LMFDB - Embedded newform 483.2.i.h.415.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(277,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("483.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{19} + 22 x^{18} - 43 x^{17} + 245 x^{16} - 416 x^{15} + 1707 x^{14} - 2021 x^{13} + \cdots + 4 $ x^20 - 3x^19 + 22x^18 - 43x^17 + 245x^16 - 416x^15 + 1707x^14 - 2021x^13 + 7135x^12 - 6640x^11 + 20315x^10 - 10565x^9 + 29358x^8 - 9009x^7 + 30661x^6 - 4026x^5 + 15786x^4 - 84x^3 + 5800x^2 + 152*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			415.9
Root			$-1.03253 - 1.78839i$ of defining polynomial
Character	$\chi$	$=$	483.415
Dual form			483.2.i.h.277.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.03253 - 1.78839i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.13223 - 1.96108i) q^{4} +(0.304427 - 0.527282i) q^{5} +2.06506 q^{6} +(2.05425 + 1.66735i) q^{7} -0.546135 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.628658 - 1.08887i) q^{10} +(0.551216 + 0.954735i) q^{11} +(1.13223 - 1.96108i) q^{12} +1.84712 q^{13} +(5.10295 - 1.95222i) q^{14} +0.608853 q^{15} +(1.70056 - 2.94546i) q^{16} +(-2.94288 - 5.09722i) q^{17} +(1.03253 + 1.78839i) q^{18} +(-0.544070 + 0.942358i) q^{19} -1.37873 q^{20} +(-0.416841 + 2.61271i) q^{21} +2.27659 q^{22} +(-0.500000 + 0.866025i) q^{23} +(-0.273068 - 0.472967i) q^{24} +(2.31465 + 4.00909i) q^{25} +(1.90720 - 3.30337i) q^{26} -1.00000 q^{27} +(0.943923 - 5.91639i) q^{28} -0.804169 q^{29} +(0.628658 - 1.08887i) q^{30} +(-4.38680 - 7.59816i) q^{31} +(-4.05790 - 7.02849i) q^{32} +(-0.551216 + 0.954735i) q^{33} -12.1544 q^{34} +(1.50453 - 0.575585i) q^{35} +2.26446 q^{36} +(-4.55764 + 7.89406i) q^{37} +(1.12354 + 1.94602i) q^{38} +(0.923560 + 1.59965i) q^{39} +(-0.166258 + 0.287967i) q^{40} -9.79559 q^{41} +(4.24215 + 3.44317i) q^{42} +5.23469 q^{43} +(1.24821 - 2.16196i) q^{44} +(0.304427 + 0.527282i) q^{45} +(1.03253 + 1.78839i) q^{46} +(2.95439 - 5.11716i) q^{47} +3.40113 q^{48} +(1.43989 + 6.85031i) q^{49} +9.55977 q^{50} +(2.94288 - 5.09722i) q^{51} +(-2.09137 - 3.62236i) q^{52} +(-2.25507 - 3.90589i) q^{53} +(-1.03253 + 1.78839i) q^{54} +0.671220 q^{55} +(-1.12190 - 0.910598i) q^{56} -1.08814 q^{57} +(-0.830328 + 1.43817i) q^{58} +(3.70032 + 6.40914i) q^{59} +(-0.689363 - 1.19401i) q^{60} +(-2.51384 + 4.35410i) q^{61} -18.1180 q^{62} +(-2.47109 + 0.945359i) q^{63} -9.95734 q^{64} +(0.562312 - 0.973953i) q^{65} +(1.13829 + 1.97158i) q^{66} +(-1.03153 - 1.78666i) q^{67} +(-6.66405 + 11.5425i) q^{68} -1.00000 q^{69} +(0.524102 - 3.28500i) q^{70} +4.30092 q^{71} +(0.273068 - 0.472967i) q^{72} +(0.578067 + 1.00124i) q^{73} +(9.41179 + 16.3017i) q^{74} +(-2.31465 + 4.00909i) q^{75} +2.46406 q^{76} +(-0.459540 + 2.88034i) q^{77} +3.81441 q^{78} +(-7.58579 + 13.1390i) q^{79} +(-1.03539 - 1.79335i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-10.1142 + 17.5184i) q^{82} -10.7196 q^{83} +(5.59570 - 2.14073i) q^{84} -3.58356 q^{85} +(5.40497 - 9.36169i) q^{86} +(-0.402085 - 0.696431i) q^{87} +(-0.301039 - 0.521414i) q^{88} +(3.96083 - 6.86036i) q^{89} +1.25732 q^{90} +(3.79445 + 3.07979i) q^{91} +2.26446 q^{92} +(4.38680 - 7.59816i) q^{93} +(-6.10099 - 10.5672i) q^{94} +(0.331259 + 0.573757i) q^{95} +(4.05790 - 7.02849i) q^{96} -17.0648 q^{97} +(13.7378 + 4.49805i) q^{98} -1.10243 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 3 q^{2} + 10 q^{3} - 15 q^{4} + 5 q^{5} - 6 q^{6} + 18 q^{8} - 10 q^{9} - 11 q^{10} - 8 q^{11} + 15 q^{12} + 11 q^{14} + 10 q^{15} - 37 q^{16} + 11 q^{17} - 3 q^{18} - q^{19} - 30 q^{20} + 12 q^{22}+ \cdots + 16 q^{99}+O(q^{100}) $ 20 * q - 3 * q^2 + 10 * q^3 - 15 * q^4 + 5 * q^5 - 6 * q^6 + 18 * q^8 - 10 * q^9 - 11 * q^10 - 8 * q^11 + 15 * q^12 + 11 * q^14 + 10 * q^15 - 37 * q^16 + 11 * q^17 - 3 * q^18 - q^19 - 30 * q^20 + 12 * q^22 - 10 * q^23 + 9 * q^24 - 21 * q^25 - q^26 - 20 * q^27 + 44 * q^28 + 44 * q^29 + 11 * q^30 + 3 * q^31 - 11 * q^32 + 8 * q^33 - 6 * q^34 - 9 * q^35 + 30 * q^36 + 3 * q^37 - 16 * q^38 - 39 * q^40 - 52 * q^41 + 7 * q^42 + 54 * q^43 - 16 * q^44 + 5 * q^45 - 3 * q^46 - 11 * q^47 - 74 * q^48 + 22 * q^49 + 4 * q^50 - 11 * q^51 - 29 * q^52 - 5 * q^53 + 3 * q^54 - 36 * q^55 + 43 * q^56 - 2 * q^57 - 16 * q^58 + 10 * q^59 - 15 * q^60 - 22 * q^61 - 64 * q^62 + 138 * q^64 + 11 * q^65 + 6 * q^66 + 2 * q^67 + 21 * q^68 - 20 * q^69 + 84 * q^70 + 54 * q^71 - 9 * q^72 + 8 * q^73 - 14 * q^74 + 21 * q^75 - 44 * q^76 + 8 * q^77 - 2 * q^78 - 21 * q^79 + 53 * q^80 - 10 * q^81 - 36 * q^82 - 24 * q^83 + 25 * q^84 + 46 * q^85 - 18 * q^86 + 22 * q^87 + 10 * q^88 - 6 * q^89 + 22 * q^90 - 62 * q^91 + 30 * q^92 - 3 * q^93 - 35 * q^94 - 44 * q^95 + 11 * q^96 + 12 * q^97 + 2 * q^98 + 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	1.03253	−	1.78839i	0.730108	−	1.26458i	−0.226728	−	0.973958i	$-0.572803\pi$
$2$	1.03253	−	1.78839i	0.730108	−	1.26458i	0.956837	−	0.290627i	$-0.0938637\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−1.13223	−	1.96108i	−0.566116	−	0.980542i
$5$	0.304427	−	0.527282i	0.136144	−	0.235808i	−0.789890	−	0.613248i	$-0.789862\pi$
$5$	0.304427	−	0.527282i	0.136144	−	0.235808i	0.926034	+	0.377441i	$0.123196\pi$
$6$	2.06506			0.843056
$7$	2.05425	+	1.66735i	0.776434	+	0.630199i
$7$	2.05425	+	1.66735i	0.776434	+	0.630199i
$8$	−0.546135			−0.193088
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.628658	−	1.08887i	−0.198799	−	0.344330i
$11$	0.551216	+	0.954735i	0.166198	+	0.287863i	0.937080	−	0.349115i	$-0.113518\pi$
$11$	0.551216	+	0.954735i	0.166198	+	0.287863i	−0.770882	+	0.636978i	$0.780184\pi$
$12$	1.13223	−	1.96108i	0.326847	−	0.566116i
$13$	1.84712			0.512299			0.256149	−	0.966637i	$-0.417546\pi$
$13$	1.84712			0.512299			0.256149	+	0.966637i	$0.417546\pi$
$14$	5.10295	−	1.95222i	1.36382	−	0.521753i
$15$	0.608853			0.157205
$16$	1.70056	−	2.94546i	0.425141	−	0.736366i
$17$	−2.94288	−	5.09722i	−0.713753	−	1.23626i	−0.963438	−	0.267930i	$-0.913661\pi$
$17$	−2.94288	−	5.09722i	−0.713753	−	1.23626i	0.249685	−	0.968327i	$-0.419673\pi$
$18$	1.03253	+	1.78839i	0.243369	+	0.421528i
$19$	−0.544070	+	0.942358i	−0.124818	+	0.216192i	−0.921662	−	0.387994i	$-0.873168\pi$
$19$	−0.544070	+	0.942358i	−0.124818	+	0.216192i	0.796844	+	0.604186i	$0.206501\pi$
$20$	−1.37873			−0.308293
$21$	−0.416841	+	2.61271i	−0.0909623	+	0.570140i
$22$	2.27659			0.485370
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i
$24$	−0.273068	−	0.472967i	−0.0557397	−	0.0965440i
$25$	2.31465	+	4.00909i	0.462930	+	0.801818i
$26$	1.90720	−	3.30337i	0.374034	−	0.647845i
$27$	−1.00000			−0.192450
$28$	0.943923	−	5.91639i	0.178385	−	1.11809i
$29$	−0.804169			−0.149330			−0.0746652	−	0.997209i	$-0.523789\pi$
$29$	−0.804169			−0.149330			−0.0746652	+	0.997209i	$0.523789\pi$
$30$	0.628658	−	1.08887i	0.114777	−	0.198799i
$31$	−4.38680	−	7.59816i	−0.787893	−	1.36467i	−0.927256	−	0.374429i	$-0.877839\pi$
$31$	−4.38680	−	7.59816i	−0.787893	−	1.36467i	0.139363	−	0.990241i	$-0.455495\pi$
$32$	−4.05790	−	7.02849i	−0.717342	−	1.24247i
$33$	−0.551216	+	0.954735i	−0.0959545	+	0.166198i
$34$	−12.1544			−2.08447
$35$	1.50453	−	0.575585i	0.254312	−	0.0972915i
$36$	2.26446			0.377411
$37$	−4.55764	+	7.89406i	−0.749271	+	1.29778i	0.198901	+	0.980020i	$0.436263\pi$
$37$	−4.55764	+	7.89406i	−0.749271	+	1.29778i	−0.948172	+	0.317756i	$0.897071\pi$
$38$	1.12354	+	1.94602i	0.182262	+	0.315687i
$39$	0.923560	+	1.59965i	0.147888	+	0.256149i
$40$	−0.166258	+	0.287967i	−0.0262877	+	0.0455317i
$41$	−9.79559			−1.52981			−0.764907	−	0.644140i	$-0.777215\pi$
$41$	−9.79559			−1.52981			−0.764907	+	0.644140i	$0.777215\pi$
$42$	4.24215	+	3.44317i	0.654578	+	0.531293i
$43$	5.23469			0.798283			0.399142	−	0.916889i	$-0.369308\pi$
$43$	5.23469			0.798283			0.399142	+	0.916889i	$0.369308\pi$
$44$	1.24821	−	2.16196i	0.188175	−	0.325928i
$45$	0.304427	+	0.527282i	0.0453812	+	0.0786026i
$46$	1.03253	+	1.78839i	0.152238	+	0.263684i
$47$	2.95439	−	5.11716i	0.430942	−	0.746414i	−0.566012	−	0.824397i	$-0.691515\pi$
$47$	2.95439	−	5.11716i	0.430942	−	0.746414i	0.996955	+	0.0779827i	$0.0248479\pi$
$48$	3.40113			0.490911
$49$	1.43989	+	6.85031i	0.205699	+	0.978615i
$50$	9.55977			1.35196
$51$	2.94288	−	5.09722i	0.412086	−	0.713753i
$52$	−2.09137	−	3.62236i	−0.290021	−	0.502330i
$53$	−2.25507	−	3.90589i	−0.309757	−	0.536515i	0.668552	−	0.743666i	$-0.266914\pi$
$53$	−2.25507	−	3.90589i	−0.309757	−	0.536515i	−0.978309	+	0.207150i	$0.933581\pi$
$54$	−1.03253	+	1.78839i	−0.140509	+	0.243369i
$55$	0.671220			0.0905072
$56$	−1.12190	−	0.910598i	−0.149920	−	0.121684i
$57$	−1.08814			−0.144128
$58$	−0.830328	+	1.43817i	−0.109027	+	0.188841i
$59$	3.70032	+	6.40914i	0.481741	+	0.834399i	0.999780	−	0.0209574i	$-0.00667143\pi$
