LMFDB - Embedded newform 950.2.l.c.701.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(101,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("950.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.l (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			701.1
Root			$-0.766044 - 0.642788i$ of defining polynomial
Character	$\chi$	$=$	950.701
Dual form			950.2.l.c.351.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 + 0.984808i) q^{2} +(0.266044 + 0.223238i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.266044 + 0.223238i) q^{6} +(1.87939 + 3.25519i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.500000 - 2.83564i) q^{9} +O(q^{10})$	\(q+(-0.173648 + 0.984808i) q^{2} +(0.266044 + 0.223238i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.266044 + 0.223238i) q^{6} +(1.87939 + 3.25519i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.500000 - 2.83564i) q^{9} +(2.76604 - 4.79093i) q^{11} +(-0.173648 - 0.300767i) q^{12} +(1.00000 - 0.839100i) q^{13} +(-3.53209 + 1.28558i) q^{14} +(0.766044 + 0.642788i) q^{16} +(0.826352 - 4.68647i) q^{17} +2.87939 q^{18} +(2.77719 + 3.35965i) q^{19} +(-0.226682 + 1.28558i) q^{21} +(4.23783 + 3.55596i) q^{22} +(-3.10607 - 1.13052i) q^{23} +(0.326352 - 0.118782i) q^{24} +(0.652704 + 1.13052i) q^{26} +(1.02094 - 1.76833i) q^{27} +(-0.652704 - 3.70167i) q^{28} +(-1.65270 - 9.37295i) q^{29} +(3.18479 + 5.51622i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(1.80541 - 0.657115i) q^{33} +(4.47178 + 1.62760i) q^{34} +(-0.500000 + 2.83564i) q^{36} +4.00000 q^{37} +(-3.79086 + 2.15160i) q^{38} +0.453363 q^{39} +(6.13429 + 5.14728i) q^{41} +(-1.22668 - 0.446476i) q^{42} +(-6.77719 + 2.46669i) q^{43} +(-4.23783 + 3.55596i) q^{44} +(1.65270 - 2.86257i) q^{46} +(2.12061 + 12.0266i) q^{47} +(0.0603074 + 0.342020i) q^{48} +(-3.56418 + 6.17334i) q^{49} +(1.26604 - 1.06234i) q^{51} +(-1.22668 + 0.446476i) q^{52} +(1.65270 + 0.601535i) q^{53} +(1.56418 + 1.31250i) q^{54} +3.75877 q^{56} +(-0.0111444 + 1.51379i) q^{57} +9.51754 q^{58} +(1.12314 - 6.36965i) q^{59} +(2.10607 + 0.766546i) q^{61} +(-5.98545 + 2.17853i) q^{62} +(8.29086 - 6.95686i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.333626 + 1.89209i) q^{66} +(-2.14930 - 12.1893i) q^{67} +(-2.37939 + 4.12122i) q^{68} +(-0.573978 - 0.994159i) q^{69} +(5.53209 - 2.01352i) q^{71} +(-2.70574 - 0.984808i) q^{72} +(0.890530 + 0.747243i) q^{73} +(-0.694593 + 3.93923i) q^{74} +(-1.46064 - 4.10689i) q^{76} +20.7939 q^{77} +(-0.0787257 + 0.446476i) q^{78} +(6.75877 + 5.67128i) q^{79} +(-7.45084 + 2.71188i) q^{81} +(-6.13429 + 5.14728i) q^{82} +(6.06805 + 10.5102i) q^{83} +(0.652704 - 1.13052i) q^{84} +(-1.25237 - 7.10257i) q^{86} +(1.65270 - 2.86257i) q^{87} +(-2.76604 - 4.79093i) q^{88} +(8.62314 - 7.23567i) q^{89} +(4.61081 + 1.67820i) q^{91} +(2.53209 + 2.12467i) q^{92} +(-0.384133 + 2.17853i) q^{93} -12.2121 q^{94} -0.347296 q^{96} +(1.31180 - 7.43961i) q^{97} +(-5.46064 - 4.58202i) q^{98} +(-14.9684 - 5.44804i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{3} + 3 q^{6} + 3 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q - 3 * q^3 + 3 * q^6 + 3 * q^8 - 3 * q^9	$ 6 q - 3 q^{3} + 3 q^{6} + 3 q^{8} - 3 q^{9} + 12 q^{11} + 6 q^{13} - 12 q^{14} + 6 q^{17} + 6 q^{18} + 6 q^{19} + 12 q^{21} + 6 q^{22} + 6 q^{23} + 3 q^{24} + 6 q^{26} + 3 q^{27} - 6 q^{28} - 12 q^{29} + 12 q^{31} + 15 q^{33} + 12 q^{34} - 3 q^{36} + 24 q^{37} + 9 q^{38} - 24 q^{39} + 27 q^{41} + 6 q^{42} - 30 q^{43} - 6 q^{44} + 12 q^{46} + 24 q^{47} + 6 q^{48} - 3 q^{49} + 3 q^{51} + 6 q^{52} + 12 q^{53} - 9 q^{54} + 6 q^{57} + 12 q^{58} + 3 q^{59} - 12 q^{61} + 18 q^{63} - 3 q^{64} + 21 q^{66} + 27 q^{67} - 3 q^{68} + 12 q^{69} + 24 q^{71} - 6 q^{72} - 12 q^{73} + 12 q^{77} - 18 q^{78} + 18 q^{79} - 33 q^{81} - 27 q^{82} - 6 q^{83} + 6 q^{84} - 24 q^{86} + 12 q^{87} - 12 q^{88} + 48 q^{89} + 36 q^{91} + 6 q^{92} - 24 q^{93} - 24 q^{94} - 27 q^{97} - 24 q^{98} - 33 q^{99}+O(q^{100}) $ 6 * q - 3 * q^3 + 3 * q^6 + 3 * q^8 - 3 * q^9 + 12 * q^11 + 6 * q^13 - 12 * q^14 + 6 * q^17 + 6 * q^18 + 6 * q^19 + 12 * q^21 + 6 * q^22 + 6 * q^23 + 3 * q^24 + 6 * q^26 + 3 * q^27 - 6 * q^28 - 12 * q^29 + 12 * q^31 + 15 * q^33 + 12 * q^34 - 3 * q^36 + 24 * q^37 + 9 * q^38 - 24 * q^39 + 27 * q^41 + 6 * q^42 - 30 * q^43 - 6 * q^44 + 12 * q^46 + 24 * q^47 + 6 * q^48 - 3 * q^49 + 3 * q^51 + 6 * q^52 + 12 * q^53 - 9 * q^54 + 6 * q^57 + 12 * q^58 + 3 * q^59 - 12 * q^61 + 18 * q^63 - 3 * q^64 + 21 * q^66 + 27 * q^67 - 3 * q^68 + 12 * q^69 + 24 * q^71 - 6 * q^72 - 12 * q^73 + 12 * q^77 - 18 * q^78 + 18 * q^79 - 33 * q^81 - 27 * q^82 - 6 * q^83 + 6 * q^84 - 24 * q^86 + 12 * q^87 - 12 * q^88 + 48 * q^89 + 36 * q^91 + 6 * q^92 - 24 * q^93 - 24 * q^94 - 27 * q^97 - 24 * q^98 - 33 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{5}{9}\right)$

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 $

$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$3$	0.266044	+	0.223238i	0.153601	+	0.128886i	0.716349	−	0.697742i	$-0.245812\pi$
$3$	0.266044	+	0.223238i	0.153601	+	0.128886i	−0.562749	+	0.826628i	$0.690256\pi$
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$		0			0
$5$		0			0
$6$	−0.266044	+	0.223238i	−0.108612	+	0.0911364i
$7$	1.87939	+	3.25519i	0.710341	+	1.23035i	0.964729	+	0.263244i	$0.0847925\pi$
$7$	1.87939	+	3.25519i	0.710341	+	1.23035i	−0.254388	+	0.967102i	$0.581874\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	−0.500000	−	2.83564i	−0.166667	−	0.945214i
$10$		0			0
$11$	2.76604	−	4.79093i	0.833994	−	1.44452i	−0.0608533	−	0.998147i	$-0.519382\pi$
$11$	2.76604	−	4.79093i	0.833994	−	1.44452i	0.894847	−	0.446373i	$-0.147284\pi$
$12$	−0.173648	−	0.300767i	−0.0501279	−	0.0868241i
$13$	1.00000	−	0.839100i	0.277350	−	0.232724i	−0.493492	−	0.869750i	$-0.664280\pi$
$13$	1.00000	−	0.839100i	0.277350	−	0.232724i	0.770843	+	0.637026i	$0.219836\pi$
$14$	−3.53209	+	1.28558i	−0.943990	+	0.343584i
$15$		0			0
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	0.826352	−	4.68647i	0.200420	−	1.13664i	−0.704066	−	0.710134i	$-0.748634\pi$
$17$	0.826352	−	4.68647i	0.200420	−	1.13664i	0.904486	−	0.426503i	$-0.140255\pi$
$18$	2.87939			0.678678
$19$	2.77719	+	3.35965i	0.637131	+	0.770756i
$19$	2.77719	+	3.35965i	0.637131	+	0.770756i
$20$		0			0
$21$	−0.226682	+	1.28558i	−0.0494660	+	0.280536i
$22$	4.23783	+	3.55596i	0.903508	+	0.758133i
$23$	−3.10607	−	1.13052i	−0.647660	−	0.235729i	−0.00276015	−	0.999996i	$-0.500879\pi$
$23$	−3.10607	−	1.13052i	−0.647660	−	0.235729i	−0.644900	+	0.764267i	$0.723101\pi$
$24$	0.326352	−	0.118782i	0.0666163	−	0.0242463i
$25$		0			0
$26$	0.652704	+	1.13052i	0.128006	+	0.221712i
$27$	1.02094	−	1.76833i	0.196481	−	0.340315i
$28$	−0.652704	−	3.70167i	−0.123349	−	0.699549i
$29$	−1.65270	−	9.37295i	−0.306899	−	1.74051i	−0.614427	−	0.788974i	$-0.710613\pi$
$29$	−1.65270	−	9.37295i	−0.306899	−	1.74051i	0.307528	−	0.951539i	$-0.400498\pi$
$30$		0			0
$31$	3.18479	+	5.51622i	0.572006	+	0.990743i	0.996360	+	0.0852466i	$0.0271678\pi$
$31$	3.18479	+	5.51622i	0.572006	+	0.990743i	−0.424354	+	0.905496i	$0.639499\pi$
$32$	−0.766044	+	0.642788i	−0.135419	+	0.113630i
$33$	1.80541	−	0.657115i	0.314281	−	0.114389i
$34$	4.47178	+	1.62760i	0.766904	+	0.279130i
$35$		0			0
$36$	−0.500000	+	2.83564i	−0.0833333	+	0.472607i
$37$	4.00000			0.657596			0.328798	−	0.944400i	$-0.393356\pi$
$37$	4.00000			0.657596			0.328798	+	0.944400i	$0.393356\pi$
$38$	−3.79086	+	2.15160i	−0.614959	+	0.349036i
$39$	0.453363			0.0725962
$40$		0			0
$41$	6.13429	+	5.14728i	0.958014	+	0.803870i	0.980629	−	0.195875i	$-0.0627546\pi$
$41$	6.13429	+	5.14728i	0.958014	+	0.803870i	−0.0226145	+	0.999744i	$0.507199\pi$
$42$	−1.22668	−	0.446476i	−0.189281	−	0.0688927i
$43$	−6.77719	+	2.46669i	−1.03351	+	0.376167i	−0.802417	−	0.596764i	$-0.796453\pi$
$43$	−6.77719	+	2.46669i	−1.03351	+	0.376167i	−0.231095	+	0.972931i	$0.574231\pi$
$44$	−4.23783	+	3.55596i	−0.638876	+	0.536081i
$45$		0			0
$46$	1.65270	−	2.86257i	0.243678	−	0.422062i
$47$	2.12061	+	12.0266i	0.309323	+	1.75426i	0.602422	+	0.798178i	$0.294203\pi$
$47$	2.12061	+	12.0266i	0.309323	+	1.75426i	−0.293098	+	0.956082i	$0.594686\pi$
$48$	0.0603074	+	0.342020i	0.00870462	+	0.0493664i
$49$	−3.56418	+	6.17334i	−0.509168	+	0.881905i
$50$		0			0
$51$	1.26604	−	1.06234i	0.177282	−	0.148757i
$52$	−1.22668	+	0.446476i	−0.170110	+	0.0619150i
$53$	1.65270	+	0.601535i	0.227016	+	0.0826272i	0.453024	−	0.891498i	$-0.350345\pi$
$53$	1.65270	+	0.601535i	0.227016	+	0.0826272i	−0.226008	+	0.974126i	$0.572567\pi$
$54$	1.56418	+	1.31250i	0.212858	+	0.178609i
$55$		0			0
$56$	3.75877			0.502287
