LMFDB - Embedded newform 322.2.e.d.93.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(93,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("322.93");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.e (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:	$2.57118294509$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.6498455769.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} + 3x^{5} + 25x^{4} - 3x^{3} + 6x^{2} + x + 1 $ x^8 - x^7 + 6x^6 + 3x^5 + 25x^4 - 3x^3 + 6*x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			93.1
Root			$1.33821 + 2.31784i$ of defining polynomial
Character	$\chi$	$=$	322.93
Dual form			322.2.e.d.277.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-1.33821 - 2.31784i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.93020 - 3.34320i) q^{5} -2.67641 q^{6} +(-2.21184 - 1.45181i) q^{7} -1.00000 q^{8} +(-2.08159 + 3.60541i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-1.33821 - 2.31784i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.93020 - 3.34320i) q^{5} -2.67641 q^{6} +(-2.21184 - 1.45181i) q^{7} -1.00000 q^{8} +(-2.08159 + 3.60541i) q^{9} +(-1.93020 - 3.34320i) q^{10} +(3.04616 + 5.27610i) q^{11} +(-1.33821 + 2.31784i) q^{12} +5.97919 q^{13} +(-2.36323 + 1.18960i) q^{14} -10.3320 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.430199 - 0.745126i) q^{17} +(2.08159 + 3.60541i) q^{18} +(-0.556564 + 0.963997i) q^{19} -3.86040 q^{20} +(-0.405176 + 7.06951i) q^{21} +6.09231 q^{22} +(0.500000 - 0.866025i) q^{23} +(1.33821 + 2.31784i) q^{24} +(-4.95133 - 8.57596i) q^{25} +(2.98959 - 5.17813i) q^{26} +3.11313 q^{27} +(-0.151388 + 2.64142i) q^{28} +0.670749 q^{29} +(-5.16600 + 8.94778i) q^{30} +(2.11702 + 3.66678i) q^{31} +(0.500000 + 0.866025i) q^{32} +(8.15277 - 14.1210i) q^{33} -0.860397 q^{34} +(-9.12300 + 4.59234i) q^{35} +4.16317 q^{36} +(1.71078 - 2.96316i) q^{37} +(0.556564 + 0.963997i) q^{38} +(-8.00138 - 13.8588i) q^{39} +(-1.93020 + 3.34320i) q^{40} -9.45817 q^{41} +(5.91979 + 3.88565i) q^{42} -3.73949 q^{43} +(3.04616 - 5.27610i) q^{44} +(8.03575 + 13.9183i) q^{45} +(-0.500000 - 0.866025i) q^{46} +(2.00283 - 3.46900i) q^{47} +2.67641 q^{48} +(2.78447 + 6.42236i) q^{49} -9.90267 q^{50} +(-1.15139 + 1.99426i) q^{51} +(-2.98959 - 5.17813i) q^{52} +(1.01462 + 1.75737i) q^{53} +(1.55656 - 2.69605i) q^{54} +23.5187 q^{55} +(2.21184 + 1.45181i) q^{56} +2.97919 q^{57} +(0.335374 - 0.580886i) q^{58} +(0.580208 + 1.00495i) q^{59} +(5.16600 + 8.94778i) q^{60} +(4.10661 - 7.11286i) q^{61} +4.23403 q^{62} +(9.83853 - 4.95252i) q^{63} +1.00000 q^{64} +(11.5410 - 19.9896i) q^{65} +(-8.15277 - 14.1210i) q^{66} +(0.0278533 + 0.0482434i) q^{67} +(-0.430199 + 0.745126i) q^{68} -2.67641 q^{69} +(-0.584417 + 10.1969i) q^{70} +0.863943 q^{71} +(2.08159 - 3.60541i) q^{72} +(8.46984 + 14.6702i) q^{73} +(-1.71078 - 2.96316i) q^{74} +(-13.2518 + 22.9528i) q^{75} +1.11313 q^{76} +(0.922302 - 16.0923i) q^{77} -16.0028 q^{78} +(-1.24055 + 2.14870i) q^{79} +(1.93020 + 3.34320i) q^{80} +(2.07876 + 3.60051i) q^{81} +(-4.72909 + 8.19102i) q^{82} -1.05005 q^{83} +(6.32497 - 3.18386i) q^{84} -3.32147 q^{85} +(-1.86975 + 3.23850i) q^{86} +(-0.897600 - 1.55469i) q^{87} +(-3.04616 - 5.27610i) q^{88} +(3.44344 - 5.96421i) q^{89} +16.0715 q^{90} +(-13.2250 - 8.68067i) q^{91} -1.00000 q^{92} +(5.66600 - 9.81381i) q^{93} +(-2.00283 - 3.46900i) q^{94} +(2.14856 + 3.72141i) q^{95} +(1.33821 - 2.31784i) q^{96} -12.8932 q^{97} +(6.95416 + 0.799757i) q^{98} -25.3634 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - q^{3} - 4 q^{4} + 5 q^{5} - 2 q^{6} - 3 q^{7} - 8 q^{8} + q^{9}+O(q^{10}) $ 8 * q + 4 * q^2 - q^3 - 4 * q^4 + 5 * q^5 - 2 * q^6 - 3 * q^7 - 8 * q^8 + q^9	\( 8 q + 4 q^{2} - q^{3} - 4 q^{4} + 5 q^{5} - 2 q^{6} - 3 q^{7} - 8 q^{8} + q^{9} - 5 q^{10} + 2 q^{11} - q^{12} + 14 q^{13} + 3 q^{14} - 10 q^{15} - 4 q^{16} + 7 q^{17} - q^{18} + q^{19} - 10 q^{20} - 5 q^{21} + 4 q^{22} + 4 q^{23} + q^{24} - 19 q^{25} + 7 q^{26} + 14 q^{27} + 6 q^{28} - 12 q^{29} - 5 q^{30} + 4 q^{31} + 4 q^{32} + 13 q^{33} + 14 q^{34} - 14 q^{35} - 2 q^{36} - q^{38} - 19 q^{39} - 5 q^{40} - 30 q^{41} + 20 q^{42} - 24 q^{43} + 2 q^{44} + 25 q^{45} - 4 q^{46} + 15 q^{47} + 2 q^{48} + 17 q^{49} - 38 q^{50} - 2 q^{51} - 7 q^{52} - 21 q^{53} + 7 q^{54} + 24 q^{55} + 3 q^{56} - 10 q^{57} - 6 q^{58} + 32 q^{59} + 5 q^{60} + 3 q^{61} + 8 q^{62} + 25 q^{63} + 8 q^{64} + 6 q^{65} - 13 q^{66} - 13 q^{67} + 7 q^{68} - 2 q^{69} + 14 q^{70} - 14 q^{71} - q^{72} + 16 q^{73} - 6 q^{75} - 2 q^{76} + 23 q^{77} - 38 q^{78} - 3 q^{79} + 5 q^{80} - 15 q^{82} + 16 q^{83} + 25 q^{84} - 48 q^{85} - 12 q^{86} + 9 q^{87} - 2 q^{88} + 33 q^{89} + 50 q^{90} - 18 q^{91} - 8 q^{92} + 9 q^{93} - 15 q^{94} + 11 q^{95} + q^{96} - 24 q^{97} + 34 q^{98} - 70 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 - q^3 - 4 * q^4 + 5 * q^5 - 2 * q^6 - 3 * q^7 - 8 * q^8 + q^9 - 5 * q^10 + 2 * q^11 - q^12 + 14 * q^13 + 3 * q^14 - 10 * q^15 - 4 * q^16 + 7 * q^17 - q^18 + q^19 - 10 * q^20 - 5 * q^21 + 4 * q^22 + 4 * q^23 + q^24 - 19 * q^25 + 7 * q^26 + 14 * q^27 + 6 * q^28 - 12 * q^29 - 5 * q^30 + 4 * q^31 + 4 * q^32 + 13 * q^33 + 14 * q^34 - 14 * q^35 - 2 * q^36 - q^38 - 19 * q^39 - 5 * q^40 - 30 * q^41 + 20 * q^42 - 24 * q^43 + 2 * q^44 + 25 * q^45 - 4 * q^46 + 15 * q^47 + 2 * q^48 + 17 * q^49 - 38 * q^50 - 2 * q^51 - 7 * q^52 - 21 * q^53 + 7 * q^54 + 24 * q^55 + 3 * q^56 - 10 * q^57 - 6 * q^58 + 32 * q^59 + 5 * q^60 + 3 * q^61 + 8 * q^62 + 25 * q^63 + 8 * q^64 + 6 * q^65 - 13 * q^66 - 13 * q^67 + 7 * q^68 - 2 * q^69 + 14 * q^70 - 14 * q^71 - q^72 + 16 * q^73 - 6 * q^75 - 2 * q^76 + 23 * q^77 - 38 * q^78 - 3 * q^79 + 5 * q^80 - 15 * q^82 + 16 * q^83 + 25 * q^84 - 48 * q^85 - 12 * q^86 + 9 * q^87 - 2 * q^88 + 33 * q^89 + 50 * q^90 - 18 * q^91 - 8 * q^92 + 9 * q^93 - 15 * q^94 + 11 * q^95 + q^96 - 24 * q^97 + 34 * q^98 - 70 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−1.33821	−	2.31784i	−0.772613	−	1.33821i	−0.936126	−	0.351664i	$-0.885616\pi$
$3$	−1.33821	−	2.31784i	−0.772613	−	1.33821i	0.163513	−	0.986541i	$-0.447717\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.93020	−	3.34320i	0.863211	−	1.49513i	−0.00560159	−	0.999984i	$-0.501783\pi$
$5$	1.93020	−	3.34320i	0.863211	−	1.49513i	0.868813	−	0.495141i	$-0.164884\pi$
$6$	−2.67641			−1.09264
$7$	−2.21184	−	1.45181i	−0.835997	−	0.548734i
$7$	−2.21184	−	1.45181i	−0.835997	−	0.548734i
$8$	−1.00000			−0.353553
$9$	−2.08159	+	3.60541i	−0.693862	+	1.20180i
$10$	−1.93020	−	3.34320i	−0.610382	−	1.05721i
$11$	3.04616	+	5.27610i	0.918451	+	1.59080i	0.801769	+	0.597634i	$0.203892\pi$
$11$	3.04616	+	5.27610i	0.918451	+	1.59080i	0.116682	+	0.993169i	$0.462774\pi$
$12$	−1.33821	+	2.31784i	−0.386307	+	0.669103i
$13$	5.97919			1.65833			0.829164	−	0.559006i	$-0.188817\pi$
$13$	5.97919			1.65833			0.829164	+	0.559006i	$0.188817\pi$
$14$	−2.36323	+	1.18960i	−0.631599	+	0.317935i
$15$	−10.3320			−2.66771
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.430199	−	0.745126i	−0.104338	−	0.180720i	0.809129	−	0.587631i	$-0.199939\pi$
$17$	−0.430199	−	0.745126i	−0.104338	−	0.180720i	−0.913468	+	0.406911i	$0.866606\pi$
$18$	2.08159	+	3.60541i	0.490635	+	0.849804i
$19$	−0.556564	+	0.963997i	−0.127684	+	0.221156i	−0.922779	−	0.385329i	$-0.874088\pi$
$19$	−0.556564	+	0.963997i	−0.127684	+	0.221156i	0.795095	+	0.606485i	$0.207421\pi$
$20$	−3.86040			−0.863211
$21$	−0.405176	+	7.06951i	−0.0884166	+	1.54269i
$22$	6.09231			1.29889
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i
$24$	1.33821	+	2.31784i	0.273160	+	0.473127i
$25$	−4.95133	−	8.57596i	−0.990267	−	1.71519i
$26$	2.98959	−	5.17813i	0.586307	−	1.01551i
$27$	3.11313			0.599122
$28$	−0.151388	+	2.64142i	−0.0286096	+	0.499181i
$29$	0.670749			0.124555			0.0622775	−	0.998059i	$-0.480164\pi$
$29$	0.670749			0.124555			0.0622775	+	0.998059i	$0.480164\pi$
$30$	−5.16600	+	8.94778i	−0.943179	+	1.63363i
$31$	2.11702	+	3.66678i	0.380227	+	0.658573i	0.991095	−	0.133160i	$-0.0425124\pi$