$59$	3.70032	+	6.40914i	0.481741	+	0.834399i	−0.518040	+	0.855357i	$0.673338\pi$
$60$	−0.689363	−	1.19401i	−0.0889964	−	0.154146i
$61$	−2.51384	+	4.35410i	−0.321864	+	0.557486i	−0.980873	−	0.194650i	$-0.937643\pi$
$61$	−2.51384	+	4.35410i	−0.321864	+	0.557486i	0.659008	+	0.752136i	$0.270976\pi$
$62$	−18.1180			−2.30099
$63$	−2.47109	+	0.945359i	−0.311328	+	0.119104i
$64$	−9.95734			−1.24467
$65$	0.562312	−	0.973953i	0.0697462	−	0.120804i
$66$	1.13829	+	1.97158i	0.140114	+	0.242685i
$67$	−1.03153	−	1.78666i	−0.126021	−	0.218275i	0.796111	−	0.605151i	$-0.206887\pi$
$67$	−1.03153	−	1.78666i	−0.126021	−	0.218275i	−0.922132	+	0.386876i	$0.873554\pi$
$68$	−6.66405	+	11.5425i	−0.808134	+	1.39973i
$69$	−1.00000			−0.120386
$70$	0.524102	−	3.28500i	0.0626422	−	0.392633i
$71$	4.30092			0.510425			0.255213	−	0.966885i	$-0.417855\pi$
$71$	4.30092			0.510425			0.255213	+	0.966885i	$0.417855\pi$
$72$	0.273068	−	0.472967i	0.0321813	−	0.0557397i
$73$	0.578067	+	1.00124i	0.0676577	+	0.117187i	0.897870	−	0.440261i	$-0.145114\pi$
$73$	0.578067	+	1.00124i	0.0676577	+	0.117187i	−0.830212	+	0.557448i	$0.811781\pi$
$74$	9.41179	+	16.3017i	1.09410	+	1.89503i
$75$	−2.31465	+	4.00909i	−0.267273	+	0.462930i
$76$	2.46406			0.282647
$77$	−0.459540	+	2.88034i	−0.0523694	+	0.328245i
$78$	3.81441			0.431897
$79$	−7.58579	+	13.1390i	−0.853469	+	1.47825i	0.0245899	+	0.999698i	$0.492172\pi$
$79$	−7.58579	+	13.1390i	−0.853469	+	1.47825i	−0.878058	+	0.478553i	$0.841161\pi$
$80$	−1.03539	−	1.79335i	−0.115761	−	0.200503i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−10.1142	+	17.5184i	−1.11693	+	1.93458i
$83$	−10.7196			−1.17663			−0.588315	−	0.808632i	$-0.700209\pi$
$83$	−10.7196			−1.17663			−0.588315	+	0.808632i	$0.700209\pi$
$84$	5.59570	−	2.14073i	0.610541	−	0.233573i
$85$	−3.58356			−0.388692
$86$	5.40497	−	9.36169i	0.582833	−	1.00950i
$87$	−0.402085	−	0.696431i	−0.0431080	−	0.0746652i
$88$	−0.301039	−	0.521414i	−0.0320908	−	0.0555830i
$89$	3.96083	−	6.86036i	0.419847	−	0.727197i	−0.576076	−	0.817396i	$-0.695417\pi$
$89$	3.96083	−	6.86036i	0.419847	−	0.727197i	0.995924	+	0.0901988i	$0.0287502\pi$
$90$	1.25732			0.132533
$91$	3.79445	+	3.07979i	0.397766	+	0.322850i
$92$	2.26446			0.236087
$93$	4.38680	−	7.59816i	0.454890	−	0.787893i
$94$	−6.10099	−	10.5672i	−0.629269	−	1.08993i
$95$	0.331259	+	0.573757i	0.0339864	+	0.0588663i
$96$	4.05790	−	7.02849i	0.414158	−	0.717342i
$97$	−17.0648			−1.73267			−0.866336	−	0.499461i	$-0.833531\pi$
$97$	−17.0648			−1.73267			−0.866336	+	0.499461i	$0.833531\pi$
$98$	13.7378	+	4.49805i	1.38772	+	0.454371i
$99$	−1.10243			−0.110799
$100$	5.24144	−	9.07844i	0.524144	−	0.907844i
$101$	4.28278	+	7.41800i	0.426153	+	0.738118i	0.996527	−	0.0832664i	$-0.0265352\pi$
$101$	4.28278	+	7.41800i	0.426153	+	0.738118i	−0.570374	+	0.821385i	$0.693202\pi$
$102$	−6.07722	−	10.5260i	−0.601734	−	1.04223i
$103$	−5.21864	+	9.03895i	−0.514208	+	0.890634i	0.485656	+	0.874150i	$0.338581\pi$
$103$	−5.21864	+	9.03895i	−0.514208	+	0.890634i	−0.999864	+	0.0164842i	$0.994753\pi$
$104$	−1.00878			−0.0989187
$105$	1.25074	+	1.01517i	0.122059	+	0.0990705i
$106$	−9.31369			−0.904625
$107$	4.03634	−	6.99115i	0.390208	−	0.675860i	−0.602269	−	0.798293i	$-0.705737\pi$
$107$	4.03634	−	6.99115i	0.390208	−	0.675860i	0.992477	+	0.122434i	$0.0390699\pi$
$108$	1.13223	+	1.96108i	0.108949	+	0.188705i
$109$	−1.90581	−	3.30097i	−0.182544	−	0.316175i	0.760202	−	0.649686i	$-0.225100\pi$
$109$	−1.90581	−	3.30097i	−0.182544	−	0.316175i	−0.942746	+	0.333511i	$0.891766\pi$
$110$	0.693054	−	1.20040i	0.0660801	−	0.114454i
$111$	−9.11528			−0.865184
$112$	8.40450	−	3.21529i	0.794151	−	0.303816i
$113$	8.89428			0.836703			0.418352	−	0.908285i	$-0.362608\pi$
$113$	8.89428			0.836703			0.418352	+	0.908285i	$0.362608\pi$
$114$	−1.12354	+	1.94602i	−0.105229	+	0.182262i
$115$	0.304427	+	0.527282i	0.0283879	+	0.0491693i
$116$	0.910506	+	1.57704i	0.0845384	+	0.146425i
$117$	−0.923560	+	1.59965i	−0.0853831	+	0.147888i
$118$	15.2827			1.40689
$119$	2.45343	−	15.3778i	0.224905	−	1.40968i
$120$	−0.332516			−0.0303544
$121$	4.89232	−	8.47375i	0.444756	−	0.770341i
$122$	5.19123	+	8.99147i	0.469992	+	0.814050i
$123$	−4.89780	−	8.48323i	−0.441619	−	0.764907i
$124$	−9.93376	+	17.2058i	−0.892078	+	1.54512i
$125$	5.86283			0.524387
$126$	−0.860802	+	5.39539i	−0.0766863	+	0.480660i
$127$	7.91043			0.701937			0.350969	−	0.936387i	$-0.385852\pi$
$127$	7.91043			0.701937			0.350969	+	0.936387i	$0.385852\pi$
$128$	−2.16544	+	3.75066i	−0.191400	+	0.331514i
$129$	2.61735	+	4.53338i	0.230445	+	0.399142i
$130$	−1.16121	−	2.01127i	−0.101845	−	0.176400i
$131$	−0.237853	+	0.411974i	−0.0207813	+	0.0359943i	−0.876229	−	0.481895i	$-0.839949\pi$
$131$	−0.237853	+	0.411974i	−0.0207813	+	0.0359943i	0.855448	+	0.517889i	$0.173282\pi$
$132$	2.49642			0.217286
$133$	−2.68890	+	1.02868i	−0.233157	+	0.0891982i
$134$	−4.26033			−0.368036
$135$	−0.304427	+	0.527282i	−0.0262009	+	0.0453812i
$136$	1.60721	+	2.78377i	0.137817	+	0.238706i
$137$	4.13651	+	7.16465i	0.353406	+	0.612117i	0.986844	−	0.161677i	$-0.0516901\pi$
$137$	4.13651	+	7.16465i	0.353406	+	0.612117i	−0.633438	+	0.773794i	$0.718357\pi$
$138$	−1.03253	+	1.78839i	−0.0878947	+	0.152238i
$139$	−2.48191			−0.210513			−0.105257	−	0.994445i	$-0.533566\pi$
$139$	−2.48191			−0.210513			−0.105257	+	0.994445i	$0.533566\pi$
$140$	−2.83225	−	2.29882i	−0.239369	−	0.194286i
$141$	5.90878			0.497609
$142$	4.44082	−	7.69173i	0.372666	−	0.645476i
$143$	1.01816	+	1.76351i	0.0851430	+	0.147472i
$144$	1.70056	+	2.94546i	0.141714	+	0.245455i
$145$	−0.244810	+	0.424024i	−0.0203304	+	0.0352133i
$146$	2.38749			0.197590
$147$	−5.21259	+	4.67214i	−0.429928	+	0.385351i
$148$	20.6412			1.69670
$149$	−10.2978	+	17.8364i	−0.843631	+	1.46121i	0.0431743	+	0.999068i	$0.486253\pi$
$149$	−10.2978	+	17.8364i	−0.843631	+	1.46121i	−0.886805	+	0.462144i	$0.847080\pi$
$150$	4.77988	+	8.27900i	0.390276	+	0.675978i
$151$	−6.39740	−	11.0806i	−0.520613	−	0.901728i	−0.999713	−	0.0239678i	$-0.992370\pi$
$151$	−6.39740	−	11.0806i	−0.520613	−	0.901728i	0.479100	−	0.877761i	$-0.340963\pi$
$152$	0.297136	−	0.514655i	0.0241009	−	0.0417440i
$153$	5.88576			0.475835
$154$	4.67668	+	3.79587i	0.376858	+	0.305880i
$155$	−5.34183			−0.429066
$156$	2.09137	−	3.62236i	0.167443	−	0.290021i
$157$	2.28502	+	3.95778i	0.182365	+	0.315865i	0.942685	−	0.333683i	$-0.108291\pi$
$157$	2.28502	+	3.95778i	0.182365	+	0.315865i	−0.760321	+	0.649548i	$0.774958\pi$
$158$	15.6651	+	27.1328i	1.24625	+	2.15857i
$159$	2.25507	−	3.90589i	0.178838	−	0.309757i
$160$	−4.94133			−0.390646
$161$	−2.47109	+	0.945359i	−0.194749	+	0.0745047i
$162$	−2.06506			−0.162246
$163$	10.8772	−	18.8398i	0.851967	−	1.47565i	−0.0274642	−	0.999623i	$-0.508743\pi$
$163$	10.8772	−	18.8398i	0.851967	−	1.47565i	0.879431	−	0.476027i	$-0.157923\pi$
$164$	11.0909	+	19.2100i	0.866053	+	1.50005i
$165$	0.335610	+	0.581293i	0.0261272	+	0.0452536i
$166$	−11.0683	+	19.1709i	−0.859068	+	1.48795i
$167$	−3.92341			−0.303602			−0.151801	−	0.988411i	$-0.548507\pi$
$167$	−3.92341			−0.303602			−0.151801	+	0.988411i	$0.548507\pi$
$168$	0.227652	−	1.42689i	0.0175637	−	0.110087i
$169$	−9.58815			−0.737550
$170$	−3.70013	+	6.40882i	−0.283787	+	0.491534i
$171$	−0.544070	−	0.942358i	−0.0416061	−	0.0720639i
$172$	−5.92689	−	10.2657i	−0.451921	−	0.782750i
$173$	12.0085	−	20.7994i	0.912993	−	1.58135i	0.103179	−	0.994663i	$-0.467098\pi$
$173$	12.0085	−	20.7994i	0.912993	−	1.58135i	0.809814	−	0.586687i	$-0.199568\pi$
$174$	−1.66066			−0.125894
$175$	−1.92968	+	12.0950i	−0.145870	+	0.914296i
$176$	3.74952			0.282630
$177$	−3.70032	+	6.40914i	−0.278133	+	0.481741i
$178$	−8.17935	−	14.1670i	−0.613068	−	1.06187i
$179$	−10.0845	−	17.4669i	−0.753752	−	1.30554i	−0.945993	−	0.324188i	$-0.894909\pi$
$179$	−10.0845	−	17.4669i	−0.753752	−	1.30554i	0.192241	−	0.981348i	$-0.438424\pi$
$180$	0.689363	−	1.19401i	0.0513821	−	0.0889964i
$181$	16.7087			1.24195			0.620973	−	0.783832i	$-0.286738\pi$
$181$	16.7087			1.24195			0.620973	+	0.783832i	$0.286738\pi$
$182$	9.42576	−	3.60598i	0.698684	−	0.267293i
$183$	−5.02768			−0.371657
$184$	0.273068	−	0.472967i	0.0201308	−	0.0348676i
$185$	2.77493	+	4.80632i	0.204017	+	0.353368i
$186$	−9.05900	−	15.6906i	−0.664238	−	1.15049i
$187$	3.24433	−	5.61934i	0.237249	−	0.410927i
$188$	−13.3802			−0.975854
$189$	−2.05425	−	1.66735i	−0.149425	−	0.121282i
$190$	1.36814			0.0992551
$191$	−1.75479	+	3.03938i	−0.126972	+	0.219922i	−0.922502	−	0.385992i	$-0.873859\pi$
$191$	−1.75479	+	3.03938i	−0.126972	+	0.219922i	0.795530	+	0.605914i	$0.207193\pi$
$192$	−4.97867	−	8.62331i	−0.359305	−	0.622334i
$193$	6.82110	+	11.8145i	0.490993	+	0.850426i	0.999946	−	0.0103688i	$-0.00330056\pi$
$193$	6.82110	+	11.8145i	0.490993	+	0.850426i	−0.508953	+	0.860794i	$0.669967\pi$