$57$	−0.0111444	+	1.51379i	−0.00147611	+	0.200506i
$58$	9.51754			1.24971
$59$	1.12314	−	6.36965i	0.146221	−	0.829258i	−0.820159	−	0.572136i	$-0.806115\pi$
$59$	1.12314	−	6.36965i	0.146221	−	0.829258i	0.966379	−	0.257121i	$-0.0827740\pi$
$60$		0			0
$61$	2.10607	+	0.766546i	0.269654	+	0.0981461i	0.473308	−	0.880897i	$-0.343060\pi$
$61$	2.10607	+	0.766546i	0.269654	+	0.0981461i	−0.203654	+	0.979043i	$0.565282\pi$
$62$	−5.98545	+	2.17853i	−0.760153	+	0.276673i
$63$	8.29086	−	6.95686i	1.04455	−	0.876482i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$		0			0
$66$	0.333626	+	1.89209i	0.0410665	+	0.232900i
$67$	−2.14930	−	12.1893i	−0.262579	−	1.48916i	−0.775842	−	0.630927i	$-0.782675\pi$
$67$	−2.14930	−	12.1893i	−0.262579	−	1.48916i	0.513263	−	0.858231i	$-0.328436\pi$
$68$	−2.37939	+	4.12122i	−0.288543	+	0.499771i
$69$	−0.573978	−	0.994159i	−0.0690988	−	0.119683i
$70$		0			0
$71$	5.53209	−	2.01352i	0.656538	−	0.238960i	0.00779714	−	0.999970i	$-0.497518\pi$
$71$	5.53209	−	2.01352i	0.656538	−	0.238960i	0.648741	+	0.761009i	$0.275296\pi$
$72$	−2.70574	−	0.984808i	−0.318874	−	0.116061i
$73$	0.890530	+	0.747243i	0.104229	+	0.0874582i	0.693413	−	0.720541i	$-0.256106\pi$
$73$	0.890530	+	0.747243i	0.104229	+	0.0874582i	−0.589184	+	0.807999i	$0.700551\pi$
$74$	−0.694593	+	3.93923i	−0.0807448	+	0.457926i
$75$		0			0
$76$	−1.46064	−	4.10689i	−0.167547	−	0.471093i
$77$	20.7939			2.36968
$78$	−0.0787257	+	0.446476i	−0.00891393	+	0.0505534i
$79$	6.75877	+	5.67128i	0.760421	+	0.638069i	0.938236	−	0.345995i	$-0.112459\pi$
$79$	6.75877	+	5.67128i	0.760421	+	0.638069i	−0.177815	+	0.984064i	$0.556903\pi$
$80$		0			0
$81$	−7.45084	+	2.71188i	−0.827871	+	0.301320i
$82$	−6.13429	+	5.14728i	−0.677418	+	0.568422i
$83$	6.06805	+	10.5102i	0.666055	+	1.15364i	0.978998	+	0.203869i	$0.0653517\pi$
$83$	6.06805	+	10.5102i	0.666055	+	1.15364i	−0.312943	+	0.949772i	$0.601315\pi$
$84$	0.652704	−	1.13052i	0.0712158	−	0.123349i
$85$		0			0
$86$	−1.25237	−	7.10257i	−0.135047	−	0.765889i
$87$	1.65270	−	2.86257i	0.177188	−	0.306899i
$88$	−2.76604	−	4.79093i	−0.294861	−	0.510715i
$89$	8.62314	−	7.23567i	0.914051	−	0.766980i	−0.0588343	−	0.998268i	$-0.518738\pi$
$89$	8.62314	−	7.23567i	0.914051	−	0.766980i	0.972885	+	0.231288i	$0.0742939\pi$
$90$		0			0
$91$	4.61081	+	1.67820i	0.483345	+	0.175923i
$92$	2.53209	+	2.12467i	0.263989	+	0.221513i
$93$	−0.384133	+	2.17853i	−0.0398327	+	0.225903i
$94$	−12.2121			−1.25959
$95$		0			0
$96$	−0.347296			−0.0354458
$97$	1.31180	−	7.43961i	0.133194	−	0.755378i	−0.842907	−	0.538059i	$-0.819158\pi$
$97$	1.31180	−	7.43961i	0.133194	−	0.755378i	0.976101	−	0.217319i	$-0.0697311\pi$
$98$	−5.46064	−	4.58202i	−0.551608	−	0.462854i
$99$	−14.9684	−	5.44804i	−1.50438	−	0.547549i
$100$		0			0
$101$	−12.6040	+	10.5760i	−1.25415	+	1.05235i	−0.257865	+	0.966181i	$0.583019\pi$
$101$	−12.6040	+	10.5760i	−1.25415	+	1.05235i	−0.996280	+	0.0861723i	$0.972536\pi$
$102$	0.826352	+	1.43128i	0.0818210	+	0.141718i
$103$	−3.70233	+	6.41263i	−0.364802	+	0.631855i	−0.988744	−	0.149615i	$-0.952197\pi$
$103$	−3.70233	+	6.41263i	−0.364802	+	0.631855i	0.623943	+	0.781470i	$0.285530\pi$
$104$	−0.226682	−	1.28558i	−0.0222280	−	0.126061i
$105$		0			0
$106$	−0.879385	+	1.52314i	−0.0854134	+	0.147940i
$107$	−0.152704	−	0.264490i	−0.0147624	−	0.0255693i	0.858550	−	0.512730i	$-0.171366\pi$
$107$	−0.152704	−	0.264490i	−0.0147624	−	0.0255693i	−0.873312	+	0.487161i	$0.838033\pi$
$108$	−1.56418	+	1.31250i	−0.150513	+	0.126295i
$109$	−14.4338	+	5.25346i	−1.38250	+	0.503190i	−0.922936	−	0.384953i	$-0.874218\pi$
$109$	−14.4338	+	5.25346i	−1.38250	+	0.503190i	−0.459567	+	0.888143i	$0.651996\pi$
$110$		0			0
$111$	1.06418	+	0.892951i	0.101007	+	0.0847552i
$112$	−0.652704	+	3.70167i	−0.0616747	+	0.349775i
$113$	−8.22668			−0.773901			−0.386951	−	0.922100i	$-0.626472\pi$
$113$	−8.22668			−0.773901			−0.386951	+	0.922100i	$0.626472\pi$
$114$	−1.48886	−	0.273842i	−0.139444	−	0.0256476i
$115$		0			0
$116$	−1.65270	+	9.37295i	−0.153450	+	0.870256i
$117$	−2.87939	−	2.41609i	−0.266199	−	0.223368i
$118$	6.07785	+	2.21216i	0.559511	+	0.203645i
$119$	16.8084	−	6.11776i	1.54082	−	0.560814i
$120$		0			0
$121$	−9.80200	−	16.9776i	−0.891091	−	1.54342i
$122$	−1.12061	+	1.94096i	−0.101456	+	0.175726i
$123$	0.482926	+	2.73881i	0.0435440	+	0.246950i
$124$	−1.10607	−	6.27282i	−0.0993277	−	0.563316i
$125$		0			0
$126$	5.41147	+	9.37295i	0.482092	+	0.835009i
$127$	−0.347296	+	0.291416i	−0.0308176	+	0.0258590i	−0.658066	−	0.752960i	$-0.728625\pi$
$127$	−0.347296	+	0.291416i	−0.0308176	+	0.0258590i	0.627249	+	0.778819i	$0.284181\pi$
$128$	0.939693	−	0.342020i	0.0830579	−	0.0302306i
$129$	−2.35369	−	0.856674i	−0.207231	−	0.0754260i
$130$		0			0
$131$	−0.648833	+	3.67972i	−0.0566888	+	0.321498i	−0.999944	−	0.0105701i	$-0.996635\pi$
$131$	−0.648833	+	3.67972i	−0.0566888	+	0.321498i	0.943255	+	0.332068i	$0.107746\pi$
$132$	−1.92127			−0.167225
$133$	−5.71688	+	15.3543i	−0.495716	+	1.33139i
$134$	12.3773			1.06924
$135$		0			0
$136$	−3.64543	−	3.05888i	−0.312593	−	0.262297i
$137$	−9.72328	−	3.53898i	−0.830716	−	0.302356i	−0.108563	−	0.994090i	$-0.534625\pi$
$137$	−9.72328	−	3.53898i	−0.830716	−	0.302356i	−0.722153	+	0.691734i	$0.756847\pi$
$138$	1.07873	−	0.392624i	0.0918272	−	0.0334224i
$139$	1.50387	−	1.26190i	0.127557	−	0.107033i	−0.576778	−	0.816901i	$-0.695690\pi$
$139$	1.50387	−	1.26190i	0.127557	−	0.107033i	0.704334	+	0.709868i	$0.251246\pi$
$140$		0			0
$141$	−2.12061	+	3.67301i	−0.178588	+	0.309323i
$142$	1.02229	+	5.79769i	0.0857886	+	0.486531i
$143$	−1.25402	−	7.11192i	−0.104867	−	0.594728i
$144$	1.43969	−	2.49362i	0.119974	−	0.207802i
$145$		0			0
$146$	−0.890530	+	0.747243i	−0.0737008	+	0.0618423i
$147$	−2.32635	+	0.846723i	−0.191874	+	0.0698365i
$148$	−3.75877	−	1.36808i	−0.308969	−	0.112456i
$149$	10.4534	+	8.77141i	0.856373	+	0.718582i	0.961183	−	0.275910i	$-0.0889792\pi$
$149$	10.4534	+	8.77141i	0.856373	+	0.718582i	−0.104811	+	0.994492i	$0.533424\pi$
$150$		0			0
$151$	−1.63041			−0.132681			−0.0663406	−	0.997797i	$-0.521132\pi$
$151$	−1.63041			−0.132681			−0.0663406	+	0.997797i	$0.521132\pi$
$152$	4.29813	−	0.725293i	0.348625	−	0.0588290i
$153$	−13.7023			−1.10777
$154$	−3.61081	+	20.4779i	−0.290968	+	1.65016i
$155$		0			0
$156$	−0.426022	−	0.155059i	−0.0341091	−	0.0124147i
$157$	5.86484	−	2.13463i	0.468065	−	0.170362i	−0.0972106	−	0.995264i	$-0.530992\pi$
$157$	5.86484	−	2.13463i	0.468065	−	0.170362i	0.565276	+	0.824902i	$0.308770\pi$
$158$	−6.75877	+	5.67128i	−0.537699	+	0.451183i
$159$	0.305407	+	0.528981i	0.0242204	+	0.0419509i
$160$		0			0
$161$	−2.15745	−	12.2355i	−0.170031	−	0.964294i
$162$	−1.37686	−	7.80856i	−0.108176	−	0.613498i
$163$	1.82635	−	3.16333i	0.143051	−	0.247771i	−0.785593	−	0.618743i	$-0.787642\pi$
$163$	1.82635	−	3.16333i	0.143051	−	0.247771i	0.928644	+	0.370972i	$0.120975\pi$
$164$	−4.00387	−	6.93491i	−0.312650	−	0.541525i
$165$		0			0
$166$	−11.4042	+	4.15079i	−0.885138	+	0.322164i
$167$	−15.0865	−	5.49102i	−1.16743	−	0.424908i	−0.315681	−	0.948865i	$-0.602233\pi$
$167$	−15.0865	−	5.49102i	−1.16743	−	0.424908i	−0.851745	+	0.523957i	$0.824455\pi$
$168$	1.00000	+	0.839100i	0.0771517	+	0.0647379i
$169$	−1.96151	+	11.1243i	−0.150886	+	0.855716i
$170$		0			0
$171$	8.13816	−	9.55493i	0.622340	−	0.730684i
$172$	7.21213			0.549920
$173$	0.125667	−	0.712694i	0.00955430	−	0.0541851i	−0.979658	−	0.200675i	$-0.935686\pi$
$173$	0.125667	−	0.712694i	0.00955430	−	0.0541851i	0.989212	+	0.146490i	$0.0467976\pi$
$174$	2.53209	+	2.12467i	0.191957	+	0.161071i
$175$		0			0
$176$	5.19846	−	1.89209i	0.391849	−	0.142621i
$177$	1.72075	−	1.44388i	0.129340	−	0.108529i
$178$	5.62836	+	9.74860i	0.421863	+	0.730688i
$179$	−2.40760	+	4.17009i	−0.179953	+	0.311687i	−0.941864	−	0.335994i	$-0.890928\pi$
$179$	−2.40760	+	4.17009i	−0.179953	+	0.311687i	0.761911	+	0.647681i	$0.224261\pi$
$180$		0			0
$181$	0.539830	+	3.06153i	0.0401252	+	0.227561i	0.998275	−	0.0587046i	$-0.0186970\pi$
$181$	0.539830	+	3.06153i	0.0401252	+	0.227561i	−0.958150	+	0.286266i	$0.907586\pi$
$182$	−2.45336	+	4.24935i	−0.181855	+	0.314983i
$183$	0.389185	+	0.674089i	0.0287694	+	0.0498301i
$184$	−2.53209	+	2.12467i	−0.186668	+	0.156633i
$185$		0			0
$186$	−2.07873	−	0.756594i	−0.152420	−	0.0554762i
$187$	−20.1668	−	16.9220i	−1.47475	−	1.23746i
$188$	2.12061	−	12.0266i	0.154662	−	0.877130i
$189$	7.67499			0.558274
$190$		0			0
$191$	−10.6655			−0.771728			−0.385864	−	0.922556i	$-0.626097\pi$
$191$	−10.6655			−0.771728			−0.385864	+	0.922556i	$0.626097\pi$
$192$	0.0603074	−	0.342020i	0.00435231	−	0.0246832i
$193$	−14.3701	−	12.0579i	−1.03438	−	0.867947i	−0.0430135	−	0.999074i	$-0.513696\pi$