$31$	2.11702	+	3.66678i	0.380227	+	0.658573i	−0.610867	+	0.791733i	$0.709179\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	8.15277	−	14.1210i	1.41921	−	2.45815i
$34$	−0.860397			−0.147557
$35$	−9.12300	+	4.59234i	−1.54207	+	0.776247i
$36$	4.16317			0.693862
$37$	1.71078	−	2.96316i	0.281251	−	0.487141i	−0.690442	−	0.723388i	$-0.742584\pi$
$37$	1.71078	−	2.96316i	0.281251	−	0.487141i	0.971693	+	0.236247i	$0.0759174\pi$
$38$	0.556564	+	0.963997i	0.0902866	+	0.156381i
$39$	−8.00138	−	13.8588i	−1.28125	−	2.21918i
$40$	−1.93020	+	3.34320i	−0.305191	+	0.528607i
$41$	−9.45817			−1.47712			−0.738559	−	0.674189i	$-0.764493\pi$
$41$	−9.45817			−1.47712			−0.738559	+	0.674189i	$0.764493\pi$
$42$	5.91979	+	3.88565i	0.913444	+	0.599569i
$43$	−3.73949			−0.570267			−0.285134	−	0.958488i	$-0.592038\pi$
$43$	−3.73949			−0.570267			−0.285134	+	0.958488i	$0.592038\pi$
$44$	3.04616	−	5.27610i	0.459225	−	0.795402i
$45$	8.03575	+	13.9183i	1.19790	+	2.07482i
$46$	−0.500000	−	0.866025i	−0.0737210	−	0.127688i
$47$	2.00283	−	3.46900i	0.292143	−	0.506006i	−0.682173	−	0.731191i	$-0.738965\pi$
$47$	2.00283	−	3.46900i	0.292143	−	0.506006i	0.974316	+	0.225184i	$0.0722984\pi$
$48$	2.67641			0.386307
$49$	2.78447	+	6.42236i	0.397782	+	0.917480i
$50$	−9.90267			−1.40045
$51$	−1.15139	+	1.99426i	−0.161227	+	0.279253i
$52$	−2.98959	−	5.17813i	−0.414582	−	0.718077i
$53$	1.01462	+	1.75737i	0.139368	+	0.241393i	0.927258	−	0.374424i	$-0.122160\pi$
$53$	1.01462	+	1.75737i	0.139368	+	0.241393i	−0.787889	+	0.615817i	$0.788826\pi$
$54$	1.55656	−	2.69605i	0.211821	−	0.366886i
$55$	23.5187			3.17127
$56$	2.21184	+	1.45181i	0.295570	+	0.194007i
$57$	2.97919			0.394603
$58$	0.335374	−	0.580886i	0.0440368	−	0.0762740i
$59$	0.580208	+	1.00495i	0.0755367	+	0.130833i	0.901320	−	0.433155i	$-0.142600\pi$
$59$	0.580208	+	1.00495i	0.0755367	+	0.130833i	−0.825783	+	0.563988i	$0.809266\pi$
$60$	5.16600	+	8.94778i	0.666928	+	1.15515i
$61$	4.10661	−	7.11286i	0.525797	−	0.910708i	−0.473751	−	0.880659i	$-0.657100\pi$
$61$	4.10661	−	7.11286i	0.525797	−	0.910708i	0.999548	−	0.0300490i	$-0.00956633\pi$
$62$	4.23403			0.537723
$63$	9.83853	−	4.95252i	1.23954	−	0.623959i
$64$	1.00000			0.125000
$65$	11.5410	−	19.9896i	1.43149	−	2.47941i
$66$	−8.15277	−	14.1210i	−1.00354	−	1.73818i
$67$	0.0278533	+	0.0482434i	0.00340283	+	0.00589387i	0.867722	−	0.497050i	$-0.165584\pi$
$67$	0.0278533	+	0.0482434i	0.00340283	+	0.00589387i	−0.864319	+	0.502944i	$0.832250\pi$
$68$	−0.430199	+	0.745126i	−0.0521692	+	0.0903598i
$69$	−2.67641			−0.322202
$70$	−0.584417	+	10.1969i	−0.0698512	+	1.21876i
$71$	0.863943			0.102531			0.0512656	−	0.998685i	$-0.483674\pi$
$71$	0.863943			0.102531			0.0512656	+	0.998685i	$0.483674\pi$
$72$	2.08159	−	3.60541i	0.245317	−	0.424902i