$194$	−17.6199	+	30.5186i	−1.26504	+	2.19111i
$195$	1.12462			0.0805360
$196$	11.8037	−	10.5799i	0.843124	−	0.755706i
$197$	−13.4651			−0.959349			−0.479675	−	0.877447i	$-0.659245\pi$
$197$	−13.4651			−0.959349			−0.479675	+	0.877447i	$0.659245\pi$
$198$	−1.13829	+	1.97158i	−0.0808950	+	0.140114i
$199$	−7.14872	−	12.3820i	−0.506760	−	0.877733i	−0.999969	−	0.00782287i	$-0.997510\pi$
$199$	−7.14872	−	12.3820i	−0.506760	−	0.877733i	0.493210	−	0.869910i	$-0.335823\pi$
$200$	−1.26411	−	2.18951i	−0.0893862	−	0.154821i
$201$	1.03153	−	1.78666i	0.0727583	−	0.126021i
$202$	17.6884			1.24455
$203$	−1.65196	−	1.34083i	−0.115945	−	0.0941079i
$204$	−13.3281			−0.933153
$205$	−2.98204	+	5.16504i	−0.208275	+	0.360742i
$206$	10.7768	+	18.6660i	0.750855	+	1.30052i
$207$	−0.500000	−	0.866025i	−0.0347524	−	0.0601929i
$208$	3.14115	−	5.44062i	0.217799	−	0.377239i
$209$	−1.19960			−0.0829782
$210$	3.10695	−	1.18862i	0.214400	−	0.0820223i
$211$	2.83108			0.194900			0.0974499	−	0.995240i	$-0.468931\pi$
$211$	2.83108			0.194900			0.0974499	+	0.995240i	$0.468931\pi$
$212$	−5.10652	+	8.84475i	−0.350717	+	0.607460i
$213$	2.15046	+	3.72471i	0.147347	+	0.255213i
$214$	−8.33528	−	14.4371i	−0.569788	−	0.986901i
$215$	1.59358	−	2.76016i	0.108681	−	0.188241i
$216$	0.546135			0.0371598
$217$	3.65720	−	22.9229i	0.248267	−	1.55611i
$218$	−7.87123			−0.533107
$219$	−0.578067	+	1.00124i	−0.0390622	+	0.0676577i
$220$	−0.759977	−	1.31632i	−0.0512376	−	0.0887461i
$221$	−5.43585	−	9.41517i	−0.365655	−	0.633333i
$222$	−9.41179	+	16.3017i	−0.631678	+	1.09410i
$223$	4.78780			0.320615			0.160307	−	0.987067i	$-0.448751\pi$
$223$	4.78780			0.320615			0.160307	+	0.987067i	$0.448751\pi$
$224$	3.38300	−	21.2042i	0.226036	−	1.41677i
$225$	−4.62930			−0.308620
$226$	9.18360	−	15.9065i	0.610884	−	1.05808i
$227$	−9.64756	−	16.7101i	−0.640331	−	1.10909i	−0.985359	−	0.170493i	$-0.945464\pi$
$227$	−9.64756	−	16.7101i	−0.640331	−	1.10909i	0.345028	−	0.938592i	$-0.387869\pi$
$228$	1.23203	+	2.13394i	0.0815931	+	0.141323i
$229$	−4.06477	+	7.04038i	−0.268607	+	0.465242i	−0.968502	−	0.249004i	$-0.919897\pi$
$229$	−4.06477	+	7.04038i	−0.268607	+	0.465242i	0.699895	+	0.714246i	$0.253230\pi$
$230$	1.25732			0.0829050
$231$	−2.72421	+	1.04219i	−0.179240	+	0.0685714i
$232$	0.439185			0.0288339
$233$	−3.97470	+	6.88438i	−0.260391	+	0.451011i	−0.966346	−	0.257246i	$-0.917185\pi$
$233$	−3.97470	+	6.88438i	−0.260391	+	0.451011i	0.705955	+	0.708257i	$0.250518\pi$
$234$	1.90720	+	3.30337i	0.124678	+	0.215948i
$235$	−1.79879	−	3.11560i	−0.117340	−	0.203239i
$236$	8.37924	−	14.5133i	0.545442	−	0.944734i
$237$	−15.1716			−0.985501
$238$	−24.9683	−	20.2657i	−1.61845	−	1.31363i
$239$	15.7789			1.02065			0.510326	−	0.859981i	$-0.329525\pi$
$239$	15.7789			1.02065			0.510326	+	0.859981i	$0.329525\pi$
$240$	1.03539	−	1.79335i	0.0668344	−	0.115761i
$241$	5.63279	+	9.75628i	0.362840	+	0.628457i	0.988427	−	0.151697i	$-0.0484738\pi$
$241$	5.63279	+	9.75628i	0.362840	+	0.628457i	−0.625587	+	0.780154i	$0.715141\pi$
$242$	−10.1029	−	17.4988i	−0.649441	−	1.12486i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	11.3850			0.728851
$245$	4.05039	+	1.32619i	0.258770	+	0.0847269i
$246$	−20.2285			−1.28972
$247$	−1.00496	+	1.74065i	−0.0639443	+	0.110755i
$248$	2.39579	+	4.14963i	0.152133	+	0.263501i
$249$	−5.35981	−	9.28346i	−0.339664	−	0.588315i
$250$	6.05354	−	10.4850i	0.382859	−	0.663132i
$251$	−2.27255			−0.143442			−0.0717209	−	0.997425i	$-0.522849\pi$
$251$	−2.27255			−0.143442			−0.0717209	+	0.997425i	$0.522849\pi$
$252$	4.65178	+	3.77565i	0.293035	+	0.237844i
$253$	−1.10243			−0.0693094
$254$	8.16775	−	14.1470i	0.512490	−	0.887659i
$255$	−1.79178	−	3.10346i	−0.112206	−	0.194346i
$256$	−5.48557	−	9.50129i	−0.342848	−	0.593831i
$257$	0.435642	−	0.754555i	0.0271746	−	0.0470678i	−0.852118	−	0.523349i	$-0.824682\pi$
$257$	0.435642	−	0.754555i	0.0271746	−	0.0470678i	0.879293	+	0.476281i	$0.158016\pi$
$258$	10.8099			0.672998
$259$	−22.5247	+	8.61721i	−1.39962	+	0.535447i
$260$	−2.54667			−0.157938
$261$	0.402085	−	0.696431i	0.0248884	−	0.0431080i
$262$	0.491181	+	0.850750i	0.0303452	+	0.0525595i
$263$	2.66738	+	4.62004i	0.164478	+	0.284884i	0.936470	−	0.350748i	$-0.114073\pi$
$263$	2.66738	+	4.62004i	0.164478	+	0.284884i	−0.771992	+	0.635632i	$0.780739\pi$
$264$	0.301039	−	0.521414i	0.0185277	−	0.0320908i
$265$	−2.74601			−0.168686
$266$	−0.936674	+	5.87095i	−0.0574311	+	0.359971i
$267$	7.92167			0.484798
$268$	−2.33586	+	4.04582i	−0.142685	+	0.247138i
$269$	−11.3694	−	19.6923i	−0.693203	−	1.20066i	−0.970783	−	0.239960i	$-0.922866\pi$
$269$	−11.3694	−	19.6923i	−0.693203	−	1.20066i	0.277580	−	0.960703i	$-0.410468\pi$
$270$	0.628658	+	1.08887i	0.0382589	+	0.0662664i
$271$	3.21075	−	5.56119i	0.195039	−	0.337818i	−0.751874	−	0.659307i	$-0.770850\pi$
$271$	3.21075	−	5.56119i	0.195039	−	0.337818i	0.946913	+	0.321489i	$0.104183\pi$
$272$	−20.0182			−1.21378
$273$	−0.769956	+	4.82598i	−0.0465999	+	0.292082i
$274$	17.0843			1.03210
$275$	−2.55175	+	4.41975i	−0.153876	+	0.266521i
$276$	1.13223	+	1.96108i	0.0681524	+	0.118043i
$277$	−7.01764	−	12.1549i	−0.421649	−	0.730317i	0.574452	−	0.818538i	$-0.305215\pi$
$277$	−7.01764	−	12.1549i	−0.421649	−	0.730317i	−0.996101	+	0.0882210i	$0.971882\pi$
$278$	−2.56265	+	4.43864i	−0.153697	+	0.266212i
$279$	8.77360			0.525262
$280$	−0.821678	+	0.314347i	−0.0491047	+	0.0187858i
$281$	24.5278			1.46321			0.731603	−	0.681731i	$-0.238773\pi$
$281$	24.5278			1.46321			0.731603	+	0.681731i	$0.238773\pi$
$282$	6.10099	−	10.5672i	0.363309	−	0.629269i
$283$	2.19970	+	3.81000i	0.130759	+	0.226481i	0.923969	−	0.382467i	$-0.124925\pi$
$283$	2.19970	+	3.81000i	0.130759	+	0.226481i	−0.793210	+	0.608948i	$0.791592\pi$
$284$	−4.86964	−	8.43446i	−0.288960	−	0.500493i
$285$	−0.331259	+	0.573757i	−0.0196221	+	0.0339864i
$286$	4.20513			0.248655
$287$	−20.1226	−	16.3327i	−1.18780	−	0.964087i
$288$	8.11580			0.478228
$289$	−8.82108	+	15.2786i	−0.518887	+	0.898739i
$290$	0.505548	+	0.875634i	0.0296868	+	0.0514190i
$291$	−8.53242	−	14.7786i	−0.500179	−	0.866336i
$292$	1.30901	−	2.26728i	0.0766042	−	0.132682i
$293$	13.3413			0.779407			0.389704	−	0.920940i	$-0.372577\pi$
$293$	13.3413			0.779407			0.389704	+	0.920940i	$0.372577\pi$
$294$	2.97346	+	14.1463i	0.173416	+	0.825028i
$295$	4.50590			0.262344
$296$	2.48909	−	4.31123i	0.144675	−	0.250585i
$297$	−0.551216	−	0.954735i	−0.0319848	−	0.0553993i
$298$	21.2656	+	36.8331i	1.23188	+	2.13369i
$299$	−0.923560	+	1.59965i	−0.0534108	+	0.0925103i
$300$	10.4829			0.605230
$301$	10.7534	+	8.72806i	0.619814	+	0.503077i
$302$	−26.4220			−1.52042
$303$	−4.28278	+	7.41800i	−0.246039	+	0.426153i
$304$	1.85045	+	3.20508i	0.106131	+	0.183824i
$305$	1.53056	+	2.65101i	0.0876396	+	0.151796i
$306$	6.07722	−	10.5260i	0.347411	−	0.601734i
$307$	24.5499			1.40114			0.700569	−	0.713585i	$-0.252930\pi$
$307$	24.5499			1.40114			0.700569	+	0.713585i	$0.252930\pi$
$308$	6.16889	−	2.36001i	0.351505	−	0.134474i
$309$	−10.4373			−0.593756
$310$	−5.51560	+	9.55330i	−0.313265	+	0.542591i
$311$	−13.0387	−	22.5836i	−0.739355	−	1.28060i	−0.952786	−	0.303643i	$-0.901797\pi$
$311$	−13.0387	−	22.5836i	−0.739355	−	1.28060i	0.213431	−	0.976958i	$-0.431536\pi$
$312$	−0.504389	−	0.873627i	−0.0285554	−	0.0494594i
$313$	−12.0987	+	20.9555i	−0.683857	+	1.18448i	0.289937	+	0.957046i	$0.406366\pi$
$313$	−12.0987	+	20.9555i	−0.683857	+	1.18448i	−0.973794	+	0.227430i	$0.926968\pi$
$314$	9.43741			0.532584
$315$	−0.253795	+	1.59076i	−0.0142997	+	0.0896289i
$316$	34.3555			1.93265
$317$	−1.80488	+	3.12614i	−0.101372	+	0.175582i	−0.912250	−	0.409633i	$-0.865657\pi$
$317$	−1.80488	+	3.12614i	−0.101372	+	0.175582i	0.810878	+	0.585215i	$0.198990\pi$
$318$	−4.65684	−	8.06589i	−0.261143	−	0.452313i
$319$	−0.443271	−	0.767768i	−0.0248184	−	0.0429868i
$320$	−3.03128	+	5.25033i	−0.169454	+	0.293502i
$321$	8.07268			0.450573
$322$	−0.860802	+	5.39539i	−0.0479706	+	0.300674i
$323$	6.40453			0.356358
$324$	−1.13223	+	1.96108i	−0.0629018	+	0.108949i
$325$	4.27543	+	7.40527i	0.237158	+	0.410770i
$326$	−22.4620	−	38.9053i	−1.24406	−	2.15477i
$327$	1.90581	−	3.30097i	0.105392	−	0.182544i
$328$	5.34972			0.295389
$329$	14.6012	−	5.58592i	0.804987	−	0.307962i
$330$	1.38611			0.0763027
$331$	−4.11702	+	7.13089i	−0.226292	+	0.391949i	−0.956706	−	0.291055i	$-0.905994\pi$
$331$	−4.11702	+	7.13089i	−0.226292	+	0.391949i	0.730414	+	0.683004i	$0.239327\pi$
$332$	12.1371	+	21.0221i	0.666110	+	1.15374i
$333$	−4.55764	−	7.89406i	−0.249757	−	0.432592i
$334$	−4.05103	+	7.01659i	−0.221663	+	0.383931i
$335$	−1.25610			−0.0686279
$336$	6.98677	+	5.67087i	0.381160	+	0.309371i
$337$	26.1865			1.42647			0.713235	−	0.700925i	$-0.247229\pi$
$337$	26.1865			1.42647			0.713235	+	0.700925i	$0.247229\pi$