$193$	−14.3701	−	12.0579i	−1.03438	−	0.867947i	−0.991366	+	0.131127i	$0.958140\pi$
$194$	7.09879	+	2.58375i	0.509664	+	0.185502i
$195$		0			0
$196$	5.46064	−	4.58202i	0.390046	−	0.327287i
$197$	−5.47565	−	9.48411i	−0.390124	−	0.675715i	0.602342	−	0.798238i	$-0.294235\pi$
$197$	−5.47565	−	9.48411i	−0.390124	−	0.675715i	−0.992466	+	0.122524i	$0.960901\pi$
$198$	7.96451	−	13.7949i	0.566013	−	0.980363i
$199$	−1.15570	−	6.55428i	−0.0819252	−	0.464621i	−0.997978	−	0.0635627i	$-0.979754\pi$
$199$	−1.15570	−	6.55428i	−0.0819252	−	0.464621i	0.916053	−	0.401058i	$-0.131357\pi$
$200$		0			0
$201$	2.14930	−	3.72270i	0.151600	−	0.262579i
$202$	−8.22668	−	14.2490i	−0.578827	−	1.00256i
$203$	27.4047	−	22.9952i	1.92343	−	1.61395i
$204$	−1.55303	+	0.565258i	−0.108734	+	0.0395760i
$205$		0			0
$206$	−5.67230	−	4.75963i	−0.395208	−	0.331619i
$207$	−1.65270	+	9.37295i	−0.114871	+	0.651465i
$208$	1.30541			0.0905137
$209$	23.7777	−	4.01239i	1.64473	−	0.277542i
$210$		0			0
$211$	3.50640	−	19.8858i	0.241390	−	1.36899i	−0.587338	−	0.809342i	$-0.699824\pi$
$211$	3.50640	−	19.8858i	0.241390	−	1.36899i	0.828729	−	0.559651i	$-0.189065\pi$
$212$	−1.34730	−	1.13052i	−0.0925327	−	0.0776441i
$213$	1.92127	+	0.699287i	0.131644	+	0.0479143i
$214$	0.286989	−	0.104455i	0.0196182	−	0.00714043i
$215$		0			0
$216$	−1.02094	−	1.76833i	−0.0694665	−	0.120319i
$217$	−11.9709	+	20.7342i	−0.812638	+	1.40753i
$218$	−2.66725	−	15.1267i	−0.180649	−	1.02451i
$219$	0.0701076	+	0.397600i	0.00473743	+	0.0268673i
$220$		0			0
$221$	−3.10607	−	5.37987i	−0.208937	−	0.361889i
$222$	−1.06418	+	0.892951i	−0.0714229	+	0.0599310i
$223$	14.7023	−	5.35121i	0.984541	−	0.358344i	0.200937	−	0.979604i	$-0.435601\pi$
$223$	14.7023	−	5.35121i	0.984541	−	0.358344i	0.783604	+	0.621261i	$0.213379\pi$
$224$	−3.53209	−	1.28558i	−0.235998	−	0.0858961i
$225$		0			0
$226$	1.42855	−	8.10170i	0.0950256	−	0.538917i
$227$	8.54488			0.567144			0.283572	−	0.958951i	$-0.408481\pi$
$227$	8.54488			0.567144			0.283572	+	0.958951i	$0.408481\pi$
$228$	0.528218	−	1.41868i	0.0349821	−	0.0939547i
$229$	−4.11287			−0.271786			−0.135893	−	0.990723i	$-0.543390\pi$
$229$	−4.11287			−0.271786			−0.135893	+	0.990723i	$0.543390\pi$
$230$		0			0
$231$	5.53209	+	4.64197i	0.363985	+	0.305419i
$232$	−8.94356	−	3.25519i	−0.587174	−	0.213714i
$233$	2.36319	−	0.860130i	0.154818	−	0.0563490i	−0.263449	−	0.964673i	$-0.584860\pi$
$233$	2.36319	−	0.860130i	0.154818	−	0.0563490i	0.418267	+	0.908324i	$0.362638\pi$
$234$	2.87939	−	2.41609i	0.188231	−	0.157945i
$235$		0			0
$236$	−3.23396	+	5.60138i	−0.210513	+	0.364618i
$237$	0.532089	+	3.01763i	0.0345629	+	0.196016i
$238$	3.10607	+	17.6154i	0.201336	+	1.14184i
$239$	4.65270	−	8.05872i	0.300958	−	0.521275i	−0.675395	−	0.737456i	$-0.736027\pi$
$239$	4.65270	−	8.05872i	0.300958	−	0.521275i	0.976353	+	0.216181i	$0.0693601\pi$
$240$		0			0
$241$	−5.45858	+	4.58029i	−0.351618	+	0.295042i	−0.801439	−	0.598076i	$-0.795932\pi$
$241$	−5.45858	+	4.58029i	−0.351618	+	0.295042i	0.449821	+	0.893119i	$0.351488\pi$
$242$	18.4217	−	6.70497i	1.18419	−	0.431012i
$243$	−8.34389	−	3.03693i	−0.535261	−	0.194819i
$244$	−1.71688	−	1.44063i	−0.109912	−	0.0922272i
$245$		0			0
$246$	−2.78106			−0.177314
$247$	5.59627	+	1.02931i	0.356082	+	0.0654933i
$248$	6.36959			0.404469
$249$	−0.731896	+	4.15079i	−0.0463820	+	0.263046i
$250$		0			0
$251$	−15.5239	−	5.65025i	−0.979862	−	0.356641i	−0.198076	−	0.980187i	$-0.563469\pi$
$251$	−15.5239	−	5.65025i	−0.979862	−	0.356641i	−0.781787	+	0.623546i	$0.785691\pi$
$252$	−10.1702	+	3.70167i	−0.640665	+	0.233183i
$253$	−14.0077	+	11.7539i	−0.880659	+	0.738961i
$254$	−0.226682	−	0.392624i	−0.0142233	−	0.0246354i
$255$		0			0
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	1.54782	+	8.77812i	0.0965503	+	0.547564i	0.994261	+	0.106979i	$0.0341178\pi$
$257$	1.54782	+	8.77812i	0.0965503	+	0.547564i	−0.897711	+	0.440585i	$0.854771\pi$
$258$	1.25237	−	2.16918i	0.0779694	−	0.135047i
$259$	7.51754	+	13.0208i	0.467117	+	0.809071i
$260$		0			0
$261$	−25.7520	+	9.37295i	−1.59401	+	0.580171i
$262$	−3.51114	−	1.27795i	−0.216919	−	0.0789521i
$263$	7.53983	+	6.32667i	0.464926	+	0.390119i	0.844940	−	0.534862i	$-0.179636\pi$
$263$	7.53983	+	6.32667i	0.464926	+	0.390119i	−0.380014	+	0.924981i	$0.624081\pi$
$264$	0.333626	−	1.89209i	0.0205332	−	0.116450i
$265$		0			0
$266$	−14.1284	−	8.29628i	−0.866265	−	0.508678i
$267$	3.90941			0.239252
$268$	−2.14930	+	12.1893i	−0.131289	+	0.744579i
$269$	−6.41147	−	5.37987i	−0.390914	−	0.328016i	0.426055	−	0.904697i	$-0.359903\pi$
$269$	−6.41147	−	5.37987i	−0.390914	−	0.328016i	−0.816969	+	0.576681i	$0.804348\pi$
$270$		0			0
$271$	−1.19934	+	0.436524i	−0.0728547	+	0.0265170i	−0.378190	−	0.925728i	$-0.623454\pi$
$271$	−1.19934	+	0.436524i	−0.0728547	+	0.0265170i	0.305336	+	0.952245i	$0.401231\pi$
$272$	3.64543	−	3.05888i	0.221037	−	0.185472i
$273$	0.852044	+	1.47578i	0.0515681	+	0.0893185i
$274$	5.17365	−	8.96102i	0.312552	−	0.541355i
$275$		0			0
$276$	0.199340	+	1.13052i	0.0119989	+	0.0680491i
$277$	−3.54664	+	6.14296i	−0.213097	+	0.369094i	−0.952682	−	0.303968i	$-0.901688\pi$
$277$	−3.54664	+	6.14296i	−0.213097	+	0.369094i	0.739585	+	0.673063i	$0.235022\pi$
$278$	0.981582	+	1.70015i	0.0588714	+	0.101968i
$279$	14.0496	−	11.7890i	0.841129	−	0.705791i
$280$		0			0
$281$	19.4033	+	7.06223i	1.15751	+	0.421297i	0.848206	−	0.529667i	$-0.177683\pi$
$281$	19.4033	+	7.06223i	1.15751	+	0.421297i	0.309300	+	0.950965i	$0.399905\pi$
$282$	−3.24897	−	2.72621i	−0.193473	−	0.162343i
$283$	2.45858	−	13.9433i	0.146147	−	0.828842i	−0.820292	−	0.571946i	$-0.806189\pi$
$283$	2.45858	−	13.9433i	0.146147	−	0.828842i	0.966439	−	0.256897i	$-0.0827001\pi$
$284$	−5.88713			−0.349337
$285$		0			0
$286$	7.22163			0.427024
$287$	−5.22668	+	29.6420i	−0.308521	+	1.74971i
$288$	2.20574	+	1.85083i	0.129974	+	0.109061i
$289$	−5.30541	−	1.93101i	−0.312083	−	0.113589i
$290$		0			0
$291$	2.00980	−	1.68642i	0.117817	−	0.0988598i
$292$	−0.581252	−	1.00676i	−0.0340152	−	0.0589160i
$293$	−11.5253	+	19.9624i	−0.673314	+	1.16621i	0.303644	+	0.952785i	$0.401797\pi$
$293$	−11.5253	+	19.9624i	−0.673314	+	1.16621i	−0.976959	+	0.213429i	$0.931537\pi$
$294$	−0.429892	−	2.43804i	−0.0250718	−	0.142189i
$295$		0			0
$296$	2.00000	−	3.46410i	0.116248	−	0.201347i
$297$	−5.64796	−	9.78255i	−0.327728	−	0.567641i
$298$	−10.4534	+	8.77141i	−0.605547	+	0.508114i
$299$	−4.05468	+	1.47578i	−0.234488	+	0.0853468i
$300$		0			0
$301$	−20.7665	−	17.4252i	−1.19696	−	1.00437i
$302$	0.283119	−	1.60565i	0.0162916	−	0.0923945i
$303$	−5.71419			−0.328272
$304$	−0.0320889	+	4.35878i	−0.00184042	+	0.249993i
$305$		0			0
$306$	2.37939	−	13.4942i	0.136020	−	0.771410i
$307$	−3.23783	−	2.71686i	−0.184792	−	0.155059i	0.545699	−	0.837982i	$-0.316264\pi$
$307$	−3.23783	−	2.71686i	−0.184792	−	0.155059i	−0.730491	+	0.682922i	$0.760709\pi$
$308$	−19.5398	−	7.11192i	−1.11339	−	0.405239i
$309$	−2.41653	+	0.879544i	−0.137471	+	0.0500355i
$310$		0			0
$311$	4.18479	+	7.24827i	0.237298	+	0.411012i	0.959938	−	0.280213i	$-0.0904049\pi$
$311$	4.18479	+	7.24827i	0.237298	+	0.411012i	−0.722640	+	0.691224i	$0.757072\pi$
$312$	0.226682	−	0.392624i	0.0128333	−	0.0222280i
$313$	3.20146	+	18.1564i	0.180957	+	1.02626i	0.931041	+	0.364915i	$0.118902\pi$
$313$	3.20146	+	18.1564i	0.180957	+	1.02626i	−0.750084	+	0.661343i	$0.769987\pi$
$314$	1.08378	+	6.14641i	0.0611611	+	0.346862i
$315$		0			0
$316$	−4.41147	−	7.64090i	−0.248165	−	0.429834i
$317$	23.7743	−	19.9490i	1.33530	−	1.12045i	0.352487	−	0.935817i	$-0.385336\pi$
$317$	23.7743	−	19.9490i	1.33530	−	1.12045i	0.982808	−	0.184629i	$-0.0591083\pi$
$318$	−0.573978	+	0.208911i	−0.0321871	+	0.0117151i
$319$	−49.4766	−	18.0080i	−2.77016	−	1.00825i
$320$		0			0
$321$	0.0184183	−	0.104455i	0.00102801	−	0.00583013i
$322$	12.4243			0.692377
$323$	18.0398	−	10.2390i	1.00376	−	0.569712i
$324$	7.92902			0.440501
$325$		0			0
$326$	2.79813	+	2.34791i	0.154974	+	0.130039i
$327$	−5.01279	−	1.82451i	−0.277208	−	0.100895i
$328$	7.52481	−	2.73881i	0.415488	−	0.151225i
$329$	−35.1634	+	29.5056i	−1.93862	+	1.62670i
$330$		0			0
$331$	4.29813	−	7.44459i	0.236247	−	0.409191i	−0.723388	−	0.690442i	$-0.757416\pi$
$331$	4.29813	−	7.44459i	0.236247	−	0.409191i	0.959634	+	0.281251i	$0.0907493\pi$
$332$	−2.10741	−	11.9517i	−0.115659	−	0.655936i
$333$	−2.00000	−	11.3426i	−0.109599	−	0.621569i
$334$	8.02734	−	13.9038i	0.439237	−	0.760780i
$335$		0			0
$336$	−1.00000	+	0.839100i	−0.0545545	+	0.0457766i
$337$	−30.0219	+	10.9271i	−1.63540	+	0.595235i	−0.986225	−	0.165407i	$-0.947106\pi$
$337$	−30.0219	+	10.9271i	−1.63540	+	0.595235i	−0.649171	+	0.760643i	$0.724884\pi$