$73$	8.46984	+	14.6702i	0.991319	+	1.71702i	0.609521	+	0.792770i	$0.291362\pi$
$73$	8.46984	+	14.6702i	0.991319	+	1.71702i	0.381799	+	0.924246i	$0.375305\pi$
$74$	−1.71078	−	2.96316i	−0.198874	−	0.344461i
$75$	−13.2518	+	22.9528i	−1.53019	+	2.65036i
$76$	1.11313			0.127684
$77$	0.922302	−	16.0923i	0.105106	−	1.83389i
$78$	−16.0028			−1.81196
$79$	−1.24055	+	2.14870i	−0.139573	+	0.241747i	−0.927335	−	0.374232i	$-0.877906\pi$
$79$	−1.24055	+	2.14870i	−0.139573	+	0.241747i	0.787762	+	0.615980i	$0.211240\pi$
$80$	1.93020	+	3.34320i	0.215803	+	0.373781i
$81$	2.07876	+	3.60051i	0.230973	+	0.400057i
$82$	−4.72909	+	8.19102i	−0.522240	+	0.904546i
$83$	−1.05005			−0.115257			−0.0576287	−	0.998338i	$-0.518354\pi$
$83$	−1.05005			−0.115257			−0.0576287	+	0.998338i	$0.518354\pi$
$84$	6.32497	−	3.18386i	0.690111	−	0.347388i
$85$	−3.32147			−0.360264
$86$	−1.86975	+	3.23850i	−0.201620	+	0.349216i
$87$	−0.897600	−	1.55469i	−0.0962328	−	0.166680i
$88$	−3.04616	−	5.27610i	−0.324721	−	0.562434i
$89$	3.44344	−	5.96421i	0.365004	−	0.632205i	−0.623773	−	0.781605i	$-0.714401\pi$
$89$	3.44344	−	5.96421i	0.365004	−	0.632205i	0.988777	+	0.149401i	$0.0477345\pi$
$90$	16.0715			1.69408
$91$	−13.2250	−	8.68067i	−1.38636	−	0.909981i
$92$	−1.00000			−0.104257
$93$	5.66600	−	9.81381i	0.587537	−	1.01764i
$94$	−2.00283	−	3.46900i	−0.206576	−	0.357801i
$95$	2.14856	+	3.72141i	0.220437	+	0.381809i
$96$	1.33821	−	2.31784i	0.136580	−	0.236563i
$97$	−12.8932			−1.30910			−0.654552	−	0.756017i	$-0.727143\pi$
$97$	−12.8932			−1.30910			−0.654552	+	0.756017i	$0.727143\pi$
$98$	6.95416	+	0.799757i	0.702477	+	0.0807876i
$99$	−25.3634			−2.54911
$100$	−4.95133	+	8.57596i	−0.495133	+	0.857596i
$101$	−1.57012	−	2.71953i	−0.156233	−	0.270603i	0.777274	−	0.629162i	$-0.216602\pi$
$101$	−1.57012	−	2.71953i	−0.156233	−	0.270603i	−0.933507	+	0.358558i	$0.883268\pi$
$102$	1.15139	+	1.99426i	0.114004	+	0.197461i
$103$	1.60924	−	2.78728i	0.158563	−	0.274639i	−0.775788	−	0.630994i	$-0.782647\pi$
$103$	1.60924	−	2.78728i	0.158563	−	0.274639i	0.934351	+	0.356355i	$0.115981\pi$
$104$	−5.97919			−0.586307
$105$	22.8527	+	15.0002i	2.23020	+	1.46386i
$106$	2.02923			0.197096
$107$	0.477093	−	0.826349i	0.0461223	−	0.0798862i	−0.842043	−	0.539411i	$-0.818647\pi$
$107$	0.477093	−	0.826349i	0.0461223	−	0.0798862i	0.888165	+	0.459525i	$0.151980\pi$
$108$	−1.55656	−	2.69605i	−0.149780	−	0.259427i
$109$	6.40267	+	11.0897i	0.613264	+	1.06220i	0.990686	+	0.136163i	$0.0434772\pi$
$109$	6.40267	+	11.0897i	0.613264	+	1.06220i	−0.377422	+	0.926041i	$0.623189\pi$
$110$	11.7594	−	20.3678i	1.12121	−	1.94200i
$111$	−9.15751			−0.869192
$112$	2.36323	−	1.18960i	0.223304	−	0.112407i