$338$	−9.90004	+	17.1474i	−0.538491	+	0.932694i
$339$	4.44714	+	7.70267i	0.241535	+	0.418352i
$340$	4.05743	+	7.02767i	0.220045	+	0.381129i
$341$	4.83615	−	8.37646i	0.261892	−	0.453611i
$342$	−2.24707			−0.121508
$343$	−8.46396	+	16.4731i	−0.457011	+	0.889461i
$344$	−2.85885			−0.154139
$345$	−0.304427	+	0.527282i	−0.0163898	+	0.0283879i
$346$	−24.7983	−	42.9520i	−1.33317	−	2.30911i
$347$	2.96367	+	5.13323i	0.159098	+	0.275566i	0.934544	−	0.355848i	$-0.115808\pi$
$347$	2.96367	+	5.13323i	0.159098	+	0.275566i	−0.775445	+	0.631415i	$0.782475\pi$
$348$	−0.910506	+	1.57704i	−0.0488083	+	0.0845384i
$349$	29.6319			1.58616			0.793080	−	0.609118i	$-0.208476\pi$
$349$	29.6319			1.58616			0.793080	+	0.609118i	$0.208476\pi$
$350$	19.6382	+	15.9395i	1.04970	+	0.852001i
$351$	−1.84712			−0.0985919
$352$	4.47356	−	7.74844i	0.238442	−	0.412993i
$353$	7.11938	+	12.3311i	0.378926	+	0.656320i	0.990906	−	0.134554i	$-0.0429600\pi$
$353$	7.11938	+	12.3311i	0.378926	+	0.656320i	−0.611980	+	0.790873i	$0.709627\pi$
$354$	7.64137	+	13.2352i	0.406134	+	0.703446i
$355$	1.30931	−	2.26780i	0.0694912	−	0.120362i
$356$	−17.9383			−0.950730
$357$	14.5443	−	5.56415i	0.769764	−	0.294486i
$358$	−41.6502			−2.20128
$359$	−1.39115	+	2.40954i	−0.0734220	+	0.127171i	−0.900399	−	0.435065i	$-0.856725\pi$
$359$	−1.39115	+	2.40954i	−0.0734220	+	0.127171i	0.826977	+	0.562236i	$0.190059\pi$
$360$	−0.166258	−	0.287967i	−0.00876257	−	0.0151772i
$361$	8.90797	+	15.4291i	0.468841	+	0.812056i
$362$	17.2522	−	29.8817i	0.906755	−	1.57055i
$363$	9.78464			0.513561
$364$	1.74354	−	10.9283i	0.0913862	−	0.572797i
$365$	0.703916			0.0368447
$366$	−5.19123	+	8.99147i	−0.271350	+	0.469992i
$367$	3.33224	+	5.77160i	0.173941	+	0.301275i	0.939794	−	0.341740i	$-0.111016\pi$
$367$	3.33224	+	5.77160i	0.173941	+	0.301275i	−0.765853	+	0.643016i	$0.777683\pi$
$368$	1.70056	+	2.94546i	0.0886480	+	0.153543i
$369$	4.89780	−	8.48323i	0.254969	−	0.441619i
$370$	11.4608			0.595818
$371$	1.88001	−	11.7837i	0.0976053	−	0.611777i
$372$	−19.8675			−1.03008
$373$	9.54119	−	16.5258i	0.494024	−	0.855675i	−0.505952	−	0.862562i	$-0.668859\pi$
$373$	9.54119	−	16.5258i	0.494024	−	0.855675i	0.999976	+	0.00688662i	$0.00219210\pi$
$374$	−6.69972	−	11.6043i	−0.346434	−	0.600042i
$375$	2.93141	+	5.07736i	0.151378	+	0.262194i
$376$	−1.61350	+	2.79466i	−0.0832098	+	0.144124i
$377$	−1.48540			−0.0765018
$378$	−5.10295	+	1.95222i	−0.262467	+	0.100411i
$379$	13.2631			0.681282			0.340641	−	0.940193i	$-0.389356\pi$
$379$	13.2631			0.681282			0.340641	+	0.940193i	$0.389356\pi$
$380$	0.750124	−	1.29925i	0.0384806	−	0.0666503i
$381$	3.95521	+	6.85063i	0.202632	+	0.350969i
$382$	3.62374	+	6.27650i	0.185407	+	0.321134i
$383$	1.55801	−	2.69855i	0.0796105	−	0.137889i	−0.823471	−	0.567358i	$-0.807966\pi$
$383$	1.55801	−	2.69855i	0.0796105	−	0.137889i	0.903082	+	0.429468i	$0.141299\pi$
$384$	−4.33089			−0.221010
$385$	1.37885	+	1.11916i	0.0702729	+	0.0570376i
$386$	28.1719			1.43391
$387$	−2.61735	+	4.53338i	−0.133047	+	0.230445i
$388$	19.3214	+	33.4656i	0.980894	+	1.69896i
$389$	4.99205	+	8.64648i	0.253107	+	0.438394i	0.964380	−	0.264522i	$-0.0852143\pi$
$389$	4.99205	+	8.64648i	0.253107	+	0.438394i	−0.711273	+	0.702916i	$0.751881\pi$
$390$	1.16121	−	2.01127i	0.0588000	−	0.101845i
$391$	5.88576			0.297656
$392$	−0.786376	−	3.74120i	−0.0397180	−	0.188959i
$393$	−0.475706			−0.0239962
$394$	−13.9031	+	24.0809i	−0.700429	+	1.21318i
$395$	4.61863	+	7.99971i	0.232389	+	0.402509i
$396$	1.24821	+	2.16196i	0.0627249	+	0.108643i
$397$	−2.82222	+	4.88823i	−0.141643	+	0.245333i	−0.928116	−	0.372292i	$-0.878572\pi$
$397$	−2.82222	+	4.88823i	−0.141643	+	0.245333i	0.786472	+	0.617626i	$0.211905\pi$
$398$	−29.5251			−1.47996
$399$	−2.23531	−	1.81431i	−0.111906	−	0.0908291i
$400$	15.7448			0.787242
$401$	−19.2811	+	33.3959i	−0.962853	+	1.66771i	−0.247576	+	0.968869i	$0.579634\pi$
$401$	−19.2811	+	33.3959i	−0.962853	+	1.66771i	−0.715277	+	0.698841i	$0.753699\pi$
$402$	−2.13016	−	3.68955i	−0.106243	−	0.184018i
$403$	−8.10294	−	14.0347i	−0.403636	−	0.699119i
$404$	9.69821	−	16.7978i	0.482504	−	0.835722i
$405$	−0.608853			−0.0302542
$406$	−4.10363	+	1.56992i	−0.203660	+	0.0779136i
$407$	−10.0490			−0.498110
$408$	−1.60721	+	2.78377i	−0.0795688	+	0.137817i
$409$	18.4036	+	31.8759i	0.909997	+	1.57616i	0.814065	+	0.580774i	$0.197250\pi$
$409$	18.4036	+	31.8759i	0.909997	+	1.57616i	0.0959322	+	0.995388i	$0.469417\pi$
$410$	6.15808	+	10.6661i	0.304126	+	0.526762i
$411$	−4.13651	+	7.16465i	−0.204039	+	0.353406i
$412$	23.6349			1.16441
$413$	−3.08489	+	19.3357i	−0.151798	+	0.951448i
$414$	−2.06506			−0.101492
$415$	−3.26334	+	5.65226i	−0.160191	+	0.277459i
$416$	−7.49542	−	12.9825i	−0.367493	−	0.636517i
$417$	−1.24096	−	2.14940i	−0.0607699	−	0.105257i
$418$	−1.23862	+	2.14536i	−0.0605831	+	0.104933i
$419$	−6.45390			−0.315293			−0.157647	−	0.987496i	$-0.550391\pi$
$419$	−6.45390			−0.315293			−0.157647	+	0.987496i	$0.550391\pi$
$420$	0.574710	−	3.60221i	0.0280430	−	0.175770i
$421$	29.9287			1.45863			0.729317	−	0.684176i	$-0.239838\pi$
$421$	29.9287			1.45863			0.729317	+	0.684176i	$0.239838\pi$
$422$	2.92318	−	5.06309i	0.142298	−	0.246467i
$423$	2.95439	+	5.11716i	0.143647	+	0.248805i
$424$	1.23157	+	2.13315i	0.0598104	+	0.103595i
$425$	13.6235	−	23.5965i	0.660835	−	1.14460i
$426$	8.88165			0.430317
$427$	−12.4239	+	4.75296i	−0.601233	+	0.230012i
$428$	−18.2803			−0.883612
$429$	−1.01816	+	1.76351i	−0.0491574	+	0.0851430i
$430$	−3.29083	−	5.69989i	−0.158698	−	0.274873i
$431$	−3.87420	−	6.71030i	−0.186613	−	0.323224i	0.757506	−	0.652829i	$-0.226418\pi$
$431$	−3.87420	−	6.71030i	−0.186613	−	0.323224i	−0.944119	+	0.329605i	$0.893085\pi$
$432$	−1.70056	+	2.94546i	−0.0818184	+	0.141714i
$433$	5.17696			0.248789			0.124394	−	0.992233i	$-0.460301\pi$
$433$	5.17696			0.248789			0.124394	+	0.992233i	$0.460301\pi$
$434$	−37.2189	−	30.2090i	−1.78656	−	1.45008i
$435$	−0.489621			−0.0234755
$436$	−4.31565	+	7.47492i	−0.206682	+	0.357984i
$437$	−0.544070	−	0.942358i	−0.0260264	−	0.0450791i
$438$	1.19374	+	2.06762i	0.0570392	+	0.0987948i
$439$	15.1460	−	26.2337i	0.722881	−	1.25207i	−0.236960	−	0.971519i	$-0.576151\pi$
$439$	15.1460	−	26.2337i	0.722881	−	1.25207i	0.959840	−	0.280547i	$-0.0905157\pi$
$440$	−0.366577			−0.0174759
$441$	−6.65249	−	2.17817i	−0.316785	−	0.103722i
$442$	−22.4507			−1.06787
$443$	−19.1011	+	33.0840i	−0.907519	+	1.57187i	−0.0900186	+	0.995940i	$0.528693\pi$
$443$	−19.1011	+	33.0840i	−0.907519	+	1.57187i	−0.817500	+	0.575928i	$0.804641\pi$
$444$	10.3206	+	17.8758i	0.489795	+	0.848349i
$445$	−2.41157	−	4.17695i	−0.114319	−	0.198007i
$446$	4.94354	−	8.56246i	0.234083	−	0.405444i
$447$	−20.5957			−0.974141
$448$	−20.4549	−	16.6024i	−0.966402	−	0.784388i
$449$	2.95568			0.139487			0.0697435	−	0.997565i	$-0.477782\pi$
$449$	2.95568			0.139487			0.0697435	+	0.997565i	$0.477782\pi$
$450$	−4.77988	+	8.27900i	−0.225326	+	0.390276i
$451$	−5.39949	−	9.35219i	−0.254252	−	0.440378i
$452$	−10.0704	−	17.4424i	−0.473671	−	0.820423i
$453$	6.39740	−	11.0806i	0.300576	−	0.520613i
$454$	−39.8455			−1.87004
$455$	2.77905	−	1.06317i	0.130284	−	0.0498423i
$456$	0.594272			0.0278293
$457$	−8.84772	+	15.3247i	−0.413879	+	0.716859i	−0.995310	−	0.0967363i	$-0.969160\pi$
$457$	−8.84772	+	15.3247i	−0.413879	+	0.716859i	0.581431	+	0.813596i	$0.302493\pi$
$458$	8.39398	+	14.5388i	0.392225	+	0.679354i
$459$	2.94288	+	5.09722i	0.137362	+	0.237918i
$460$	0.689363	−	1.19401i	0.0321417	−	0.0556711i
$461$	−11.7447			−0.547005			−0.273503	−	0.961871i	$-0.588182\pi$
$461$	−11.7447			−0.547005			−0.273503	+	0.961871i	$0.588182\pi$
$462$	−0.948976	+	5.94806i	−0.0441504	+	0.276729i
$463$	27.0872			1.25885			0.629424	−	0.777062i	$-0.283291\pi$
$463$	27.0872			1.25885			0.629424	+	0.777062i	$0.283291\pi$
$464$	−1.36754	+	2.36865i	−0.0634865	+	0.109962i
$465$	−2.67092	−	4.62616i	−0.123861	−	0.214533i
$466$	8.20799	+	14.2167i	0.380228	+	0.658574i
$467$	−11.5760	+	20.0502i	−0.535673	+	0.927813i	0.463457	+	0.886119i	$0.346609\pi$
$467$	−11.5760	+	20.0502i	−0.535673	+	0.927813i	−0.999130	+	0.0416937i	$0.986725\pi$
$468$	4.18274			0.193347
$469$	0.859967	−	5.39016i	0.0397096	−	0.248894i
$470$	−7.42921			−0.342684
$471$	−2.28502	+	3.95778i	−0.105288	+	0.182365i
$472$	−2.02088	−	3.50026i	−0.0930183	−	0.161112i
$473$	2.88545	+	4.99775i	0.132673	+	0.229797i
$474$	−15.6651	+	27.1328i	−0.719522	+	1.24625i
$475$	−5.03733			−0.231128
$476$	−32.9350	+	12.5998i	−1.50957	+	0.577512i
$477$	4.51013			0.206505
$478$	16.2922	−	28.2189i	0.745187	−	1.29070i
$479$	−11.1838	−	19.3709i	−0.510999	−	0.885077i	−0.999919	−	0.0127478i	$-0.995942\pi$
$479$	−11.1838	−	19.3709i	−0.510999	−	0.885077i	0.488919	−	0.872329i	$-0.337391\pi$