$338$	−10.6147	−	3.86343i	−0.577363	−	0.210143i
$339$	−2.18866	−	1.83651i	−0.118872	−	0.0997453i
$340$		0			0
$341$	35.2371			1.90820
$342$	7.99660	+	9.67372i	0.432406	+	0.523095i
$343$	−0.482459			−0.0260503
$344$	−1.25237	+	7.10257i	−0.0675235	+	0.382945i
$345$		0			0
$346$	0.680045	+	0.247516i	0.0365594	+	0.0133065i
$347$	4.25624	−	1.54915i	0.228487	−	0.0831625i	−0.225240	−	0.974303i	$-0.572316\pi$
$347$	4.25624	−	1.54915i	0.228487	−	0.0831625i	0.453727	+	0.891141i	$0.350094\pi$
$348$	−2.53209	+	2.12467i	−0.135734	+	0.113895i
$349$	13.5621	+	23.4903i	0.725964	+	1.25741i	0.958576	+	0.284836i	$0.0919392\pi$
$349$	13.5621	+	23.4903i	0.725964	+	1.25741i	−0.232613	+	0.972569i	$0.574727\pi$
$350$		0			0
$351$	−0.462859	−	2.62500i	−0.0247056	−	0.140112i
$352$	0.960637	+	5.44804i	0.0512021	+	0.290382i
$353$	9.86097	−	17.0797i	0.524846	−	0.909060i	−0.474735	−	0.880129i	$-0.657456\pi$
$353$	9.86097	−	17.0797i	0.524846	−	0.909060i	0.999581	−	0.0289317i	$-0.00921054\pi$
$354$	1.12314	+	1.94534i	0.0596943	+	0.103394i
$355$		0			0
$356$	−10.5778	+	3.85002i	−0.560625	+	0.204051i
$357$	5.83750	+	2.12467i	0.308953	+	0.112450i
$358$	−3.68866	−	3.09516i	−0.194952	−	0.163584i
$359$	−3.78611	+	21.4721i	−0.199823	+	1.13325i	0.705557	+	0.708653i	$0.250697\pi$
$359$	−3.78611	+	21.4721i	−0.199823	+	1.13325i	−0.905380	+	0.424601i	$0.860414\pi$
$360$		0			0
$361$	−3.57444	+	18.6607i	−0.188129	+	0.982144i
$362$	−3.10876			−0.163393
$363$	1.18227	−	6.70497i	0.0620529	−	0.351919i
$364$	−3.75877	−	3.15398i	−0.197013	−	0.165314i
$365$		0			0
$366$	−0.731429	+	0.266219i	−0.0382324	+	0.0139155i
$367$	2.81521	−	2.36224i	0.146953	−	0.123308i	−0.566348	−	0.824166i	$-0.691644\pi$
$367$	2.81521	−	2.36224i	0.146953	−	0.123308i	0.713300	+	0.700859i	$0.247200\pi$
$368$	−1.65270	−	2.86257i	−0.0861531	−	0.149222i
$369$	11.5287	−	19.9683i	0.600159	−	1.03951i
$370$		0			0
$371$	1.14796	+	6.51038i	0.0595989	+	0.338002i
$372$	1.10607	−	1.91576i	0.0573469	−	0.0993277i
$373$	6.58853	+	11.4117i	0.341141	+	0.590873i	0.984645	−	0.174569i	$-0.0558533\pi$
$373$	6.58853	+	11.4117i	0.341141	+	0.590873i	−0.643504	+	0.765443i	$0.722520\pi$
$374$	20.1668	−	16.9220i	1.04280	−	0.875015i
$375$		0			0
$376$	11.4757	+	4.17680i	0.591812	+	0.215402i
$377$	−9.51754	−	7.98617i	−0.490178	−	0.411308i
$378$	−1.33275	+	7.55839i	−0.0685492	+	0.388762i
$379$	11.2918			0.580020			0.290010	−	0.957024i	$-0.406341\pi$
$379$	11.2918			0.580020			0.290010	+	0.957024i	$0.406341\pi$
$380$		0			0
$381$	−0.157451			−0.00806648
$382$	1.85204	−	10.5035i	0.0947588	−	0.537404i
$383$	−19.6759	−	16.5101i	−1.00539	−	0.843625i	−0.0176704	−	0.999844i	$-0.505625\pi$
$383$	−19.6759	−	16.5101i	−1.00539	−	0.843625i	−0.987722	+	0.156219i	$0.950069\pi$
$384$	0.326352	+	0.118782i	0.0166541	+	0.00606159i
$385$		0			0
$386$	14.3701	−	12.0579i	0.731416	−	0.613731i
$387$	10.3833	+	17.9843i	0.527811	+	0.914195i
$388$	−3.77719	+	6.54228i	−0.191758	+	0.332134i
$389$	−1.79797	−	10.1968i	−0.0911608	−	0.516998i	−0.995856	−	0.0909399i	$-0.971013\pi$
$389$	−1.79797	−	10.1968i	−0.0911608	−	0.516998i	0.904696	−	0.426058i	$-0.140098\pi$
$390$		0			0
$391$	−7.86484	+	13.6223i	−0.397742	+	0.688909i
$392$	3.56418	+	6.17334i	0.180018	+	0.311801i
$393$	−0.994070	+	0.834124i	−0.0501442	+	0.0420760i
$394$	10.2909	−	3.74557i	0.518446	−	0.188699i
$395$		0			0
$396$	12.2023	+	10.2390i	0.613190	+	0.514528i
$397$	−1.65776	+	9.40160i	−0.0832004	+	0.471853i	0.914530	+	0.404518i	$0.132561\pi$
$397$	−1.65776	+	9.40160i	−0.0832004	+	0.471853i	−0.997730	+	0.0673349i	$0.978550\pi$
$398$	6.65539			0.333605
$399$	−4.94862	+	2.80872i	−0.247741	+	0.140612i
$400$		0			0
$401$	−5.20187	+	29.5013i	−0.259769	+	1.47322i	0.523760	+	0.851866i	$0.324529\pi$
$401$	−5.20187	+	29.5013i	−0.259769	+	1.47322i	−0.783528	+	0.621356i	$0.786582\pi$
$402$	3.29292	+	2.76309i	0.164236	+	0.137810i
$403$	7.81345	+	2.84386i	0.389216	+	0.141663i
$404$	15.4611	−	5.62738i	0.769219	−	0.279973i
$405$		0			0
$406$	17.8871	+	30.9814i	0.887723	+	1.53758i
$407$	11.0642	−	19.1637i	0.548431	−	0.949910i
$408$	−0.286989	−	1.62760i	−0.0142081	−	0.0805780i
$409$	4.27110	+	24.2226i	0.211192	+	1.19773i	0.887393	+	0.461013i	$0.152514\pi$
$409$	4.27110	+	24.2226i	0.211192	+	1.19773i	−0.676201	+	0.736717i	$0.736375\pi$
$410$		0			0
$411$	−1.79679	−	3.11213i	−0.0886291	−	0.153510i
$412$	5.67230	−	4.75963i	0.279454	−	0.234490i
$413$	22.8452	−	8.31499i	1.12414	−	0.409154i
$414$	−8.94356	−	3.25519i	−0.439552	−	0.159984i
$415$		0			0
$416$	−0.226682	+	1.28558i	−0.0111140	+	0.0630305i
$417$	0.681799			0.0333879
$418$	−0.177519	+	24.1132i	−0.00868272	+	1.17941i
$419$	−11.8075			−0.576832			−0.288416	−	0.957505i	$-0.593129\pi$
$419$	−11.8075			−0.576832			−0.288416	+	0.957505i	$0.593129\pi$
$420$		0			0
$421$	−4.66044	−	3.91058i	−0.227136	−	0.190590i	0.522116	−	0.852874i	$-0.325143\pi$
$421$	−4.66044	−	3.91058i	−0.227136	−	0.190590i	−0.749253	+	0.662284i	$0.769587\pi$
$422$	18.9748	+	6.90625i	0.923678	+	0.336191i
$423$	33.0428	−	12.0266i	1.60660	−	0.584753i
$424$	1.34730	−	1.13052i	0.0654305	−	0.0549027i
$425$		0			0
$426$	−1.02229	+	1.77066i	−0.0495300	+	0.0857886i
$427$	1.46286	+	8.29628i	0.0707927	+	0.401485i
$428$	0.0530334	+	0.300767i	0.00256347	+	0.0145381i
$429$	1.25402	−	2.17203i	0.0605448	−	0.104867i
$430$		0			0
$431$	−9.98545	+	8.37879i	−0.480982	+	0.403592i	−0.850781	−	0.525520i	$-0.823871\pi$
$431$	−9.98545	+	8.37879i	−0.480982	+	0.403592i	0.369799	+	0.929112i	$0.379426\pi$
$432$	1.91875	−	0.698367i	0.0923158	−	0.0336002i
$433$	−24.9145	−	9.06812i	−1.19731	−	0.435786i	−0.335027	−	0.942208i	$-0.608746\pi$
$433$	−24.9145	−	9.06812i	−1.19731	−	0.435786i	−0.862286	+	0.506422i	$0.830968\pi$
$434$	−18.3405	−	15.3895i	−0.880372	−	0.738720i
$435$		0			0
$436$	15.3601			0.735615
$437$	−4.82800	−	13.5749i	−0.230955	−	0.649378i
$438$	−0.403733			−0.0192911
$439$	−6.15064	+	34.8820i	−0.293554	+	1.66483i	0.379467	+	0.925205i	$0.376107\pi$
$439$	−6.15064	+	34.8820i	−0.293554	+	1.66483i	−0.673021	+	0.739623i	$0.735004\pi$
$440$		0			0
$441$	19.2875	+	7.02006i	0.918450	+	0.334289i
$442$	5.83750	−	2.12467i	0.277661	−	0.101060i
$443$	−22.8136	+	19.1429i	−1.08391	+	0.909506i	−0.996239	−	0.0866433i	$-0.972386\pi$
$443$	−22.8136	+	19.1429i	−1.08391	+	0.909506i	−0.0876682	+	0.996150i	$0.527942\pi$
$444$	−0.694593	−	1.20307i	−0.0329639	−	0.0570952i
$445$		0			0
$446$	2.71688	+	15.4082i	0.128648	+	0.729599i
$447$	0.822948	+	4.66717i	0.0389241	+	0.220750i
$448$	1.87939	−	3.25519i	0.0887926	−	0.153793i
$449$	−14.5655	−	25.2282i	−0.687389	−	1.19059i	−0.972679	−	0.232152i	$-0.925423\pi$
$449$	−14.5655	−	25.2282i	−0.687389	−	1.19059i	0.285290	−	0.958441i	$-0.407910\pi$
$450$		0			0
$451$	41.6279	−	15.1513i	1.96018	−	0.713448i
$452$	7.73055	+	2.81369i	0.363615	+	0.132345i
$453$	−0.433763	−	0.363970i	−0.0203800	−	0.0171008i
$454$	−1.48380	+	8.41507i	−0.0696383	+	0.394939i
$455$		0			0
$456$	1.30541	+	0.766546i	0.0611313	+	0.0358968i
$457$	−23.4807			−1.09838			−0.549191	−	0.835697i	$-0.685064\pi$
$457$	−23.4807			−1.09838			−0.549191	+	0.835697i	$0.685064\pi$
$458$	0.714193	−	4.05039i	0.0333721	−	0.189262i
$459$	−7.44356	−	6.24589i	−0.347436	−	0.291533i
$460$		0			0
$461$	4.85204	−	1.76600i	0.225982	−	0.0822508i	−0.226548	−	0.974000i	$-0.572744\pi$
$461$	4.85204	−	1.76600i	0.225982	−	0.0822508i	0.452530	+	0.891749i	$0.350522\pi$
$462$	−5.53209	+	4.64197i	−0.257376	+	0.215964i
$463$	12.5621	+	21.7582i	0.583811	+	1.01119i	0.995022	+	0.0996505i	$0.0317725\pi$
$463$	12.5621	+	21.7582i	0.583811	+	1.01119i	−0.411211	+	0.911540i	$0.634894\pi$
$464$	4.75877	−	8.24243i	0.220920	−	0.382645i
$465$		0			0
$466$	0.436700	+	2.47665i	0.0202297	+	0.114728i
$467$	−10.3093	+	17.8562i	−0.477056	+	0.826286i	−0.999654	−	0.0262933i	$-0.991630\pi$
$467$	−10.3093	+	17.8562i	−0.477056	+	0.826286i	0.522598	+	0.852579i	$0.324963\pi$
$468$	1.87939	+	3.25519i	0.0868746	+	0.150471i
$469$	35.6391	−	29.9047i	1.64566	−	1.38087i
$470$		0			0
$471$	2.03684	+	0.741348i	0.0938525	+	0.0341595i
$472$	−4.95471	−	4.15749i	−0.228059	−	0.191364i
$473$	−6.92824	+	39.2920i	−0.318561	+	1.80665i
$474$	−3.06418			−0.140742
$475$		0			0
$476$	−17.8871			−0.819855
$477$	0.879385	−	4.98724i	0.0402643	−	0.228350i
$478$	7.12836	+	5.98140i	0.326043	+	0.273583i
$479$	10.8648	+	3.95448i	0.496427	+	0.180685i	0.578086	−	0.815976i	$-0.303800\pi$
$479$	10.8648	+	3.95448i	0.496427	+	0.180685i	−0.0816592	+	0.996660i	$0.526022\pi$
$480$		0			0
$481$	4.00000	−	3.35640i	0.182384	−	0.153039i
$482$	−3.56283	−	6.17101i	−0.162283	−	0.281082i
$483$	2.15745	−	3.73682i	0.0981674	−	0.170031i
$484$	3.40420	+	19.3062i	0.154736	+	0.877554i
