q^{14} + 6 q^{15} - 6 q^{16} - 18 q^{17} + 12 q^{18} - 6 q^{19} + 2 q^{20} + 6 q^{22} - 6 q^{23} - 10 q^{25} - 2 q^{26} + 2 q^{28} + 14 q^{29} + 6 q^{30} + 6 q^{32} - 6 q^{33} - 22 q^{35} + 6 q^{36} + 12 q^{37} - 2 q^{39} - 2 q^{40} - 18 q^{41} + 12 q^{42} + 36 q^{43} - 2 q^{45} - 6 q^{46} - 16 q^{47} + 8 q^{49} - 20 q^{50} + 16 q^{51} - 10 q^{52} + 8 q^{55} - 2 q^{56} + 8 q^{57} - 14 q^{58} - 36 q^{59} + 10 q^{61} - 6 q^{62} - 2 q^{63} + 12 q^{64} - 44 q^{65} - 12 q^{66} - 4 q^{67} + 18 q^{68} + 16 q^{69} + 4 q^{70} - 12 q^{71} - 6 q^{72} - 28 q^{73} - 12 q^{74} + 16 q^{75} + 6 q^{76} + 2 q^{78} + 4 q^{79} - 4 q^{80} - 6 q^{81} - 18 q^{82} - 72 q^{83} + 12 q^{84} + 48 q^{85} - 6 q^{87} - 6 q^{88} + 18 q^{89} + 2 q^{90} + 2 q^{91} + 16 q^{93} - 8 q^{94} + 18 q^{95} + 48 q^{97} - 8 q^{98}+O(q^{100}) \) 12 * q + 6 * q^2 - 6 * q^4 + 2 * q^5 + 2 * q^7 - 12 * q^8 + 6 * q^9 + 4 * 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 + 2 * 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 - 22 * q^35 + 6 * q^36 + 12 * q^37 - 2 * q^39 - 2 * q^40 - 18 * q^41 + 12 * q^42 + 36 * q^43 - 2 * q^45 - 6 * q^46 - 16 * q^47 + 8 * q^49 - 20 * q^50 + 16 * q^51 - 10 * q^52 + 8 * 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 - 44 * 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 + 16 * q^75 + 6 * q^76 + 2 * q^78 + 4 * q^79 - 4 * q^80 - 6 * q^81 - 18 * q^82 - 72 * q^83 + 12 * q^84 + 48 * q^85 - 6 * q^87 - 6 * q^88 + 18 * q^89 + 2 * q^90 + 2 * q^91 + 16 * q^93 - 8 * q^94 + 18 * q^95 + 48 * q^97 - 8 * q^98

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