$480$	−2.47066	−	4.27932i	−0.112770	−	0.195323i
$481$	−8.41850	+	14.5813i	−0.383851	+	0.664849i
$482$	23.2641			1.05965
$483$	−2.05425	−	1.66735i	−0.0934716	−	0.0758670i
$484$	−22.1570			−1.00714
$485$	−5.19499	+	8.99799i	−0.235892	+	0.408578i
$486$	−1.03253	−	1.78839i	−0.0468365	−	0.0811231i
$487$	−20.9261	−	36.2451i	−0.948252	−	1.64242i	−0.749105	−	0.662452i	$-0.769516\pi$
$487$	−20.9261	−	36.2451i	−0.948252	−	1.64242i	−0.199148	−	0.979969i	$-0.563817\pi$
$488$	1.37290	−	2.37793i	0.0621482	−	0.107644i
$489$	21.7544			0.983766
$490$	6.55388	−	5.87436i	0.296074	−	0.265376i
$491$	16.2658			0.734063			0.367032	−	0.930209i	$-0.380374\pi$
$491$	16.2658			0.734063			0.367032	+	0.930209i	$0.380374\pi$
$492$	−11.0909	+	19.2100i	−0.500016	+	0.866053i
$493$	2.36657	+	4.09902i	0.106585	+	0.184611i
$494$	2.07531	+	3.59454i	0.0933725	+	0.161726i
$495$	−0.335610	+	0.581293i	−0.0150845	+	0.0261272i
$496$	−29.8401			−1.33986
$497$	8.83517	+	7.17113i	0.396311	+	0.321669i
$498$	−22.1366			−0.991966
$499$	9.91250	−	17.1689i	0.443744	−	0.768588i	−0.554219	−	0.832371i	$-0.686983\pi$
$499$	9.91250	−	17.1689i	0.443744	−	0.768588i	0.997964	+	0.0637829i	$0.0203165\pi$
$500$	−6.63808	−	11.4975i	−0.296864	−	0.514184i
$501$	−1.96170	−	3.39777i	−0.0876424	−	0.151801i
$502$	−2.34647	+	4.06420i	−0.104728	+	0.181394i
$503$	9.18201			0.409406			0.204703	−	0.978824i	$-0.434377\pi$
$503$	9.18201			0.409406			0.204703	+	0.978824i	$0.434377\pi$
$504$	1.34955	−	0.516294i	0.0601138	−	0.0229976i
$505$	5.21517			0.232072
$506$	−1.13829	+	1.97158i	−0.0506033	+	0.0876476i
$507$	−4.79408	−	8.30358i	−0.212912	−	0.368775i
$508$	−8.95644	−	15.5130i	−0.397378	−	0.688279i
$509$	16.4007	−	28.4068i	0.726948	−	1.25911i	−0.231219	−	0.972902i	$-0.574271\pi$
$509$	16.4007	−	28.4068i	0.726948	−	1.25911i	0.958167	−	0.286210i	$-0.0923954\pi$
$510$	−7.40026			−0.327689
$511$	−0.481925	+	3.02064i	−0.0213191	+	0.133625i
$512$	−31.3178			−1.38407
$513$	0.544070	−	0.942358i	0.0240213	−	0.0416061i
$514$	−0.899627	−	1.55820i	−0.0396808	−	0.0687292i
$515$	3.17738	+	5.50339i	0.140012	+	0.242508i
$516$	5.92689	−	10.2657i	0.260917	−	0.451921i
$517$	6.51404			0.286487
$518$	−7.84645	+	49.1805i	−0.344753	+	2.16087i
$519$	24.0171			1.05423
$520$	−0.307099	+	0.531910i	−0.0134672	+	0.0233258i
$521$	−3.43178	−	5.94402i	−0.150349	−	0.260412i	0.781007	−	0.624523i	$-0.214706\pi$
$521$	−3.43178	−	5.94402i	−0.150349	−	0.260412i	−0.931356	+	0.364110i	$0.881373\pi$
$522$	−0.830328	−	1.43817i	−0.0363425	−	0.0629470i
$523$	−4.88311	+	8.45780i	−0.213524	+	0.369834i	−0.952815	−	0.303552i	$-0.901827\pi$
$523$	−4.88311	+	8.45780i	−0.213524	+	0.369834i	0.739291	+	0.673386i	$0.235161\pi$
$524$	1.07722			0.0470586
$525$	−11.4394	+	4.37635i	−0.499257	+	0.190999i
$526$	11.0166			0.480347
$527$	−25.8197	+	44.7210i	−1.12472	+	1.94808i
$528$	1.87476	+	3.24718i	0.0815884	+	0.141315i
$529$	−0.500000	−	0.866025i	−0.0217391	−	0.0376533i
$530$	−2.83533	+	4.91094i	−0.123159	+	0.213318i
$531$	−7.40064			−0.321160
$532$	5.06179	+	4.10844i	0.219456	+	0.178124i
$533$	−18.0936			−0.783722
$534$	8.17935	−	14.1670i	0.353955	−	0.613068i
$535$	−2.45754	−	4.25658i	−0.106249	−	0.184028i
$536$	0.563354	+	0.975757i	0.0243332	+	0.0421463i
$537$	10.0845	−	17.4669i	0.435179	−	0.753752i
$538$	−46.9568			−2.02445
$539$	−5.74653	+	5.15072i	−0.247521	+	0.221857i
$540$	1.37873			0.0593309
$541$	2.32104	−	4.02015i	0.0997891	−	0.172840i	−0.811808	−	0.583924i	$-0.801517\pi$
$541$	2.32104	−	4.02015i	0.0997891	−	0.172840i	0.911597	+	0.411084i	$0.134850\pi$
$542$	−6.63039	−	11.4842i	−0.284800	−	0.493288i
$543$	8.35434	+	14.4701i	0.358519	+	0.620973i
$544$	−23.8838	+	41.3680i	−1.02401	+	1.77364i
$545$	−2.32072			−0.0994088
$546$	7.83575	+	6.35995i	0.335339	+	0.272181i
$547$	21.6976			0.927722			0.463861	−	0.885908i	$-0.346464\pi$
$547$	21.6976			0.927722			0.463861	+	0.885908i	$0.346464\pi$
$548$	9.36698	−	16.2241i	0.400138	−	0.693059i
$549$	−2.51384	−	4.35410i	−0.107288	−	0.185829i
$550$	5.26950	+	9.12704i	0.224692	+	0.389179i
$551$	0.437525	−	0.757815i	0.0186392	−	0.0322840i
$552$	0.546135			0.0232451
$553$	−37.4904	+	14.3426i	−1.59425	+	0.609909i
$554$	−28.9836			−1.23140
$555$	−2.77493	+	4.80632i	−0.117789	+	0.204017i
$556$	2.81010	+	4.86724i	0.119175	+	0.206417i
$557$	16.0798	+	27.8510i	0.681323	+	1.18009i	0.974577	+	0.224051i	$0.0719283\pi$
$557$	16.0798	+	27.8510i	0.681323	+	1.18009i	−0.293255	+	0.956034i	$0.594738\pi$
$558$	9.05900	−	15.6906i	0.383498	−	0.664238i
$559$	9.66910			0.408960
$560$	0.863190	−	5.41036i	0.0364764	−	0.228630i
$561$	6.48865			0.273951
$562$	25.3257	−	43.8653i	1.06830	−	1.85035i
$563$	6.15797	+	10.6659i	0.259528	+	0.449515i	0.966115	−	0.258110i	$-0.0830998\pi$
$563$	6.15797	+	10.6659i	0.259528	+	0.449515i	−0.706588	+	0.707625i	$0.749767\pi$
$564$	−6.69012	−	11.5876i	−0.281705	−	0.487927i
$565$	2.70765	−	4.68979i	0.113912	−	0.197301i
$566$	9.08503			0.381872
$567$	0.416841	−	2.61271i	0.0175057	−	0.109723i
$568$	−2.34888			−0.0985570
$569$	13.1175	−	22.7202i	0.549914	−	0.952479i	−0.448366	−	0.893850i	$-0.647994\pi$
$569$	13.1175	−	22.7202i	0.549914	−	0.952479i	0.998280	−	0.0586291i	$-0.0186729\pi$
$570$	0.684069	+	1.18484i	0.0286525	+	0.0496276i
$571$	2.79914	+	4.84826i	0.117141	+	0.202893i	0.918633	−	0.395111i	$-0.129294\pi$
$571$	2.79914	+	4.84826i	0.117141	+	0.202893i	−0.801493	+	0.598004i	$0.795961\pi$
$572$	2.30559	−	3.99340i	0.0964017	−	0.166973i
$573$	−3.50958			−0.146615
$574$	−49.9864	+	19.1232i	−2.08639	+	0.798185i
$575$	−4.62930			−0.193055
$576$	4.97867	−	8.62331i	0.207445	−	0.359305i
$577$	5.06738	+	8.77696i	0.210958	+	0.365390i	0.952015	−	0.306053i	$-0.0990084\pi$
$577$	5.06738	+	8.77696i	0.210958	+	0.365390i	−0.741057	+	0.671442i	$0.765675\pi$
$578$	18.2160	+	31.5511i	0.757688	+	1.31235i
$579$	−6.82110	+	11.8145i	−0.283475	+	0.490993i
$580$	1.10873			0.0460375
$581$	−22.0208	−	17.8733i	−0.913576	−	0.741511i
$582$	−35.2399			−1.46074
$583$	2.48606	−	4.30598i	0.102962	−	0.178336i
$584$	−0.315703	−	0.546814i	−0.0130639	−	0.0226273i
$585$	0.562312	+	0.973953i	0.0232487	+	0.0402680i
$586$	13.7753	−	23.8595i	0.569052	−	0.985627i
$587$	27.2323			1.12400			0.561999	−	0.827138i	$-0.310032\pi$
$587$	27.2323			1.12400			0.561999	+	0.827138i	$0.310032\pi$
$588$	15.0643	+	4.93239i	0.621242	+	0.203408i
$589$	9.54691			0.393374
$590$	4.65247	−	8.05832i	0.191539	−	0.331756i
$591$	−6.73255	−	11.6611i	−0.276940	−	0.479675i
$592$	15.5011	+	26.8487i	0.637092	+	1.10348i
$593$	−19.1773	+	33.2161i	−0.787519	+	1.36402i	0.139964	+	0.990157i	$0.455301\pi$
$593$	−19.1773	+	33.2161i	−0.787519	+	1.36402i	−0.927483	+	0.373866i	$0.878032\pi$
$594$	−2.27659			−0.0934095
$595$	−7.36154	−	5.97505i	−0.301794	−	0.244953i
$596$	46.6381			1.91037
$597$	7.14872	−	12.3820i	0.292578	−	0.506760i
$598$	1.90720	+	3.30337i	0.0779914	+	0.135085i
$599$	3.44189	+	5.96153i	0.140632	+	0.243581i	0.927735	−	0.373240i	$-0.121753\pi$
$599$	3.44189	+	5.96153i	0.140632	+	0.243581i	−0.787103	+	0.616822i	$0.788420\pi$
$600$	1.26411	−	2.18951i	0.0516071	−	0.0893862i
$601$	1.80012			0.0734283			0.0367141	−	0.999326i	$-0.488311\pi$
$601$	1.80012			0.0734283			0.0367141	+	0.999326i	$0.488311\pi$
$602$	26.7124	−	10.2193i	1.08872	−	0.416507i
$603$	2.06305			0.0840141
$604$	−14.4867	+	25.0917i	−0.589455	+	1.02097i
$605$	−2.97870	−	5.15927i	−0.121102	−	0.209754i
$606$	8.84420	+	15.3186i	0.359271	+	0.622275i
$607$	−1.46758	+	2.54193i	−0.0595674	+	0.103174i	−0.894271	−	0.447525i	$-0.852305\pi$
$607$	−1.46758	+	2.54193i	−0.0595674	+	0.103174i	0.834704	+	0.550699i	$0.185639\pi$
$608$	8.83113			0.358150
$609$	0.335211	−	2.10106i	0.0135834	−	0.0851392i
$610$	6.32139			0.255946
$611$	5.45711	−	9.45200i	0.220771	−	0.382387i
$612$	−6.66405	−	11.5425i	−0.269378	−	0.466577i
$613$	−15.8695	−	27.4867i	−0.640962	−	1.11018i	−0.985218	−	0.171303i	$-0.945202\pi$
$613$	−15.8695	−	27.4867i	−0.640962	−	1.11018i	0.344256	−	0.938876i	$-0.388131\pi$
$614$	25.3485	−	43.9049i	1.02298	−	1.77186i
$615$	−5.96408			−0.240495
$616$	0.250971	−	1.57305i	0.0101119	−	0.0633801i
$617$	−41.7807			−1.68203			−0.841013	−	0.541015i	$-0.818040\pi$
$617$	−41.7807			−1.68203			−0.841013	+	0.541015i	$0.818040\pi$
$618$	−10.7768	+	18.6660i	−0.433506	+	0.750855i
$619$	−13.6085	−	23.5706i	−0.546972	−	0.947383i	−0.998480	−	0.0551163i	$-0.982447\pi$
$619$	−13.6085	−	23.5706i	−0.546972	−	0.947383i	0.451508	−	0.892267i	$-0.350886\pi$
$620$	6.04820	+	10.4758i	0.242901	+	0.420718i
$621$	0.500000	−	0.866025i	0.0200643	−	0.0347524i
$622$	−53.8512			−2.15924
$623$	19.5752	−	7.48882i	0.784263	−	0.300033i
$624$	6.28229			0.251493
$625$	−9.78844	+	16.9541i	−0.391538	+	0.678163i
$626$	24.9845	+	43.2743i	0.998580	+	1.72959i
$627$	−0.599801	−	1.03889i	−0.0239537	−	0.0414891i