$485$		0			0
$486$	4.43969	−	7.68977i	0.201389	−	0.348815i
$487$	2.45336	+	4.24935i	0.111172	+	0.192556i	0.916243	−	0.400622i	$-0.131206\pi$
$487$	2.45336	+	4.24935i	0.111172	+	0.192556i	−0.805071	+	0.593179i	$0.797873\pi$
$488$	1.71688	−	1.44063i	0.0777196	−	0.0652145i
$489$	1.19207	−	0.433877i	0.0539071	−	0.0196206i
$490$		0			0
$491$	9.80793	+	8.22983i	0.442626	+	0.371407i	0.836691	−	0.547675i	$-0.184487\pi$
$491$	9.80793	+	8.22983i	0.442626	+	0.371407i	−0.394065	+	0.919083i	$0.628932\pi$
$492$	0.482926	−	2.73881i	0.0217720	−	0.123475i
$493$	−45.2918			−2.03984
$494$	−1.98545	+	5.33251i	−0.0893297	+	0.239921i
$495$		0			0
$496$	−1.10607	+	6.27282i	−0.0496639	+	0.281658i
$497$	16.9513	+	14.2238i	0.760370	+	0.638026i
$498$	−3.96064	−	1.44155i	−0.177480	−	0.0645976i
$499$	−3.86571	+	1.40701i	−0.173053	+	0.0629862i	−0.427094	−	0.904207i	$-0.640463\pi$
$499$	−3.86571	+	1.40701i	−0.173053	+	0.0629862i	0.254041	+	0.967194i	$0.418240\pi$
$500$		0			0
$501$	−2.78787	−	4.82873i	−0.124553	−	0.215732i
$502$	8.26011	−	14.3069i	0.368667	−	0.638550i
$503$	−3.48070	−	19.7401i	−0.155197	−	0.880166i	−0.958606	−	0.284737i	$-0.908094\pi$
$503$	−3.48070	−	19.7401i	−0.155197	−	0.880166i	0.803409	−	0.595428i	$-0.203018\pi$
$504$	−1.87939	−	10.6585i	−0.0837145	−	0.474768i
$505$		0			0
$506$	−9.14290	−	15.8360i	−0.406452	−	0.703995i
$507$	−3.00521	+	2.52167i	−0.133466	+	0.111991i
$508$	0.426022	−	0.155059i	0.0189017	−	0.00687965i
$509$	−11.3824	−	4.14285i	−0.504515	−	0.183628i	0.0772086	−	0.997015i	$-0.475399\pi$
$509$	−11.3824	−	4.14285i	−0.504515	−	0.183628i	−0.581724	+	0.813387i	$0.697621\pi$
$510$		0			0
$511$	−0.758770	+	4.30320i	−0.0335660	+	0.190362i
$512$	−1.00000			−0.0441942
$513$	8.77631	−	1.48097i	0.387484	−	0.0653863i
$514$	−8.91353			−0.393159
$515$		0			0
$516$	1.91875	+	1.61002i	0.0844682	+	0.0708772i
$517$	63.4843	+	23.1064i	2.79204	+	1.01622i
$518$	−14.1284	+	5.14230i	−0.620764	+	0.225940i
$519$	0.192533	−	0.161555i	0.00845127	−	0.00709146i
$520$		0			0
$521$	−12.6202	+	21.8588i	−0.552901	+	0.957653i	0.445162	+	0.895450i	$0.353146\pi$
$521$	−12.6202	+	21.8588i	−0.552901	+	0.957653i	−0.998064	+	0.0622031i	$0.980187\pi$
$522$	−4.75877	−	26.9883i	−0.208286	−	1.18125i
$523$	−3.33450	−	18.9109i	−0.145808	−	0.826916i	−0.966715	−	0.255855i	$-0.917643\pi$
$523$	−3.33450	−	18.9109i	−0.145808	−	0.826916i	0.820908	−	0.571061i	$-0.193468\pi$
$524$	1.86824	−	3.23589i	0.0816145	−	0.141360i
$525$		0			0
$526$	−7.53983	+	6.32667i	−0.328752	+	0.275856i
$527$	28.4834	−	10.3671i	1.24076	−	0.451598i
$528$	1.80541	+	0.657115i	0.0785703	+	0.0285972i
$529$	−9.24944	−	7.76120i	−0.402149	−	0.337443i
$530$		0			0
$531$	−18.6236			−0.808196
$532$	10.6236	−	12.4731i	0.460592	−	0.540777i
$533$	10.4534			0.452785
$534$	−0.678863	+	3.85002i	−0.0293773	+	0.166607i
$535$		0			0
$536$	−11.6309	−	4.23329i	−0.502378	−	0.182850i
$537$	−1.57145	+	0.571962i	−0.0678131	+	0.0246820i
$538$	6.41147	−	5.37987i	0.276418	−	0.231942i
$539$	19.7173	+	34.1514i	0.849286	+	1.47101i
$540$		0			0
$541$	−0.0273411	−	0.155059i	−0.00117549	−	0.00666652i	0.984214	−	0.176980i	$-0.0566329\pi$
$541$	−0.0273411	−	0.155059i	−0.00117549	−	0.00666652i	−0.985390	+	0.170314i	$0.945522\pi$
$542$	−0.221629	−	1.25692i	−0.00951979	−	0.0539894i
$543$	−0.539830	+	0.935012i	−0.0231663	+	0.0401252i
$544$	2.37939	+	4.12122i	0.102015	+	0.176696i
$545$		0			0
$546$	−1.60132	+	0.582832i	−0.0685301	+	0.0249429i
$547$	32.3025	+	11.7571i	1.38115	+	0.502699i	0.922528	−	0.385930i	$-0.126120\pi$
$547$	32.3025	+	11.7571i	1.38115	+	0.502699i	0.458626	+	0.888629i	$0.348342\pi$
$548$	7.92649	+	6.65111i	0.338603	+	0.284122i
$549$	1.12061	−	6.35532i	0.0478267	−	0.271239i
$550$		0			0
$551$	26.8999	−	31.5829i	1.14598	−	1.34548i
$552$	−1.14796			−0.0488602
$553$	−5.75877	+	32.6596i	−0.244888	+	1.38883i
$554$	−5.43376	−	4.55947i	−0.230858	−	0.193713i
$555$		0			0
$556$	−1.84477	+	0.671441i	−0.0782357	+	0.0284755i
$557$	−10.1480	+	8.51515i	−0.429983	+	0.360798i	−0.831945	−	0.554858i	$-0.812773\pi$
$557$	−10.1480	+	8.51515i	−0.429983	+	0.360798i	0.401963	+	0.915656i	$0.368328\pi$
$558$	9.17024	+	15.8833i	0.388207	+	0.672395i
$559$	−4.70739	+	8.15343i	−0.199101	+	0.344853i
$560$		0			0
$561$	−1.58765	−	9.00400i	−0.0670306	−	0.380149i
$562$	−10.3243	+	17.8822i	−0.435504	+	0.754315i
$563$	19.1630	+	33.1912i	0.807623	+	1.39884i	0.914506	+	0.404572i	$0.132580\pi$
$563$	19.1630	+	33.1912i	0.807623	+	1.39884i	−0.106883	+	0.994272i	$0.534087\pi$
$564$	3.24897	−	2.72621i	0.136806	−	0.114794i
$565$		0			0
$566$	13.3045	+	4.84245i	0.559231	+	0.203543i
$567$	−22.8307	−	19.1572i	−0.958799	−	0.804528i
$568$	1.02229	−	5.79769i	0.0428943	−	0.243266i
$569$	−32.1634			−1.34836			−0.674181	−	0.738566i	$-0.735503\pi$
$569$	−32.1634			−1.34836			−0.674181	+	0.738566i	$0.735503\pi$
$570$		0			0
$571$	16.2635			0.680607			0.340304	−	0.940316i	$-0.389470\pi$
$571$	16.2635			0.680607			0.340304	+	0.940316i	$0.389470\pi$
$572$	−1.25402	+	7.11192i	−0.0524333	+	0.297364i
$573$	−2.83750	−	2.38094i	−0.118538	−	0.0994653i
$574$	−28.2841	−	10.2946i	−1.18055	−	0.429686i
$575$		0			0
$576$	−2.20574	+	1.85083i	−0.0919057	+	0.0771180i
$577$	10.4829	+	18.1570i	0.436410	+	0.755884i	0.997410	−	0.0719319i	$-0.0229164\pi$
$577$	10.4829	+	18.1570i	0.436410	+	0.755884i	−0.561000	+	0.827816i	$0.689583\pi$
$578$	2.82295	−	4.88949i	0.117419	−	0.203376i
$579$	−1.13129	−	6.41588i	−0.0470149	−	0.266635i
$580$		0			0
$581$	−22.8084	+	39.5053i	−0.946252	+	1.63896i
$582$	1.31180	+	2.27211i	0.0543760	+	0.0941820i
$583$	7.45336	−	6.25411i	0.308687	−	0.259019i
$584$	1.09240	−	0.397600i	0.0452037	−	0.0164528i
$585$		0			0
$586$	−17.6578	−	14.8166i	−0.729435	−	0.612069i
$587$	−6.12671	+	34.7463i	−0.252876	+	1.43413i	0.548590	+	0.836092i	$0.315165\pi$
$587$	−6.12671	+	34.7463i	−0.252876	+	1.43413i	−0.801466	+	0.598041i	$0.795946\pi$
$588$	2.47565			0.102094
$589$	−9.68779	+	26.0194i	−0.399178	+	1.07211i
$590$		0			0
$591$	0.660444	−	3.74557i	0.0271671	−	0.154072i
$592$	3.06418	+	2.57115i	0.125937	+	0.105674i
$593$	−15.2208	−	5.53990i	−0.625041	−	0.227496i	0.0100303	−	0.999950i	$-0.496807\pi$
$593$	−15.2208	−	5.53990i	−0.625041	−	0.227496i	−0.635072	+	0.772453i	$0.719029\pi$
$594$	10.6147	−	3.86343i	0.435526	−	0.158518i
$595$		0			0
$596$	−6.82295	−	11.8177i	−0.279479	−	0.484072i
$597$	1.15570	−	2.00173i	0.0472995	−	0.0819252i
$598$	−0.749275	−	4.24935i	−0.0306401	−	0.173769i
$599$	−2.70502	−	15.3409i	−0.110524	−	0.626814i	−0.988869	−	0.148787i	$-0.952463\pi$
$599$	−2.70502	−	15.3409i	−0.110524	−	0.626814i	0.878345	−	0.478027i	$-0.158648\pi$
$600$		0			0
$601$	10.9089	+	18.8949i	0.444985	+	0.770737i	0.998051	−	0.0624004i	$-0.0198756\pi$
$601$	10.9089	+	18.8949i	0.444985	+	0.770737i	−0.553066	+	0.833137i	$0.686542\pi$
$602$	20.7665	−	17.4252i	0.846380	−	0.710197i
$603$	−33.4898	+	12.1893i	−1.36381	+	0.496386i
$604$	1.53209	+	0.557635i	0.0623398	+	0.0226898i
$605$		0			0
$606$	0.992259	−	5.62738i	0.0403078	−	0.228597i
$607$	−32.2722			−1.30989			−0.654944	−	0.755677i	$-0.727308\pi$
$607$	−32.2722			−1.30989			−0.654944	+	0.755677i	$0.727308\pi$
$608$	−4.28699	−	0.788496i	−0.173860	−	0.0319777i
$609$	12.4243			0.503457
$610$		0			0
$611$	12.2121	+	10.2472i	0.494050	+	0.414557i
$612$	12.8760	+	4.68647i	0.520481	+	0.189439i
$613$	34.7597	−	12.6515i	1.40393	−	0.510989i	0.474589	−	0.880208i	$-0.342597\pi$
$613$	34.7597	−	12.6515i	1.40393	−	0.510989i	0.929343	+	0.369219i	$0.120375\pi$
$614$	3.23783	−	2.71686i	0.130668	−	0.109643i
$615$		0			0
$616$	10.3969	−	18.0080i	0.418904	−	0.725563i
$617$	−0.453525	−	2.57207i	−0.0182582	−	0.103548i	0.974317	−	0.225182i	$-0.0722976\pi$
$617$	−0.453525	−	2.57207i	−0.0182582	−	0.103548i	−0.992575	+	0.121634i	$0.961187\pi$
$618$	−0.446556	−	2.53255i	−0.0179631	−	0.101874i
$619$	−4.61381	+	7.99135i	−0.185445	+	0.321199i	−0.943726	−	0.330728i	$-0.892706\pi$
$619$	−4.61381	+	7.99135i	−0.185445	+	0.321199i	0.758282	+	0.651927i	$0.226039\pi$
$620$		0			0
$621$	−5.17024	+	4.33835i	−0.207475	+	0.174092i
$622$	−7.86484	+	2.86257i	−0.315351	+	0.114778i
$623$	39.7597	+	14.4713i	1.59294	+	0.579782i
$624$	0.347296	+	0.291416i	0.0139030	+	0.0116660i
$625$		0			0
$626$	−18.4365			−0.736869
$627$	7.22163	+	4.24060i	0.288404	+	0.169353i
$628$	−6.24123			−0.249052
$629$	3.30541	−	18.7459i	0.131795	−	0.747448i
$630$		0			0
$631$	26.1925	+	9.53330i	1.04271	+	0.379515i	0.805906	−	0.592043i	$-0.201679\pi$
$631$	26.1925	+	9.53330i	1.04271	+	0.379515i	0.236802	+	0.971558i	$0.423901\pi$
$632$	8.29086	−	3.01763i	0.329793	−	0.120035i
$633$	5.37211	−	4.50774i	0.213522	−	0.179166i
$634$	15.5175	+	26.8772i	0.616280	+	1.06743i
$635$		0			0
$636$	−0.106067	−	0.601535i	−0.00420582	−	0.0238524i
$637$	1.61587	+	9.16404i	0.0640230	+	0.363092i
$638$	26.3259	−	45.5979i	1.04225	−	1.80524i
$639$	−8.47565	−	14.6803i	−0.335292	−	0.580742i
$640$		0			0
$641$	28.7866	−	10.4775i	1.13700	−	0.413835i	0.296172	−	0.955135i	$-0.404290\pi$
$641$	28.7866	−	10.4775i	1.13700	−	0.413835i	0.840830	+	0.541300i	$0.182068\pi$
$642$	0.0996702	+	0.0362770i	0.00393367	+	0.00143174i
$643$	22.6748	+	19.0264i	0.894208	+	0.750330i	0.969050	−	0.246866i	$-0.0794007\pi$
$643$	22.6748	+	19.0264i	0.894208	+	0.750330i	−0.0748417	+	0.997195i	$0.523845\pi$
$644$	−2.15745	+	12.2355i	−0.0850155	+	0.482147i
$645$		0			0
$646$	6.95084	+	19.5437i	0.273477	+	0.768938i
$647$	−30.4635			−1.19764			−0.598821	−	0.800883i	$-0.704364\pi$
$647$	−30.4635			−1.19764			−0.598821	+	0.800883i	$0.704364\pi$
$648$	−1.37686	+	7.80856i	−0.0540881	+	0.306749i
$649$	−27.4099	−	22.9996i	−1.07593	−	0.902814i
$650$		0			0
$651$	−7.81345	+	2.84386i	−0.306233	+	0.111460i
$652$	−2.79813	+	2.34791i	−0.109583	+	0.0919514i
$653$	−19.9513	−	34.5567i	−0.780755	−	1.35231i	−0.931503	−	0.363735i	$-0.881501\pi$
$653$	−19.9513	−	34.5567i	−0.780755	−	1.35231i	0.150748	−	0.988572i	$-0.451832\pi$
$654$	2.66725	−	4.61982i	0.104298	−	0.180649i
$655$		0			0
$656$	1.39053	+	7.88609i	0.0542911	+	0.307900i
$657$	1.67365	−	2.89884i	0.0652952	−	0.113095i
$658$	−22.9513	−	39.7528i	−0.894735	−	1.54973i
$659$	32.3214	−	27.1208i	1.25906	−	1.05648i	0.263280	−	0.964719i	$-0.415196\pi$
$659$	32.3214	−	27.1208i	1.25906	−	1.05648i	0.995781	−	0.0917584i	$-0.0292487\pi$
$660$		0			0
$661$	−15.6186	−	5.68469i	−0.607491	−	0.221109i	0.0199139	−	0.999802i	$-0.493661\pi$
$661$	−15.6186	−	5.68469i	−0.607491	−	0.221109i	−0.627405	+	0.778693i	$0.715883\pi$
$662$	6.58512	+	5.52557i	0.255938	+	0.214758i
$663$	0.374638	−	2.12467i	0.0145497	−	0.0825155i
$664$	12.1361			0.470972
$665$		0			0
$666$	11.5175			0.446296
$667$	−5.46286	+	30.9814i	−0.211523	+	1.19961i
$668$	12.2986	+	10.3198i	0.475847	+	0.399283i
$669$	5.10607	+	1.85846i	0.197412	+	0.0718521i
$670$		0			0
$671$	9.49794	−	7.96972i	0.366664	−	0.307668i
$672$	−0.652704	−	1.13052i	−0.0251786	−	0.0436106i
$673$	11.6361	−	20.1543i	0.448539	−	0.776892i	−0.549753	−	0.835328i	$-0.685278\pi$
$673$	11.6361	−	20.1543i	0.448539	−	0.776892i	0.998291	+	0.0584360i	$0.0186113\pi$
$674$	−5.54782	−	31.4632i	−0.213694	−	1.21192i
$675$		0			0
$676$	5.64796	−	9.78255i	0.217229	−	0.376252i
$677$	−15.8726	−	27.4921i	−0.610033	−	1.05661i	−0.991234	−	0.132116i	$-0.957823\pi$
$677$	−15.8726	−	27.4921i	−0.610033	−	1.05661i	0.381202	−	0.924492i	$-0.375510\pi$
$678$	2.18866	−	1.83651i	0.0840551	−	0.0705306i
$679$	26.6827	−	9.71172i	1.02399	−	0.372702i
$680$		0			0
$681$	2.27332	+	1.90754i	0.0871138	+	0.0730971i
$682$	−6.11886	+	34.7018i	−0.234303	+	1.32880i
$683$	6.87702			0.263142			0.131571	−	0.991307i	$-0.457998\pi$
$683$	6.87702			0.263142			0.131571	+	0.991307i	$0.457998\pi$
$684$	−10.9153	+	6.19529i	−0.417359	+	0.236883i
$685$		0			0
$686$	0.0837781	−	0.475129i	0.00319866	−	0.0181405i
$687$	−1.09421	−	0.918149i	−0.0417466	−	0.0350296i
$688$	−6.77719	−	2.46669i	−0.258378	−	0.0940419i
$689$	2.15745	−	0.785248i	0.0821924	−	0.0299156i
$690$		0			0
$691$	−8.83544	−	15.3034i	−0.336116	−	0.582170i	0.647583	−	0.761995i	$-0.275780\pi$
$691$	−8.83544	−	15.3034i	−0.336116	−	0.582170i	−0.983699	+	0.179825i	$0.942447\pi$
$692$	−0.361844	+	0.626733i	−0.0137553	+	0.0238248i
$693$	−10.3969	−	58.9639i	−0.394947	−	2.23985i
$694$	0.786522	+	4.46059i	0.0298560	+	0.169322i
$695$		0			0
$696$	−1.65270	−	2.86257i	−0.0626456	−	0.108505i
$697$	29.1917	−	24.4947i	1.10571	−	0.927803i
$698$	−25.4884	+	9.27704i	−0.964752	+	0.351141i
$699$	0.820727	+	0.298720i	0.0310427	+	0.0112986i
$700$		0			0
$701$	8.21987	−	46.6172i	0.310460	−	1.76071i	−0.286157	−	0.958183i	$-0.592378\pi$
$701$	8.21987	−	46.6172i	0.310460	−	1.76071i	0.596618	−	0.802526i	$-0.296511\pi$
$702$	2.66550			0.100603
$703$	11.1088	+	13.4386i	0.418975	+	0.506846i
$704$	−5.53209			−0.208498
$705$		0			0
$706$	15.1079	+	12.6770i	0.568592	+	0.477106i
$707$	−58.1147	−	21.1520i	−2.18563	−	0.795504i
$708$	−2.11081	+	0.768274i	−0.0793293	+	0.0288735i
$709$	−12.3892	+	10.3958i	−0.465286	+	0.390421i	−0.845071	−	0.534653i	$-0.820442\pi$
$709$	−12.3892	+	10.3958i	−0.465286	+	0.390421i	0.379786	+	0.925074i	$0.375998\pi$
$710$		0			0
$711$	12.7023	−	22.0011i	0.476375	−	0.825105i
$712$	−1.95471	−	11.0857i	−0.0732558	−	0.415454i
$713$	−3.65600	−	20.7342i	−0.136918	−	0.776502i
$714$	−3.10607	+	5.37987i	−0.116242	+	0.201336i
$715$		0			0
$716$	3.68866	−	3.09516i	0.137852	−	0.115671i
$717$	3.03684	−	1.10532i	0.113413	−	0.0412789i
$718$	−20.4884	−	7.45718i	−0.764622	−	0.278300i
$719$	−11.0942	−	9.30915i	−0.413744	−	0.347173i	0.412033	−	0.911169i	$-0.364819\pi$
$719$	−11.0942	−	9.30915i	−0.413744	−	0.347173i	−0.825777	+	0.563996i	$0.809263\pi$
$720$		0			0
$721$	−27.8324			−1.03653
$722$	−17.7565	−	6.76055i	−0.660830	−	0.251601i
$723$	−2.47472			−0.0920358
$724$	0.539830	−	3.06153i	0.0200626	−	0.113781i
$725$		0			0
$726$	6.39780	+	2.32861i	0.237445	+	0.0864228i
$727$	−11.4483	+	4.16684i	−0.424594	+	0.154540i	−0.545475	−	0.838127i	$-0.683651\pi$
$727$	−11.4483	+	4.16684i	−0.424594	+	0.154540i	0.120880	+	0.992667i	$0.461428\pi$
$728$	3.75877	−	3.15398i	0.139309	−	0.116894i
$729$	10.3516	+	17.9296i	0.383394	+	0.664058i
$730$		0			0
$731$	5.95976	+	33.7995i	0.220430	+	1.25012i
$732$	−0.135163	−	0.766546i	−0.00499576	−	0.0283323i
$733$	−24.1584	+	41.8436i	−0.892310	+	1.54553i	−0.0552118	+	0.998475i	$0.517583\pi$
$733$	−24.1584	+	41.8436i	−0.892310	+	1.54553i	−0.837099	+	0.547052i	$0.815750\pi$
$734$	1.83750	+	3.18264i	0.0678232	+	0.117473i
$735$		0			0
$736$	3.10607	−	1.13052i	0.114491	−	0.0416714i
$737$	−64.3431	−	23.4190i	−2.37011	−	0.862649i
$738$	17.6630	+	14.8210i	0.650183	+	0.545568i
$739$	−8.71317	+	49.4149i	−0.320519	+	1.81776i	0.218934	+	0.975740i	$0.429742\pi$
$739$	−8.71317	+	49.4149i	−0.320519	+	1.81776i	−0.539453	+	0.842015i	$0.681369\pi$
$740$		0			0
$741$	1.25908	+	1.52314i	0.0462533	+	0.0559539i
$742$	−6.61081			−0.242691
$743$	−0.0428227	+	0.242860i	−0.00157101	+	0.00890966i	−0.985583	−	0.169192i	$-0.945884\pi$
$743$	−0.0428227	+	0.242860i	−0.00157101	+	0.00890966i	0.984012	+	0.178101i	$0.0569955\pi$
$744$	1.69459	+	1.42193i	0.0621268	+	0.0521306i
$745$		0			0
$746$	−12.3824	+	4.50682i	−0.453351	+	0.165006i
$747$	26.7690	−	22.4619i	0.979428	−	0.821838i
$748$	13.1630	+	22.7989i	0.481286	+	0.833612i
$749$	0.573978	−	0.994159i	0.0209727	−	0.0363258i
$750$		0			0
$751$	−4.00681	−	22.7237i	−0.146210	−	0.829201i	−0.966387	−	0.257091i	$-0.917236\pi$
$751$	−4.00681	−	22.7237i	−0.146210	−	0.829201i	0.820177	−	0.572110i	$-0.193875\pi$
$752$	−6.10607	+	10.5760i	−0.222665	+	0.385668i
$753$	−2.86871	−	4.96875i	−0.104542	−	0.181071i
$754$	9.51754	−	7.98617i	0.346608	−	0.290839i
$755$		0			0
$756$	−7.21213	−	2.62500i	−0.262303	−	0.0954704i
$757$	33.0770	+	27.7549i	1.20220	+	1.00877i	0.999564	+	0.0295145i	$0.00939611\pi$
$757$	33.0770	+	27.7549i	1.20220	+	1.00877i	0.202639	+	0.979254i	$0.435048\pi$
$758$	−1.96080	+	11.1202i	−0.0712194	+	0.403905i
$759$	−6.35059			−0.230512
$760$		0			0
$761$	−26.2499			−0.951558			−0.475779	−	0.879565i	$-0.657834\pi$
$761$	−26.2499			−0.951558			−0.475779	+	0.879565i	$0.657834\pi$
$762$	0.0273411	−	0.155059i	0.000990465	−	0.00561721i
$763$	−44.2276	−	37.1114i	−1.60115	−	1.34352i
$764$	10.0223	+	3.64781i	0.362594	+	0.131973i
$765$		0			0
$766$	19.6759	−	16.5101i	0.710920	−	0.596533i
$767$	−4.22163	−	7.31208i	−0.152434	−	0.264024i
$768$	−0.173648	+	0.300767i	−0.00626599	+	0.0108530i
$769$	−1.61422	−	9.15469i	−0.0582102	−	0.330126i	0.941771	−	0.336255i	$-0.109160\pi$
$769$	−1.61422	−	9.15469i	−0.0582102	−	0.330126i	−0.999981	+	0.00612844i	$0.998049\pi$
$770$		0			0
$771$	−1.54782	+	2.68090i	−0.0557433	+	0.0965503i
$772$	9.37939	+	16.2456i	0.337571	+	0.584691i
$773$	22.5330	−	18.9075i	0.810456	−	0.680054i	−0.140260	−	0.990115i	$-0.544794\pi$
$773$	22.5330	−	18.9075i	0.810456	−	0.680054i	0.950717	+	0.310061i	$0.100349\pi$
$774$	−19.5141	+	7.10257i	−0.701421	+	0.255296i
$775$		0			0
$776$	−5.78699	−	4.85586i	−0.207741	−	0.174315i
$777$	−0.906726	+	5.14230i	−0.0325286	+	0.184479i
$778$	10.3541			0.371213
$779$	−0.256959	+	34.9040i	−0.00920653	+	1.25057i
$780$		0			0
$781$	5.65539	−	32.0733i	0.202366	−	1.14767i
$782$	−12.0496	−	10.1108i	−0.430894	−	0.361563i
$783$	−18.2618	−	6.64674i	−0.652622	−	0.237535i
$784$	−6.69846	+	2.43804i	−0.239231	+	0.0870729i
$785$		0			0
$786$	−0.648833	−	1.12381i	−0.0231431	−	0.0400851i