$628$	5.17436	−	8.96225i	0.206479	−	0.357633i
$629$	53.6503			2.13918
$630$	2.58284	+	2.09639i	0.102903	+	0.0835220i
$631$	25.8728			1.02998			0.514990	−	0.857196i	$-0.327795\pi$
$631$	25.8728			1.02998			0.514990	+	0.857196i	$0.327795\pi$
$632$	4.14287	−	7.17566i	0.164795	−	0.285433i
$633$	1.41554	+	2.45179i	0.0562627	+	0.0974499i
$634$	3.72718	+	6.45567i	0.148025	+	0.256387i
$635$	2.40814	−	4.17103i	0.0955643	−	0.165522i
$636$	−10.2130			−0.404973
$637$	2.65965	+	12.6533i	0.105379	+	0.501343i
$638$	−1.83076			−0.0724805
$639$	−2.15046	+	3.72471i	−0.0850709	+	0.147347i
$640$	1.31844	+	2.28360i	0.0521158	+	0.0902672i
$641$	6.67953	+	11.5693i	0.263826	+	0.456959i	0.967255	−	0.253805i	$-0.0816823\pi$
$641$	6.67953	+	11.5693i	0.263826	+	0.456959i	−0.703430	+	0.710765i	$0.748349\pi$
$642$	8.33528	−	14.4371i	0.328967	−	0.569788i
$643$	43.4719			1.71436			0.857182	−	0.515014i	$-0.172213\pi$
$643$	43.4719			1.71436			0.857182	+	0.515014i	$0.172213\pi$
$644$	4.65178	+	3.77565i	0.183306	+	0.148782i
$645$	3.18716			0.125494
$646$	6.61287	−	11.4538i	0.260180	−	0.450645i
$647$	23.0757	+	39.9683i	0.907201	+	1.57132i	0.817936	+	0.575310i	$0.195118\pi$
$647$	23.0757	+	39.9683i	0.907201	+	1.57132i	0.0892649	+	0.996008i	$0.471548\pi$
$648$	0.273068	+	0.472967i	0.0107271	+	0.0185799i
$649$	−4.07935	+	7.06565i	−0.160129	+	0.277351i
$650$	17.6580			0.692605
$651$	21.6804	−	8.29420i	0.849721	−	0.325075i
$652$	−49.2620			−1.92925
$653$	16.7983	−	29.0955i	0.657367	−	1.13859i	−0.323928	−	0.946082i	$-0.605003\pi$
$653$	16.7983	−	29.0955i	0.657367	−	1.13859i	0.981295	−	0.192511i	$-0.0616633\pi$
$654$	−3.93562	−	6.81669i	−0.153895	−	0.266554i
$655$	0.144818	+	0.250832i	0.00565849	+	0.00980080i
$656$	−16.6580	+	28.8526i	−0.650387	+	1.12650i
$657$	−1.15613			−0.0451051
$658$	5.08629	−	31.8802i	0.198284	−	1.24282i
$659$	10.2122			0.397809			0.198905	−	0.980019i	$-0.436262\pi$
$659$	10.2122			0.397809			0.198905	+	0.980019i	$0.436262\pi$
$660$	0.759977	−	1.31632i	0.0295820	−	0.0512376i
$661$	−9.00998	−	15.6057i	−0.350448	−	0.606993i	0.635880	−	0.771788i	$-0.280637\pi$
$661$	−9.00998	−	15.6057i	−0.350448	−	0.606993i	−0.986328	+	0.164795i	$0.947304\pi$
$662$	8.50189	+	14.7257i	0.330435	+	0.572331i
$663$	5.43585	−	9.41517i	0.211111	−	0.365655i
$664$	5.85436			0.227193
$665$	−0.276165	+	1.73097i	−0.0107092	+	0.0671240i
$666$	−18.8236			−0.729399
$667$	0.402085	−	0.696431i	0.0155688	−	0.0269659i
$668$	4.44221	+	7.69413i	0.171874	+	0.297695i
$669$	2.39390	+	4.14635i	0.0925534	+	0.160307i
$670$	−1.29696	+	2.24640i	−0.0501058	+	0.0867858i
$671$	−5.54268			−0.213973
$672$	20.0549	−	7.67234i	0.773634	−	0.295967i
$673$	−40.5777			−1.56415			−0.782077	−	0.623181i	$-0.785840\pi$
$673$	−40.5777			−1.56415			−0.782077	+	0.623181i	$0.785840\pi$
$674$	27.0383	−	46.8318i	1.04148	−	1.80389i
$675$	−2.31465	−	4.00909i	−0.0890909	−	0.154310i
$676$	10.8560	+	18.8032i	0.417539	+	0.723199i
$677$	−12.9712	+	22.4667i	−0.498522	+	0.863466i	−0.999999	−	0.00170564i	$-0.999457\pi$
$677$	−12.9712	+	22.4667i	−0.498522	+	0.863466i	0.501476	+	0.865171i	$0.332790\pi$
$678$	18.3672			0.705388
$679$	−35.0555	−	28.4531i	−1.34531	−	1.09193i
$680$	1.95711			0.0750518
$681$	9.64756	−	16.7101i	0.369695	−	0.640331i
$682$	−9.98694	−	17.2979i	−0.382420	−	0.662370i
$683$	12.9083	+	22.3579i	0.493924	+	0.855502i	0.999975	−	0.00700177i	$-0.00222875\pi$
$683$	12.9083	+	22.3579i	0.493924	+	0.855502i	−0.506051	+	0.862503i	$0.668895\pi$
$684$	−1.23203	+	2.13394i	−0.0471078	+	0.0815931i
$685$	5.03705			0.192456
$686$	20.7210	+	32.1458i	0.791132	+	1.22733i
$687$	−8.12954			−0.310161
$688$	8.90193	−	15.4186i	0.339383	−	0.587829i
$689$	−4.16538	−	7.21465i	−0.158688	−	0.274856i
$690$	0.628658	+	1.08887i	0.0239326	+	0.0414525i
$691$	7.80100	−	13.5117i	0.296764	−	0.514010i	−0.678630	−	0.734480i	$-0.737426\pi$
$691$	7.80100	−	13.5117i	0.296764	−	0.514010i	0.975394	+	0.220470i	$0.0707592\pi$
$692$	−54.3859			−2.06744
$693$	−2.26467	−	1.83814i	−0.0860278	−	0.0698252i
$694$	12.2403			0.464636
$695$	−0.755561	+	1.30867i	−0.0286600	+	0.0496407i
$696$	0.219593	+	0.380346i	0.00832364	+	0.0144170i
$697$	28.8272	+	49.9303i	1.09191	+	1.89124i
$698$	30.5958	−	52.9935i	1.15807	−	2.00583i
$699$	−7.94940			−0.300674
$700$	25.9042	−	9.91008i	0.979086	−	0.374566i
$701$	38.6350			1.45922			0.729612	−	0.683861i	$-0.239701\pi$
$701$	38.6350			1.45922			0.729612	+	0.683861i	$0.239701\pi$
$702$	−1.90720	+	3.30337i	−0.0719828	+	0.124678i
$703$	−4.95935	−	8.58985i	−0.187046	−	0.323972i
$704$	−5.48865	−	9.50662i	−0.206861	−	0.358294i
$705$	1.79879	−	3.11560i	0.0677464	−	0.117340i
$706$	29.4039			1.10663
$707$	−3.57048	+	22.3793i	−0.134282	+	0.841661i
$708$	16.7585			0.629823
$709$	21.6716	−	37.5363i	0.813894	−	1.40971i	−0.0962250	−	0.995360i	$-0.530677\pi$
$709$	21.6716	−	37.5363i	0.813894	−	1.40971i	0.910119	−	0.414346i	$-0.135990\pi$
$710$	−2.70381	−	4.68313i	−0.101472	−	0.175755i
$711$	−7.58579	−	13.1390i	−0.284490	−	0.492750i
$712$	−2.16315	+	3.74669i	−0.0810675	+	0.140413i
$713$	8.77360			0.328574
$714$	5.06647	−	31.7560i	0.189608	−	1.18844i
$715$	1.23982			0.0463667
$716$	−22.8360	+	39.5531i	−0.853422	+	1.47817i
$717$	7.88945	+	13.6649i	0.294637	+	0.510326i
$718$	2.87280	+	4.97584i	0.107212	+	0.185697i
$719$	14.7243	−	25.5032i	0.549122	−	0.951107i	−0.449213	−	0.893425i	$-0.648296\pi$
$719$	14.7243	−	25.5032i	0.549122	−	0.951107i	0.998335	−	0.0576826i	$-0.0183711\pi$
$720$	2.07079			0.0771737
$721$	−25.7915	+	9.86697i	−0.960525	+	0.367465i
$722$	36.7910			1.36922
$723$	−5.63279	+	9.75628i	−0.209486	+	0.362840i
$724$	−18.9181	−	32.7671i	−0.703086	−	1.21778i
$725$	−1.86137	−	3.22399i	−0.0691295	−	0.119736i
$726$	10.1029	−	17.4988i	0.374955	−	0.649441i
$727$	−50.1254			−1.85905			−0.929524	−	0.368763i	$-0.879782\pi$
$727$	−50.1254			−1.85905			−0.929524	+	0.368763i	$0.879782\pi$
$728$	−2.07228	−	1.68198i	−0.0768039	−	0.0623385i
$729$	1.00000			0.0370370
$730$	0.726814	−	1.25888i	0.0269006	−	0.0465932i
$731$	−15.4051	−	26.6824i	−0.569777	−	0.986883i
$732$	5.69251	+	9.85971i	0.210401	+	0.364425i
$733$	10.4880	−	18.1657i	0.387383	−	0.670967i	−0.604714	−	0.796443i	$-0.706712\pi$
$733$	10.4880	−	18.1657i	0.387383	−	0.670967i	0.992097	+	0.125476i	$0.0400458\pi$
$734$	13.7625			0.507984
$735$	0.876683	+	4.17083i	0.0323369	+	0.153843i
$736$	8.11580			0.299152
$737$	1.13719	−	1.96967i	0.0418889	−	0.0725537i
$738$	−10.1142	−	17.5184i	−0.372310	−	0.644860i
$739$	−5.79259	−	10.0331i	−0.213084	−	0.369072i	0.739594	−	0.673053i	$-0.235017\pi$
$739$	−5.79259	−	10.0331i	−0.213084	−	0.369072i	−0.952678	+	0.303981i	$0.901684\pi$
$740$	6.28374	−	10.8838i	0.230995	−	0.400095i
$741$	−2.00993			−0.0738365
$742$	−19.1327	−	15.5292i	−0.702382	−	0.570094i
$743$	−44.7847			−1.64299			−0.821495	−	0.570216i	$-0.806860\pi$
$743$	−44.7847			−1.64299			−0.821495	+	0.570216i	$0.806860\pi$
$744$	−2.39579	+	4.14963i	−0.0878338	+	0.152133i
$745$	6.26986	+	10.8597i	0.229710	+	0.397869i
$746$	−19.7031	−	34.1268i	−0.721382	−	1.24947i
$747$	5.35981	−	9.28346i	0.196105	−	0.339664i
$748$	−14.6933			−0.537241
$749$	19.9483	−	7.63158i	0.728896	−	0.278852i
$750$	12.1071			0.442088
$751$	11.1443	−	19.3025i	0.406662	−	0.704360i	−0.587851	−	0.808969i	$-0.700026\pi$
$751$	11.1443	−	19.3025i	0.406662	−	0.704360i	0.994513	+	0.104609i	$0.0333592\pi$
$752$	−10.0483	−	17.4041i	−0.366423	−	0.634663i
$753$	−1.13627	−	1.96808i	−0.0414081	−	0.0717209i
$754$	−1.53371	+	2.65647i	−0.0558546	+	0.0967430i
$755$	−7.79015			−0.283513
$756$	−0.943923	+	5.91639i	−0.0343301	+	0.215177i
$757$	−34.3724			−1.24929			−0.624643	−	0.780910i	$-0.714756\pi$
$757$	−34.3724			−1.24929			−0.624643	+	0.780910i	$0.714756\pi$
$758$	13.6946	−	23.7197i	0.497410	−	0.861539i
$759$	−0.551216	−	0.954735i	−0.0200079	−	0.0346547i
$760$	−0.180912	−	0.313349i	−0.00656238	−	0.0113664i
$761$	−21.8603	+	37.8632i	−0.792435	+	1.37254i	0.132020	+	0.991247i	$0.457854\pi$
$761$	−21.8603	+	37.8632i	−0.792435	+	1.37254i	−0.924455	+	0.381291i	$0.875480\pi$
$762$	16.3355			0.591773
$763$	1.58884	−	9.95867i	0.0575200	−	0.360528i
$764$	7.94731			0.287524
$765$	1.79178	−	3.10346i	0.0647820	−	0.112206i
$766$	−3.21738	−	5.57266i	−0.116249	−	0.201349i
$767$	6.83493	+	11.8384i	0.246795	+	0.427462i
$768$	5.48557	−	9.50129i	0.197944	−	0.342848i
$769$	−2.96450			−0.106903			−0.0534513	−	0.998570i	$-0.517022\pi$
$769$	−2.96450			−0.106903			−0.0534513	+	0.998570i	$0.517022\pi$
$770$	3.42520	−	1.31037i	0.123436	−	0.0472224i
$771$	0.871285			0.0313785
$772$	15.4461	−	26.7535i	0.555919	−	0.962879i
$773$	−11.1019	−	19.2290i	−0.399307	−	0.691621i	0.594333	−	0.804219i	$-0.297416\pi$
$773$	−11.1019	−	19.2290i	−0.399307	−	0.691621i	−0.993641	+	0.112598i	$0.964083\pi$
$774$	5.40497	+	9.36169i	0.194278	+	0.336499i