$787$	26.0005	−	45.0341i	0.926817	−	1.60529i	0.138203	−	0.990404i	$-0.455867\pi$
$787$	26.0005	−	45.0341i	0.926817	−	1.60529i	0.788613	−	0.614889i	$-0.210799\pi$
$788$	1.90167	+	10.7849i	0.0677443	+	0.384197i
$789$	0.593578	+	3.36635i	0.0211319	+	0.119845i
$790$		0			0
$791$	−15.4611	−	26.7794i	−0.549734	−	0.952166i
$792$	−12.2023	+	10.2390i	−0.433591	+	0.363826i
$793$	2.74928	−	1.00065i	0.0976296	−	0.0355343i
$794$	−8.97090	−	3.26514i	−0.318365	−	0.115876i
$795$		0			0
$796$	−1.15570	+	6.55428i	−0.0409626	+	0.232310i
$797$	32.4296			1.14872			0.574358	−	0.818604i	$-0.305252\pi$
$797$	32.4296			1.14872			0.574358	+	0.818604i	$0.305252\pi$
$798$	−1.90673	−	5.36116i	−0.0674974	−	0.189783i
$799$	58.1147			2.05595
$800$		0			0
$801$	−24.8293	−	20.8343i	−0.877302	−	0.736144i
$802$	−28.1498	−	10.2457i	−0.994003	−	0.361787i
$803$	6.04323	−	2.19956i	0.213261	−	0.0776207i
$804$	−3.29292	+	2.76309i	−0.116132	+	0.0974466i
$805$		0			0
$806$	−4.15745	+	7.20092i	−0.146440	+	0.253641i
$807$	−0.504748	−	2.86257i	−0.0177680	−	0.100767i
$808$	2.85710	+	16.2034i	0.100512	+	0.570034i
$809$	−15.6190	+	27.0529i	−0.549136	+	0.951131i	0.449198	+	0.893432i	$0.351710\pi$
$809$	−15.6190	+	27.0529i	−0.549136	+	0.951131i	−0.998334	+	0.0576987i	$0.981624\pi$
$810$		0			0
$811$	−17.1480	+	14.3888i	−0.602146	+	0.505261i	−0.892135	−	0.451769i	$-0.850793\pi$
$811$	−17.1480	+	14.3888i	−0.602146	+	0.505261i	0.289989	+	0.957030i	$0.406349\pi$
$812$	−33.6168	+	12.2355i	−1.17972	+	0.429382i
$813$	−0.416527	−	0.151603i	−0.0146082	−	0.00531696i
$814$	16.9513	+	14.2238i	0.594143	+	0.498545i
$815$		0			0
$816$	1.65270			0.0578562
$817$	−27.1088	−	15.9185i	−0.948415	−	0.556917i
$818$	−24.5963			−0.859988
$819$	2.45336	−	13.9137i	0.0857274	−	0.486185i
$820$		0			0
$821$	16.9949	+	6.18566i	0.593128	+	0.215881i	0.621105	−	0.783728i	$-0.286684\pi$
$821$	16.9949	+	6.18566i	0.593128	+	0.215881i	−0.0279768	+	0.999609i	$0.508906\pi$
$822$	3.37686	−	1.22908i	0.117781	−	0.0428690i
$823$	−40.6049	+	34.0716i	−1.41540	+	1.18766i	−0.461648	+	0.887063i	$0.652742\pi$
$823$	−40.6049	+	34.0716i	−1.41540	+	1.18766i	−0.953751	+	0.300598i	$0.902814\pi$
$824$	3.70233	+	6.41263i	0.128977	+	0.223395i
$825$		0			0
$826$	4.22163	+	23.9420i	0.146889	+	0.833050i
$827$	−1.21641	−	6.89863i	−0.0422989	−	0.239889i	0.956327	−	0.292300i	$-0.0944205\pi$
$827$	−1.21641	−	6.89863i	−0.0422989	−	0.239889i	−0.998626	+	0.0524110i	$0.983309\pi$
$828$	4.75877	−	8.24243i	0.165379	−	0.286444i
$829$	−5.49020	−	9.50931i	−0.190683	−	0.330272i	0.754794	−	0.655962i	$-0.227737\pi$
$829$	−5.49020	−	9.50931i	−0.190683	−	0.330272i	−0.945477	+	0.325690i	$0.894403\pi$
$830$		0			0
$831$	−2.31490	+	0.842556i	−0.0803031	+	0.0292279i
$832$	−1.22668	−	0.446476i	−0.0425275	−	0.0154788i
$833$	25.9859	+	21.8048i	0.900359	+	0.755491i
$834$	−0.118393	+	0.671441i	−0.00409962	+	0.0232501i
$835$		0			0
$836$	−23.7160	−	4.36203i	−0.820235	−	0.150864i
$837$	13.0060			0.449553
$838$	2.05035	−	11.6281i	0.0708280	−	0.401686i
$839$	−10.1284	−	8.49870i	−0.349670	−	0.293408i	0.450988	−	0.892530i	$-0.351072\pi$
$839$	−10.1284	−	8.49870i	−0.349670	−	0.293408i	−0.800657	+	0.599122i	$0.795516\pi$
$840$		0			0
$841$	−57.8696	+	21.0628i	−1.99550	+	0.726304i
$842$	4.66044	−	3.91058i	0.160610	−	0.134767i
$843$	3.58559	+	6.21042i	0.123494	+	0.213898i
$844$	−10.0963	+	17.4872i	−0.347528	+	0.601936i
$845$		0			0
$846$	6.10607	+	34.6292i	0.209931	+	1.19058i
$847$	36.8435	−	63.8148i	1.26596	−	2.19270i
$848$	0.879385	+	1.52314i	0.0301982	+	0.0523048i
$849$	3.76676	−	3.16069i	0.129275	−	0.108474i
$850$		0			0
$851$	−12.4243	−	4.52206i	−0.425898	−	0.155014i
$852$	−1.56624	−	1.31423i	−0.0536584	−	0.0450247i
$853$	−2.41384	+	13.6896i	−0.0826482	+	0.468721i	0.915191	+	0.403020i	$0.132040\pi$
$853$	−2.41384	+	13.6896i	−0.0826482	+	0.468721i	−0.997839	+	0.0657013i	$0.979072\pi$
$854$	−8.42427			−0.288272
$855$		0			0
$856$	−0.305407			−0.0104386
$857$	1.83599	−	10.4124i	0.0627162	−	0.355681i	−0.937259	−	0.348634i	$-0.886646\pi$
$857$	1.83599	−	10.4124i	0.0627162	−	0.355681i	0.999975	−	0.00704736i	$-0.00224326\pi$
$858$	1.92127	+	1.61214i	0.0655912	+	0.0550376i
$859$	−26.7606	−	9.74006i	−0.913059	−	0.332326i	−0.157586	−	0.987505i	$-0.550371\pi$
$859$	−26.7606	−	9.74006i	−0.913059	−	0.332326i	−0.755474	+	0.655179i	$0.772593\pi$
$860$		0			0
$861$	−8.00774	+	6.71929i	−0.272903	+	0.228993i
$862$	−6.51754	−	11.2887i	−0.221988	−	0.384495i
$863$	7.12836	−	12.3467i	0.242652	−	0.420286i	−0.718817	−	0.695200i	$-0.755316\pi$
$863$	7.12836	−	12.3467i	0.242652	−	0.420286i	0.961469	+	0.274914i	$0.0886493\pi$
$864$	0.354570	+	2.01087i	0.0120627	+	0.0684111i
$865$		0			0
$866$	13.2567	−	22.9613i	0.450481	−	0.780257i
$867$	−0.980400	−	1.69810i	−0.0332961	−	0.0576706i
$868$	18.3405	−	15.3895i	0.622517	−	0.522354i
$869$	45.8658	−	16.6938i	1.55589	−	0.566298i
$870$		0			0
$871$	−12.3773	−	10.3858i	−0.419390	−	0.351910i
$872$	−2.66725	+	15.1267i	−0.0903245	+	0.512256i
$873$	−21.7520			−0.736192
$874$	14.2071	−	2.39739i	0.480562	−	0.0810929i
$875$		0			0
$876$	0.0701076	−	0.397600i	0.00236871	−	0.0134336i
$877$	33.3860	+	28.0142i	1.12737	+	0.945972i	0.998953	−	0.0457492i	$-0.0145675\pi$
$877$	33.3860	+	28.0142i	1.12737	+	0.945972i	0.128412	+	0.991721i	$0.459012\pi$
$878$	−33.2841	−	12.1144i	−1.12328	−	0.408841i
$879$	−7.52259	+	2.73800i	−0.253731	+	0.0923505i
$880$		0			0
$881$	−20.3075	−	35.1737i	−0.684178	−	1.18503i	−0.973694	−	0.227858i	$-0.926828\pi$
$881$	−20.3075	−	35.1737i	−0.684178	−	1.18503i	0.289517	−	0.957173i	$-0.406505\pi$
$882$	−10.2626	+	17.7754i	−0.345561	+	0.598529i
$883$	−3.08512	−	17.4966i	−0.103823	−	0.588807i	−0.991684	−	0.128696i	$-0.958921\pi$
$883$	−3.08512	−	17.4966i	−0.103823	−	0.588807i	0.887861	−	0.460111i	$-0.152190\pi$
$884$	1.07873	+	6.11776i	0.0362815	+	0.205762i
$885$		0			0
$886$	−14.8905	−	25.7912i	−0.500257	−	0.866471i
$887$	−16.4534	+	13.8060i	−0.552450	+	0.463560i	−0.875770	−	0.482729i	$-0.839646\pi$
$887$	−16.4534	+	13.8060i	−0.552450	+	0.463560i	0.323320	+	0.946290i	$0.395201\pi$
$888$	1.30541	−	0.475129i	0.0438066	−	0.0159443i
$889$	−1.60132	−	0.582832i	−0.0537065	−	0.0195476i
$890$		0			0
$891$	−7.61691	+	43.1976i	−0.255176	+	1.44717i
$892$	−15.6459			−0.523863
$893$	−34.5158	+	40.5247i	−1.15503	+	1.35611i
$894$	−4.73917			−0.158502
$895$		0			0
$896$	2.87939	+	2.41609i	0.0961935	+	0.0807159i
$897$	−1.40818	−	0.512534i	−0.0470176	−	0.0171130i
$898$	27.3742	−	9.96340i	0.913490	−	0.332483i
$899$	46.4397	−	38.9676i	1.54885	−	1.29964i
$900$		0			0
$901$	4.18479	−	7.24827i	0.139416	−	0.241475i
$902$	7.69253	+	43.6265i	0.256133	+	1.45260i
$903$	−1.63486	−	9.27174i	−0.0544047	−	0.308544i
$904$	−4.11334	+	7.12452i	−0.136808	+	0.236958i
$905$		0			0
$906$	0.433763	−	0.363970i	0.0144108	−	0.0120921i
$907$	−45.2362	+	16.4646i	−1.50204	+	0.546699i	−0.956589	−	0.291440i	$-0.905866\pi$
$907$	−45.2362	+	16.4646i	−1.50204	+	0.546699i	−0.545455	+	0.838140i	$0.683643\pi$
$908$	−8.02956	−	2.92252i	−0.266470	−	0.0969873i
$909$	36.2918	+	30.4524i	1.20372	+	1.01004i
$910$		0			0
$911$	11.8527			0.392696			0.196348	−	0.980534i	$-0.437092\pi$
$911$	11.8527			0.392696			0.196348	+	0.980534i	$0.437092\pi$
$912$	−0.981582	+	1.15247i	−0.0325034	+	0.0381620i
$913$	67.1380			2.22194
$914$	4.07738	−	23.1240i	0.134868	−	0.764873i
$915$		0			0
$916$	3.86484	+	1.40669i	0.127698	+	0.0464782i
$917$	−13.1976	+	4.80353i	−0.435823	+	0.158626i
$918$	7.44356	−	6.24589i	0.245674	−	0.206145i
$919$	−10.2686	−	17.7857i	−0.338729	−	0.586696i	0.645465	−	0.763790i	$-0.276664\pi$
$919$	−10.2686	−	17.7857i	−0.338729	−	0.586696i	−0.984194	+	0.177094i	$0.943330\pi$
$920$		0			0
$921$	−0.254900	−	1.44561i	−0.00839924	−	0.0476345i
$922$	0.896622	+	5.08499i	0.0295287	+	0.167465i
$923$	3.84255	−	6.65549i	0.126479	−	0.219068i
$924$	−3.61081	−	6.25411i	−0.118787	−	0.205745i
$925$		0			0
$926$	−23.6091	+	8.59300i	−0.775842	+	0.282383i
$927$	20.0351	+	7.29217i	0.658038	+	0.239506i
$928$	7.29086	+	6.11776i	0.239334	+	0.200825i
$929$	−3.65523	+	20.7298i	−0.119924	+	0.680124i	0.864270	+	0.503029i	$0.167781\pi$
$929$	−3.65523	+	20.7298i	−0.119924	+	0.680124i	−0.984194	+	0.177095i	$0.943330\pi$
$930$		0			0
$931$	−30.6386	+	5.17015i	−1.00414	+	0.169445i
$932$	−2.51485			−0.0823767
$933$	−0.504748	+	2.86257i	−0.0165247	+	0.0937162i
$934$	−15.7947	−	13.2534i	−0.516819	−	0.433663i
$935$		0			0
$936$	−3.53209	+	1.28558i	−0.115450	+	0.0420203i
$937$	−16.4244	+	13.7817i	−0.536563	+	0.450230i	−0.870360	−	0.492415i	$-0.836114\pi$
$937$	−16.4244	+	13.7817i	−0.536563	+	0.450230i	0.333798	+	0.942645i	$0.391670\pi$
$938$	23.2618	+	40.2906i	0.759524	+	1.31553i
$939$	−3.20146	+	5.54508i	−0.104476	+	0.180957i