$775$	20.3078	−	35.1742i	0.729478	−	1.26349i
$776$	9.31971			0.334558
$777$	−18.7251	−	15.1984i	−0.671758	−	0.545238i
$778$	20.6177			0.739181
$779$	5.32949	−	9.23095i	0.190949	−	0.330733i
$780$	−1.27334	−	2.20548i	−0.0455927	−	0.0789690i
$781$	2.37074	+	4.10624i	0.0848316	+	0.146933i
$782$	6.07722	−	10.5260i	0.217321	−	0.376411i
$783$	0.804169			0.0287387
$784$	22.6260	+	7.40824i	0.808070	+	0.264580i
$785$	2.78249			0.0993112
$786$	−0.491181	+	0.850750i	−0.0175198	+	0.0303452i
$787$	17.3258	+	30.0091i	0.617596	+	1.06971i	0.989923	+	0.141607i	$0.0452268\pi$
$787$	17.3258	+	30.0091i	0.617596	+	1.06971i	−0.372327	+	0.928102i	$0.621440\pi$
$788$	15.2456	+	26.4062i	0.543103	+	0.940682i
$789$	−2.66738	+	4.62004i	−0.0949613	+	0.164478i
$790$	19.0755			0.678676
$791$	18.2711	+	14.8299i	0.649645	+	0.527289i
$792$	0.602078			0.0213939
$793$	−4.64337	+	8.04255i	−0.164891	+	0.285599i
$794$	5.82805	+	10.0945i	0.206830	+	0.358240i
$795$	−1.37300	−	2.37811i	−0.0486955	−	0.0843430i
$796$	−16.1880	+	28.0385i	−0.573770	+	0.993798i
$797$	−22.4200			−0.794158			−0.397079	−	0.917784i	$-0.629976\pi$
$797$	−22.4200			−0.794158			−0.397079	+	0.917784i	$0.629976\pi$
$798$	−5.55273	+	2.12429i	−0.196564	+	0.0751991i
$799$	−34.7777			−1.23035
$800$	18.7852	−	32.5370i	0.664158	−	1.15036i
$801$	3.96083	+	6.86036i	0.139949	+	0.242399i
$802$	39.8166	+	68.9644i	1.40597	+	2.43522i
$803$	−0.637280	+	1.10380i	−0.0224891	+	0.0389523i
$804$	−4.67171			−0.164759
$805$	−0.253795	+	1.59076i	−0.00894511	+	0.0560668i
$806$	−33.4661			−1.17879
$807$	11.3694	−	19.6923i	0.400221	−	0.693203i
$808$	−2.33898	−	4.05123i	−0.0822850	−	0.142522i
$809$	−13.0122	−	22.5378i	−0.457485	−	0.792387i	0.541342	−	0.840802i	$-0.317916\pi$
$809$	−13.0122	−	22.5378i	−0.457485	−	0.792387i	−0.998827	+	0.0484149i	$0.984583\pi$
$810$	−0.628658	+	1.08887i	−0.0220888	+	0.0382589i
$811$	−45.2644			−1.58945			−0.794724	−	0.606970i	$-0.792385\pi$
$811$	−45.2644			−1.58945			−0.794724	+	0.606970i	$0.792385\pi$
$812$	−0.759074	+	4.75777i	−0.0266383	+	0.166965i
$813$	6.42151			0.225212
$814$	−10.3759	+	17.9715i	−0.363674	+	0.629902i
$815$	−6.62261	−	11.4707i	−0.231980	−	0.401801i
$816$	−10.0091	−	17.3363i	−0.350389	−	0.606892i
$817$	−2.84804	+	4.93295i	−0.0996404	+	0.172582i
$818$	76.0088			2.65759
$819$	−4.56440	+	1.74619i	−0.159493	+	0.0610168i
$820$	13.5054			0.471630
$821$	−3.64364	+	6.31098i	−0.127164	+	0.220255i	−0.922577	−	0.385814i	$-0.873921\pi$
$821$	−3.64364	+	6.31098i	−0.127164	+	0.220255i	0.795413	+	0.606068i	$0.207254\pi$
$822$	8.54213	+	14.7954i	0.297941	+	0.516049i
$823$	−1.64934	−	2.85675i	−0.0574925	−	0.0995800i	0.835847	−	0.548963i	$-0.184977\pi$
$823$	−1.64934	−	2.85675i	−0.0574925	−	0.0995800i	−0.893339	+	0.449383i	$0.851644\pi$
$824$	2.85008	−	4.93649i	0.0992874	−	0.171971i
$825$	−5.10349			−0.177681
$826$	31.3946	+	25.4817i	1.09236	+	0.886621i
$827$	−48.8022			−1.69702			−0.848510	−	0.529179i	$-0.822500\pi$
$827$	−48.8022			−1.69702			−0.848510	+	0.529179i	$0.822500\pi$
$828$	−1.13223	+	1.96108i	−0.0393478	+	0.0681524i
$829$	−12.3989	−	21.4755i	−0.430631	−	0.745875i	0.566296	−	0.824202i	$-0.308376\pi$
$829$	−12.3989	−	21.4755i	−0.430631	−	0.745875i	−0.996928	+	0.0783263i	$0.975042\pi$
$830$	6.73898	+	11.6723i	0.233913	+	0.405150i
$831$	7.01764	−	12.1549i	0.243439	−	0.421649i
$832$	−18.3924			−0.637642
$833$	30.6801	−	27.4991i	1.06300	−	0.952786i
$834$	−5.12530			−0.177475
$835$	−1.19439	+	2.06874i	−0.0413335	+	0.0715918i
$836$	1.35823	+	2.35252i	0.0469753	+	0.0813636i
$837$	4.38680	+	7.59816i	0.151630	+	0.262631i
$838$	−6.66383	+	11.5421i	−0.230198	+	0.398715i
$839$	−6.27230			−0.216544			−0.108272	−	0.994121i	$-0.534532\pi$
$839$	−6.27230			−0.216544			−0.108272	+	0.994121i	$0.534532\pi$
$840$	−0.683072	−	0.554421i	−0.0235682	−	0.0191293i
$841$	−28.3533			−0.977700
$842$	30.9022	−	53.5242i	1.06496	−	1.84457i
$843$	12.2639	+	21.2417i	0.422391	+	0.731603i
$844$	−3.20544	−	5.55199i	−0.110336	−	0.191107i
$845$	−2.91889	+	5.05566i	−0.100413	+	0.173920i
$846$	12.2020			0.419513
$847$	24.1788	−	9.25000i	0.830792	−	0.317834i
$848$	−15.3395			−0.526762
$849$	−2.19970	+	3.81000i	−0.0754936	+	0.130759i
$850$	−28.1332	−	48.7282i	−0.964963	−	1.67136i
$851$	−4.55764	−	7.89406i	−0.156234	−	0.270605i
$852$	4.86964	−	8.43446i	0.166831	−	0.288960i
$853$	−1.75188			−0.0599834			−0.0299917	−	0.999550i	$-0.509548\pi$
$853$	−1.75188			−0.0599834			−0.0299917	+	0.999550i	$0.509548\pi$
$854$	−4.32784	+	27.1263i	−0.148096	+	0.928244i
$855$	−0.662518			−0.0226576
$856$	−2.20439	+	3.81811i	−0.0753444	+	0.130500i
$857$	7.54775	+	13.0731i	0.257826	+	0.446568i	0.965659	−	0.259812i	$-0.0836604\pi$
$857$	7.54775	+	13.0731i	0.257826	+	0.446568i	−0.707833	+	0.706380i	$0.750327\pi$
$858$	2.10256	+	3.64175i	0.0717804	+	0.124327i
$859$	−4.79401	+	8.30346i	−0.163569	+	0.283310i	−0.936146	−	0.351611i	$-0.885634\pi$
$859$	−4.79401	+	8.30346i	−0.163569	+	0.283310i	0.772577	+	0.634921i	$0.218967\pi$
$860$	−7.21721			−0.246105
$861$	4.08321	−	25.5930i	0.139155	−	0.872208i
$862$	−16.0009			−0.544992
$863$	−17.1667	+	29.7336i	−0.584362	+	1.01215i	0.410592	+	0.911819i	$0.365322\pi$
$863$	−17.1667	+	29.7336i	−0.584362	+	1.01215i	−0.994955	+	0.100326i	$0.968011\pi$
$864$	4.05790	+	7.02849i	0.138053	+	0.239114i
$865$	−7.31144	−	12.6638i	−0.248596	−	0.430582i
$866$	5.34536	−	9.25844i	0.181643	−	0.314614i
$867$	−17.6422			−0.599159
$868$	−49.0945	+	18.7819i	−1.66637	+	0.637500i
$869$	−16.7257			−0.567379
$870$	−0.505548	+	0.875634i	−0.0171397	+	0.0296868i
$871$	−1.90535	−	3.30017i	−0.0645605	−	0.111822i
$872$	1.04083	+	1.80277i	0.0352470	+	0.0610497i
$873$	8.53242	−	14.7786i	0.288779	−	0.500179i
$874$	−2.24707			−0.0760084
$875$	12.0437	+	9.77538i	0.407152	+	0.330468i
$876$	2.61803			0.0884549
$877$	−8.80288	+	15.2470i	−0.297252	+	0.514856i	−0.975506	−	0.219971i	$-0.929404\pi$
$877$	−8.80288	+	15.2470i	−0.297252	+	0.514856i	0.678254	+	0.734828i	$0.262737\pi$
$878$	−31.2774	−	54.1741i	−1.05556	−	1.82829i
$879$	6.67065	+	11.5539i	0.224996	+	0.389704i
$880$	1.14145	−	1.97705i	0.0384783	−	0.0666464i
$881$	39.5494			1.33245			0.666227	−	0.745749i	$-0.267908\pi$
$881$	39.5494			1.33245			0.666227	+	0.745749i	$0.267908\pi$
$882$	−10.7643	+	9.64823i	−0.362453	+	0.324873i
$883$	0.340528			0.0114597			0.00572983	−	0.999984i	$-0.498176\pi$
$883$	0.340528			0.0114597			0.00572983	+	0.999984i	$0.498176\pi$
$884$	−12.3093	+	21.3203i	−0.414006	+	0.717080i
$885$	2.25295	+	3.90223i	0.0757321	+	0.131172i
$886$	39.4448	+	68.3204i	1.32517	+	2.29527i
$887$	−15.0481	+	26.0641i	−0.505266	+	0.875146i	0.494716	+	0.869055i	$0.335272\pi$
$887$	−15.0481	+	26.0641i	−0.505266	+	0.875146i	−0.999981	+	0.00609116i	$0.998061\pi$
$888$	4.97818			0.167057
$889$	16.2500	+	13.1894i	0.545008	+	0.442360i
$890$	−9.96004			−0.333861
$891$	0.551216	−	0.954735i	0.0184664	−	0.0319848i
$892$	−5.42090	−	9.38927i	−0.181505	−	0.314376i
$893$	3.21479	+	5.56819i	0.107579	+	0.186332i
$894$	−21.2656	+	36.8331i	−0.711228	+	1.23188i
$895$	−12.2800			−0.410474
$896$	−10.7020	+	4.09424i	−0.357529	+	0.136779i
$897$	−1.84712			−0.0616735
$898$	3.05182	−	5.28591i	0.101841	−	0.176393i
$899$	3.52773	+	6.11021i	0.117656	+	0.203787i
$900$	5.24144	+	9.07844i	0.174715	+	0.302615i
$901$	−13.2728	+	22.9891i	−0.442180	+	0.765879i
$902$	−22.3005			−0.742526
$903$	−2.18204	+	13.6767i	−0.0726137	+	0.455133i
$904$	−4.85748			−0.161557
$905$	5.08657	−	8.81019i	0.169083	−	0.292861i
$906$	−13.2110	−	22.8821i	−0.438906	−	0.760208i
$907$	−15.9426	−	27.6134i	−0.529366	−	0.916889i	−0.999413	−	0.0342480i	$-0.989096\pi$
$907$	−15.9426	−	27.6134i	−0.529366	−	0.916889i	0.470047	−	0.882641i	$-0.344237\pi$
$908$	−21.8465	+	37.8393i	−0.725003	+	1.25574i
$909$	−8.56557			−0.284102
$910$	0.968079	−	6.06779i	0.0320915	−	0.201145i
$911$	36.7297			1.21691			0.608454	−	0.793589i	$-0.291790\pi$
$911$	36.7297			1.21691			0.608454	+	0.793589i	$0.291790\pi$
$912$	−1.85045	+	3.20508i	−0.0612746	+	0.106131i
$913$	−5.90883	−	10.2344i	−0.195554	−	0.338709i
$914$	18.2711	+	31.6464i	0.604353	+	1.04677i
$915$	−1.53056	+	2.65101i	−0.0505988	+	0.0876396i
$916$	18.4090			0.608252
$917$	−1.17551	+	0.449713i	−0.0388189	+	0.0148508i
$918$	12.1544			0.401156
$919$	14.6657	−	25.4018i	0.483778	−	0.837928i	−0.516049	−	0.856559i	$-0.672598\pi$
$919$	14.6657	−	25.4018i	0.483778	−	0.837928i	0.999826	+	0.0186315i	$0.00593094\pi$
$920$	−0.166258	−	0.287967i	−0.00548137	−	0.00949401i
$921$	12.2750	+	21.2609i	0.404474	+	0.700569i
$922$	−12.1267	+	21.0041i	−0.399373	+	0.691734i
$923$	7.94431			0.261490
$924$	5.12827	+	4.16241i	0.168708	+	0.136933i
$925$	−42.1973			−1.38744
$926$	27.9683	−	48.4425i	0.919095	−	1.59192i
$927$	−5.21864	−	9.03895i	−0.171403	−	0.296878i
$928$	3.26324	+	5.65209i	0.107121	+	0.185539i