$940$		0			0
$941$	4.12836	+	23.4131i	0.134581	+	0.763244i	0.975151	+	0.221542i	$0.0711089\pi$
$941$	4.12836	+	23.4131i	0.134581	+	0.763244i	−0.840570	+	0.541702i	$0.817780\pi$
$942$	−1.08378	+	1.87716i	−0.0353114	+	0.0611611i
$943$	−13.2344	−	22.9227i	−0.430972	−	0.746466i
$944$	4.95471	−	4.15749i	0.161262	−	0.135315i
$945$		0			0
$946$	−37.4920	−	13.6460i	−1.21897	−	0.443669i
$947$	31.0951	+	26.0919i	1.01046	+	0.847874i	0.988398	−	0.151883i	$-0.0485338\pi$
$947$	31.0951	+	26.0919i	1.01046	+	0.847874i	0.0220579	+	0.999757i	$0.492978\pi$
$948$	0.532089	−	3.01763i	0.0172814	−	0.0980079i
$949$	1.51754			0.0492615
$950$		0			0
$951$	10.7784			0.349513
$952$	3.10607	−	17.6154i	0.100668	−	0.570918i
$953$	46.8546	+	39.3157i	1.51777	+	1.27356i	0.846560	+	0.532294i	$0.178670\pi$
$953$	46.8546	+	39.3157i	1.51777	+	1.27356i	0.671210	+	0.741267i	$0.265775\pi$
$954$	4.75877	+	1.73205i	0.154071	+	0.0560772i
$955$		0			0
$956$	−7.12836	+	5.98140i	−0.230547	+	0.193452i
$957$	−9.14290	−	15.8360i	−0.295548	−	0.511904i
$958$	−5.78106	+	10.0131i	−0.186778	+	0.323508i
$959$	−6.75372	−	38.3022i	−0.218089	−	1.23684i
$960$		0			0
$961$	−4.78581	+	8.28926i	−0.154381	+	0.267396i
$962$	2.61081	+	4.52206i	0.0841760	+	0.145797i
$963$	−0.673648	+	0.565258i	−0.0217080	+	0.0182152i
$964$	6.69594	−	2.43712i	0.215662	−	0.0784944i
$965$		0			0
$966$	3.30541	+	2.77357i	0.106350	+	0.0892380i
$967$	8.04189	−	45.6078i	0.258610	−	1.46665i	−0.528024	−	0.849229i	$-0.677067\pi$
$967$	8.04189	−	45.6078i	0.258610	−	1.46665i	0.786634	−	0.617419i	$-0.211822\pi$
$968$	−19.6040			−0.630097
$969$	7.08512	+	1.30315i	0.227607	+	0.0418632i
$970$		0			0
$971$	2.82951	−	16.0469i	0.0908032	−	0.514971i	−0.905150	−	0.425093i	$-0.860241\pi$
$971$	2.82951	−	16.0469i	0.0908032	−	0.514971i	0.995953	−	0.0898774i	$-0.0286475\pi$
$972$	6.80200	+	5.70756i	0.218174	+	0.183070i
$973$	6.93407	+	2.52379i	0.222296	+	0.0809091i
$974$	−4.61081	+	1.67820i	−0.147740	+	0.0537730i
$975$		0			0
$976$	1.12061	+	1.94096i	0.0358700	+	0.0621287i
$977$	3.80675	−	6.59349i	0.121789	−	0.210944i	−0.798684	−	0.601750i	$-0.794470\pi$
$977$	3.80675	−	6.59349i	0.121789	−	0.210944i	0.920473	+	0.390806i	$0.127804\pi$
$978$	0.220285	+	1.24930i	0.00704394	+	0.0399482i
$979$	−10.8136	−	61.3271i	−0.345605	−	1.96002i
$980$		0			0
$981$	22.1138	+	38.3022i	0.706040	+	1.22290i
$982$	−9.80793	+	8.22983i	−0.312984	+	0.262625i
$983$	7.25402	−	2.64025i	0.231367	−	0.0842108i	−0.223735	−	0.974650i	$-0.571825\pi$
$983$	7.25402	−	2.64025i	0.231367	−	0.0842108i	0.455102	+	0.890439i	$0.349603\pi$
$984$	2.61334	+	0.951178i	0.0833103	+	0.0303225i
$985$		0			0
$986$	7.86484	−	44.6037i	0.250467	−	1.42047i
$987$	−15.9418			−0.507433
$988$	−4.90673	−	2.88127i	−0.156104	−	0.0916654i
$989$	23.8390			0.758037
$990$		0			0
$991$	−44.9341	−	37.7042i	−1.42738	−	1.19771i	−0.947243	−	0.320518i	$-0.896143\pi$
$991$	−44.9341	−	37.7042i	−1.42738	−	1.19771i	−0.480135	−	0.877195i	$-0.659412\pi$
$992$	−5.98545	−	2.17853i	−0.190038	−	0.0691683i
$993$	2.80541	−	1.02108i	0.0890269	−	0.0324031i
$994$	−16.9513	+	14.2238i	−0.537663	+	0.451153i
$995$		0			0
$996$	2.10741	−	3.65014i	0.0667759	−	0.115659i
$997$	−10.5021	−	59.5601i	−0.332604	−	1.88629i	−0.449719	−	0.893170i	$-0.648476\pi$
$997$	−10.5021	−	59.5601i	−0.332604	−	1.88629i	0.117115	−	0.993118i	$-0.462635\pi$
$998$	−0.714355	−	4.05131i	−0.0226125	−	0.128242i
$999$	4.08378	−	7.07331i	0.129205	−	0.223790i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.l.c.701.1		6
5.2	odd	4		950.2.u.c.549.1		12
5.3	odd	4		950.2.u.c.549.2		12
5.4	even	2		190.2.k.a.131.1	✓	6
19.9	even	9	inner	950.2.l.c.351.1		6
95.9	even	18		190.2.k.a.161.1	yes	6
95.28	odd	36		950.2.u.c.199.1		12
95.47	odd	36		950.2.u.c.199.2		12
95.54	even	18		3610.2.a.x.1.2		3
95.79	odd	18		3610.2.a.w.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.a.131.1	✓	6	5.4	even	2
190.2.k.a.161.1	yes	6	95.9	even	18
950.2.l.c.351.1		6	19.9	even	9	inner
950.2.l.c.701.1		6	1.1	even	1	trivial
950.2.u.c.199.1		12	95.28	odd	36
950.2.u.c.199.2		12	95.47	odd	36
950.2.u.c.549.1		12	5.2	odd	4
950.2.u.c.549.2		12	5.3	odd	4
3610.2.a.w.1.2		3	95.79	odd	18
3610.2.a.x.1.2		3	95.54	even	18

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 + 0.984808i) q^{2} +(0.266044 + 0.223238i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.266044 + 0.223238i) q^{6} +(1.87939 + 3.25519i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.500000 - 2.83564i) q^{9} +O(q^{10})\)	\(q+(-0.173648 + 0.984808i) q^{2} +(0.266044 + 0.223238i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.266044 + 0.223238i) q^{6} +(1.87939 + 3.25519i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.500000 - 2.83564i) q^{9} +(2.76604 - 4.79093i) q^{11} +(-0.173648 - 0.300767i) q^{12} +(1.00000 - 0.839100i) q^{13} +(-3.53209 + 1.28558i) q^{14} +(0.766044 + 0.642788i) q^{16} +(0.826352 - 4.68647i) q^{17} +2.87939 q^{18} +(2.77719 + 3.35965i) q^{19} +(-0.226682 + 1.28558i) q^{21} +(4.23783 + 3.55596i) q^{22} +(-3.10607 - 1.13052i) q^{23} +(0.326352 - 0.118782i) q^{24} +(0.652704 + 1.13052i) q^{26} +(1.02094 - 1.76833i) q^{27} +(-0.652704 - 3.70167i) q^{28} +(-1.65270 - 9.37295i) q^{29} +(3.18479 + 5.51622i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(1.80541 - 0.657115i) q^{33} +(4.47178 + 1.62760i) q^{34} +(-0.500000 + 2.83564i) q^{36} +4.00000 q^{37} +(-3.79086 + 2.15160i) q^{38} +0.453363 q^{39} +(6.13429 + 5.14728i) q^{41} +(-1.22668 - 0.446476i) q^{42} +(-6.77719 + 2.46669i) q^{43} +(-4.23783 + 3.55596i) q^{44} +(1.65270 - 2.86257i) q^{46} +(2.12061 + 12.0266i) q^{47} +(0.0603074 + 0.342020i) q^{48} +(-3.56418 + 6.17334i) q^{49} +(1.26604 - 1.06234i) q^{51} +(-1.22668 + 0.446476i) q^{52} +(1.65270 + 0.601535i) q^{53} +(1.56418 + 1.31250i) q^{54} +3.75877 q^{56} +(-0.0111444 + 1.51379i) q^{57} +9.51754 q^{58} +(1.12314 - 6.36965i) q^{59} +(2.10607 + 0.766546i) q^{61} +(-5.98545 + 2.17853i) q^{62} +(8.29086 - 6.95686i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.333626 + 1.89209i) q^{66} +(-2.14930 - 12.1893i) q^{67} +(-2.37939 + 4.12122i) q^{68} +(-0.573978 - 0.994159i) q^{69} +(5.53209 - 2.01352i) q^{71} +(-2.70574 - 0.984808i) q^{72} +(0.890530 + 0.747243i) q^{73} +(-0.694593 + 3.93923i) q^{74} +(-1.46064 - 4.10689i) q^{76} +20.7939 q^{77} +(-0.0787257 + 0.446476i) q^{78} +(6.75877 + 5.67128i) q^{79} +(-7.45084 + 2.71188i) q^{81} +(-6.13429 + 5.14728i) q^{82} +(6.06805 + 10.5102i) q^{83} +(0.652704 - 1.13052i) q^{84} +(-1.25237 - 7.10257i) q^{86} +(1.65270 - 2.86257i) q^{87} +(-2.76604 - 4.79093i) q^{88} +(8.62314 - 7.23567i) q^{89} +(4.61081 + 1.67820i) q^{91} +(2.53209 + 2.12467i) q^{92} +(-0.384133 + 2.17853i) q^{93} -12.2121 q^{94} -0.347296 q^{96} +(1.31180 - 7.43961i) q^{97} +(-5.46064 - 4.58202i) q^{98} +(-14.9684 - 5.44804i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{3} + 3 q^{6} + 3 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q - 3 * q^3 + 3 * q^6 + 3 * q^8 - 3 * q^9	\( 6 q - 3 q^{3} + 3 q^{6} + 3 q^{8} - 3 q^{9} + 12 q^{11} + 6 q^{13} - 12 q^{14} + 6 q^{17} + 6 q^{18} + 6 q^{19} + 12 q^{21} + 6 q^{22} + 6 q^{23} + 3 q^{24} + 6 q^{26} + 3 q^{27} - 6 q^{28} - 12 q^{29} + 12 q^{31} + 15 q^{33} + 12 q^{34} - 3 q^{36} + 24 q^{37} + 9 q^{38} - 24 q^{39} + 27 q^{41} + 6 q^{42} - 30 q^{43} - 6 q^{44} + 12 q^{46} + 24 q^{47} + 6 q^{48} - 3 q^{49} + 3 q^{51} + 6 q^{52} + 12 q^{53} - 9 q^{54} + 6 q^{57} + 12 q^{58} + 3 q^{59} - 12 q^{61} + 18 q^{63} - 3 q^{64} + 21 q^{66} + 27 q^{67} - 3 q^{68} + 12 q^{69} + 24 q^{71} - 6 q^{72} - 12 q^{73} + 12 q^{77} - 18 q^{78} + 18 q^{79} - 33 q^{81} - 27 q^{82} - 6 q^{83} + 6 q^{84} - 24 q^{86} + 12 q^{87} - 12 q^{88} + 48 q^{89} + 36 q^{91} + 6 q^{92} - 24 q^{93} - 24 q^{94} - 27 q^{97} - 24 q^{98} - 33 q^{99}+O(q^{100}) \) 6 * q - 3 * q^3 + 3 * q^6 + 3 * q^8 - 3 * q^9 + 12 * q^11 + 6 * q^13 - 12 * q^14 + 6 * q^17 + 6 * q^18 + 6 * q^19 + 12 * q^21 + 6 * q^22 + 6 * q^23 + 3 * q^24 + 6 * q^26 + 3 * q^27 - 6 * q^28 - 12 * q^29 + 12 * q^31 + 15 * q^33 + 12 * q^34 - 3 * q^36 + 24 * q^37 + 9 * q^38 - 24 * q^39 + 27 * q^41 + 6 * q^42 - 30 * q^43 - 6 * q^44 + 12 * q^46 + 24 * q^47 + 6 * q^48 - 3 * q^49 + 3 * q^51 + 6 * q^52 + 12 * q^53 - 9 * q^54 + 6 * q^57 + 12 * q^58 + 3 * q^59 - 12 * q^61 + 18 * q^63 - 3 * q^64 + 21 * q^66 + 27 * q^67 - 3 * q^68 + 12 * q^69 + 24 * q^71 - 6 * q^72 - 12 * q^73 + 12 * q^77 - 18 * q^78 + 18 * q^79 - 33 * q^81 - 27 * q^82 - 6 * q^83 + 6 * q^84 - 24 * q^86 + 12 * q^87 - 12 * q^88 + 48 * q^89 + 36 * q^91 + 6 * q^92 - 24 * q^93 - 24 * q^94 - 27 * q^97 - 24 * q^98 - 33 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more