$929$	0.653520	−	1.13193i	0.0214413	−	0.0371374i	−0.855106	−	0.518454i	$-0.826508\pi$
$929$	0.653520	−	1.13193i	0.0214413	−	0.0371374i	0.876547	+	0.481316i	$0.159841\pi$
$930$	−11.0312			−0.361727
$931$	−7.23884	−	2.37016i	−0.237243	−	0.0776787i
$932$	18.0011			0.589647
$933$	13.0387	−	22.5836i	0.426867	−	0.739355i
$934$	23.9051	+	41.4048i	0.782199	+	1.35481i
$935$	−1.97532	−	3.42135i	−0.0645998	−	0.111890i
$936$	0.504389	−	0.873627i	0.0164865	−	0.0285554i
$937$	−4.77786			−0.156086			−0.0780430	−	0.996950i	$-0.524867\pi$
$937$	−4.77786			−0.156086			−0.0780430	+	0.996950i	$0.524867\pi$
$938$	−8.75178	−	7.10345i	−0.285756	−	0.231936i
$939$	−24.1973			−0.789650
$940$	−4.07330	+	7.05516i	−0.132856	+	0.230114i
$941$	16.7002	+	28.9256i	0.544411	+	0.942947i	0.998644	+	0.0520640i	$0.0165800\pi$
$941$	16.7002	+	28.9256i	0.544411	+	0.942947i	−0.454233	+	0.890883i	$0.650087\pi$
$942$	4.71871	+	8.17304i	0.153744	+	0.266292i
$943$	4.89780	−	8.48323i	0.159494	−	0.276252i
$944$	25.1705			0.819231
$945$	−1.50453	+	0.575585i	−0.0489424	+	0.0187238i
$946$	11.9172			0.387463
$947$	−17.9455	+	31.0826i	−0.583152	+	1.01005i	0.411951	+	0.911206i	$0.364847\pi$
$947$	−17.9455	+	31.0826i	−0.583152	+	1.01005i	−0.995103	+	0.0988427i	$0.968486\pi$
$948$	17.1778	+	29.7528i	0.557908	+	0.966325i
$949$	1.06776	+	1.84941i	0.0346609	+	0.0600345i
$950$	−5.20119	+	9.00872i	−0.168749	+	0.292281i
$951$	−3.60976			−0.117055
$952$	−1.33990	+	8.39834i	−0.0434265	+	0.272192i
$953$	−42.4876			−1.37631			−0.688154	−	0.725564i	$-0.741579\pi$
$953$	−42.4876			−1.37631			−0.688154	+	0.725564i	$0.741579\pi$
$954$	4.65684	−	8.06589i	0.150771	−	0.261143i
$955$	1.06841	+	1.85054i	0.0345729	+	0.0598820i
$956$	−17.8654	−	30.9437i	−0.577808	−	1.00079i
$957$	0.443271	−	0.767768i	0.0143289	−	0.0248184i
$958$	−46.1903			−1.49234
$959$	−3.44854	+	21.6150i	−0.111359	+	0.697984i
$960$	−6.06256			−0.195668
$961$	−22.9880	+	39.8165i	−0.741550	+	1.28440i
$962$	17.3847	+	30.1112i	0.560505	+	0.970823i
$963$	4.03634	+	6.99115i	0.130069	+	0.225287i
$964$	12.7553	−	22.0928i	0.410819	−	0.711560i
$965$	8.30609			0.267383
$966$	−5.10295	+	1.95222i	−0.164185	+	0.0628117i
$967$	−50.9129			−1.63725			−0.818624	−	0.574330i	$-0.805263\pi$
$967$	−50.9129			−1.63725			−0.818624	+	0.574330i	$0.805263\pi$
$968$	−2.67187	+	4.62781i	−0.0858771	+	0.148744i
$969$	3.20227	+	5.54649i	0.102872	+	0.178179i
$970$	10.7280	+	18.5814i	0.344454	+	0.596612i
$971$	8.36861	−	14.4949i	0.268561	−	0.465162i	−0.699929	−	0.714212i	$-0.746785\pi$
$971$	8.36861	−	14.4949i	0.268561	−	0.465162i	0.968491	+	0.249050i	$0.0801184\pi$
$972$	−2.26446			−0.0726327
$973$	−5.09847	−	4.13822i	−0.163450	−	0.132665i
$974$	−86.4272			−2.76931
$975$	−4.27543	+	7.40527i	−0.136923	+	0.237158i
$976$	8.54990	+	14.8089i	0.273676	+	0.474020i
$977$	−23.6865	−	41.0261i	−0.757797	−	1.31254i	−0.943972	−	0.330026i	$-0.892943\pi$
$977$	−23.6865	−	41.0261i	−0.757797	−	1.31254i	0.186175	−	0.982517i	$-0.440391\pi$
$978$	22.4620	−	38.9053i	0.718256	−	1.24406i
$979$	8.73310			0.279111
$980$	−1.98522	−	9.44470i	−0.0634155	−	0.301700i
$981$	3.81163			0.121696
$982$	16.7949	−	29.0896i	0.535946	−	0.928285i
$983$	−17.6304	−	30.5368i	−0.562323	−	0.973972i	−0.997293	−	0.0735275i	$-0.976574\pi$
$983$	−17.6304	−	30.5368i	−0.562323	−	0.973972i	0.434970	−	0.900445i	$-0.356759\pi$
$984$	2.67486	+	4.63299i	0.0852714	+	0.147694i
$985$	−4.09914	+	7.09991i	−0.130609	+	0.226222i
$986$	9.77422			0.311275
$987$	12.1381	+	9.85201i	0.386361	+	0.313593i
$988$	4.55141			0.144800
$989$	−2.61735	+	4.53338i	−0.0832268	+	0.144153i
$990$	0.693054	+	1.20040i	0.0220267	+	0.0381514i
$991$	−8.45822	−	14.6501i	−0.268684	−	0.465375i	0.699838	−	0.714302i	$-0.253256\pi$
$991$	−8.45822	−	14.6501i	−0.268684	−	0.465375i	−0.968522	+	0.248927i	$0.919922\pi$
$992$	−35.6024	+	61.6652i	−1.13038	+	1.95787i
$993$	−8.23405			−0.261300
$994$	21.9474	−	8.39634i	0.696128	−	0.266316i
$995$	−8.70504			−0.275968
$996$	−12.1371	+	21.0221i	−0.384579	+	0.666110i
$997$	26.1823	+	45.3491i	0.829203	+	1.43622i	0.898664	+	0.438637i	$0.144539\pi$
$997$	26.1823	+	45.3491i	0.829203	+	1.43622i	−0.0694611	+	0.997585i	$0.522128\pi$
$998$	−20.4699	−	35.4549i	−0.647963	−	1.12230i
$999$	4.55764	−	7.89406i	0.144197	−	0.249757i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.i.h.415.9	yes	20
7.2	even	3		3381.2.a.bi.1.2		10
7.4	even	3	inner	483.2.i.h.277.9	✓	20
7.5	odd	6		3381.2.a.bj.1.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.i.h.277.9	✓	20	7.4	even	3	inner
483.2.i.h.415.9	yes	20	1.1	even	1	trivial
3381.2.a.bi.1.2		10	7.2	even	3
3381.2.a.bj.1.2		10	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.03253 - 1.78839i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.13223 - 1.96108i) q^{4} +(0.304427 - 0.527282i) q^{5} +2.06506 q^{6} +(2.05425 + 1.66735i) q^{7} -0.546135 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.628658 - 1.08887i) q^{10} +(0.551216 + 0.954735i) q^{11} +(1.13223 - 1.96108i) q^{12} +1.84712 q^{13} +(5.10295 - 1.95222i) q^{14} +0.608853 q^{15} +(1.70056 - 2.94546i) q^{16} +(-2.94288 - 5.09722i) q^{17} +(1.03253 + 1.78839i) q^{18} +(-0.544070 + 0.942358i) q^{19} -1.37873 q^{20} +(-0.416841 + 2.61271i) q^{21} +2.27659 q^{22} +(-0.500000 + 0.866025i) q^{23} +(-0.273068 - 0.472967i) q^{24} +(2.31465 + 4.00909i) q^{25} +(1.90720 - 3.30337i) q^{26} -1.00000 q^{27} +(0.943923 - 5.91639i) q^{28} -0.804169 q^{29} +(0.628658 - 1.08887i) q^{30} +(-4.38680 - 7.59816i) q^{31} +(-4.05790 - 7.02849i) q^{32} +(-0.551216 + 0.954735i) q^{33} -12.1544 q^{34} +(1.50453 - 0.575585i) q^{35} +2.26446 q^{36} +(-4.55764 + 7.89406i) q^{37} +(1.12354 + 1.94602i) q^{38} +(0.923560 + 1.59965i) q^{39} +(-0.166258 + 0.287967i) q^{40} -9.79559 q^{41} +(4.24215 + 3.44317i) q^{42} +5.23469 q^{43} +(1.24821 - 2.16196i) q^{44} +(0.304427 + 0.527282i) q^{45} +(1.03253 + 1.78839i) q^{46} +(2.95439 - 5.11716i) q^{47} +3.40113 q^{48} +(1.43989 + 6.85031i) q^{49} +9.55977 q^{50} +(2.94288 - 5.09722i) q^{51} +(-2.09137 - 3.62236i) q^{52} +(-2.25507 - 3.90589i) q^{53} +(-1.03253 + 1.78839i) q^{54} +0.671220 q^{55} +(-1.12190 - 0.910598i) q^{56} -1.08814 q^{57} +(-0.830328 + 1.43817i) q^{58} +(3.70032 + 6.40914i) q^{59} +(-0.689363 - 1.19401i) q^{60} +(-2.51384 + 4.35410i) q^{61} -18.1180 q^{62} +(-2.47109 + 0.945359i) q^{63} -9.95734 q^{64} +(0.562312 - 0.973953i) q^{65} +(1.13829 + 1.97158i) q^{66} +(-1.03153 - 1.78666i) q^{67} +(-6.66405 + 11.5425i) q^{68} -1.00000 q^{69} +(0.524102 - 3.28500i) q^{70} +4.30092 q^{71} +(0.273068 - 0.472967i) q^{72} +(0.578067 + 1.00124i) q^{73} +(9.41179 + 16.3017i) q^{74} +(-2.31465 + 4.00909i) q^{75} +2.46406 q^{76} +(-0.459540 + 2.88034i) q^{77} +3.81441 q^{78} +(-7.58579 + 13.1390i) q^{79} +(-1.03539 - 1.79335i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-10.1142 + 17.5184i) q^{82} -10.7196 q^{83} +(5.59570 - 2.14073i) q^{84} -3.58356 q^{85} +(5.40497 - 9.36169i) q^{86} +(-0.402085 - 0.696431i) q^{87} +(-0.301039 - 0.521414i) q^{88} +(3.96083 - 6.86036i) q^{89} +1.25732 q^{90} +(3.79445 + 3.07979i) q^{91} +2.26446 q^{92} +(4.38680 - 7.59816i) q^{93} +(-6.10099 - 10.5672i) q^{94} +(0.331259 + 0.573757i) q^{95} +(4.05790 - 7.02849i) q^{96} -17.0648 q^{97} +(13.7378 + 4.49805i) q^{98} -1.10243 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 3 q^{2} + 10 q^{3} - 15 q^{4} + 5 q^{5} - 6 q^{6} + 18 q^{8} - 10 q^{9} - 11 q^{10} - 8 q^{11} + 15 q^{12} + 11 q^{14} + 10 q^{15} - 37 q^{16} + 11 q^{17} - 3 q^{18} - q^{19} - 30 q^{20} + 12 q^{22}+ \cdots + 16 q^{99}+O(q^{100}) \) 20 * q - 3 * q^2 + 10 * q^3 - 15 * q^4 + 5 * q^5 - 6 * q^6 + 18 * q^8 - 10 * q^9 - 11 * q^10 - 8 * q^11 + 15 * q^12 + 11 * q^14 + 10 * q^15 - 37 * q^16 + 11 * q^17 - 3 * q^18 - q^19 - 30 * q^20 + 12 * q^22 - 10 * q^23 + 9 * q^24 - 21 * q^25 - q^26 - 20 * q^27 + 44 * q^28 + 44 * q^29 + 11 * q^30 + 3 * q^31 - 11 * q^32 + 8 * q^33 - 6 * q^34 - 9 * q^35 + 30 * q^36 + 3 * q^37 - 16 * q^38 - 39 * q^40 - 52 * q^41 + 7 * q^42 + 54 * q^43 - 16 * q^44 + 5 * q^45 - 3 * q^46 - 11 * q^47 - 74 * q^48 + 22 * q^49 + 4 * q^50 - 11 * q^51 - 29 * q^52 - 5 * q^53 + 3 * q^54 - 36 * q^55 + 43 * q^56 - 2 * q^57 - 16 * q^58 + 10 * q^59 - 15 * q^60 - 22 * q^61 - 64 * q^62 + 138 * q^64 + 11 * q^65 + 6 * q^66 + 2 * q^67 + 21 * q^68 - 20 * q^69 + 84 * q^70 + 54 * q^71 - 9 * q^72 + 8 * q^73 - 14 * q^74 + 21 * q^75 - 44 * q^76 + 8 * q^77 - 2 * q^78 - 21 * q^79 + 53 * q^80 - 10 * q^81 - 36 * q^82 - 24 * q^83 + 25 * q^84 + 46 * q^85 - 18 * q^86 + 22 * q^87 + 10 * q^88 - 6 * q^89 + 22 * q^90 - 62 * q^91 + 30 * q^92 - 3 * q^93 - 35 * q^94 - 44 * q^95 + 11 * q^96 + 12 * q^97 + 2 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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