$113$	2.53681			0.238643			0.119321	−	0.992856i	$-0.461928\pi$
$113$	2.53681			0.238643			0.119321	+	0.992856i	$0.461928\pi$
$114$	1.48959	−	2.58005i	0.139513	−	0.241644i
$115$	−1.93020	−	3.34320i	−0.179992	−	0.311755i
$116$	−0.335374	−	0.580886i	−0.0311387	−	0.0539339i
$117$	−12.4462	+	21.5574i	−1.15065	+	1.99299i
$118$	1.16042			0.106825
$119$	−0.130254	+	2.27267i	−0.0119403	+	0.208335i
$120$	10.3320			0.943179
$121$	−13.0581	+	22.6174i	−1.18710	+	2.05612i
$122$	−4.10661	−	7.11286i	−0.371795	−	0.643968i
$123$	12.6570	+	21.9225i	1.14124	+	1.97669i
$124$	2.11702	−	3.66678i	0.190114	−	0.329286i
$125$	−18.9262			−1.69281
$126$	0.630254	−	10.9967i	0.0561475	−	0.979662i
$127$	−13.1237			−1.16454			−0.582268	−	0.812997i	$-0.697835\pi$
$127$	−13.1237			−1.16454			−0.582268	+	0.812997i	$0.697835\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	5.00421	+	8.66754i	0.440596	+	0.763135i
$130$	−11.5410	−	19.9896i	−1.01221	−	1.75321i
$131$	6.57790	−	11.3933i	0.574714	−	0.995433i	−0.421359	−	0.906894i	$-0.638447\pi$
$131$	6.57790	−	11.3933i	0.574714	−	0.995433i	0.996073	−	0.0885393i	$-0.0282199\pi$
$132$	−16.3055			−1.41921
$133$	2.63057	−	1.32418i	0.228100	−	0.114821i
$134$	0.0557067			0.00481232
$135$	6.00895	−	10.4078i	0.517168	−	0.895762i
$136$	0.430199	+	0.745126i	0.0368892	+	0.0638940i
$137$	−5.57401	−	9.65447i	−0.476220	−	0.824837i	0.523409	−	0.852082i	$-0.324660\pi$
$137$	−5.57401	−	9.65447i	−0.476220	−	0.824837i	−0.999629	+	0.0272447i	$0.991327\pi$
$138$	−1.33821	+	2.31784i	−0.113916	+	0.197308i
$139$	−1.20309			−0.102044			−0.0510222	−	0.998698i	$-0.516248\pi$
$139$	−1.20309			−0.102044			−0.0510222	+	0.998698i	$0.516248\pi$
$140$	8.53858	+	5.60458i	0.721642	+	0.473673i
$141$	−10.7208			−0.902854
$142$	0.431972	−	0.748197i	0.0362503	−	0.0627873i
$143$	18.2135	+	31.5468i	1.52309	+	2.63807i
$144$	−2.08159	−	3.60541i	−0.173466	−	0.300451i
$145$	1.29468	−	2.24245i	0.107517	−	0.186225i
$146$	16.9397			1.40194
$147$	11.1598	−	15.0484i	0.920445	−	1.24117i
$148$	−3.42156			−0.281251
$149$	−7.33201	+	12.6994i	−0.600661	+	1.04038i	0.392060	+	0.919940i	$0.371763\pi$
$149$	−7.33201	+	12.6994i	−0.600661	+	1.04038i	−0.992721	+	0.120436i	$0.961571\pi$
$150$	13.2518	+	22.9528i	1.08200	+	1.87409i
$151$	−3.05551	−	5.29229i	−0.248654	−	0.430681i	0.714499	−	0.699637i	$-0.246655\pi$
$151$	−3.05551	−	5.29229i	−0.248654	−	0.430681i	−0.963152	+	0.268956i	$0.913321\pi$
$152$	0.556564	−	0.963997i	0.0451433	−	0.0781905i
$153$	3.58198			0.289586
$154$	−13.4752	−	8.84491i	−1.08586	−	0.712743i
$155$	16.3450			1.31287
$156$	−8.00138	+	13.8588i	−0.640623	+	1.10959i
$157$	−0.832544	−	1.44201i	−0.0664442	−	0.115085i	0.830889	−	0.556437i	$-0.187832\pi$
$157$	−0.832544	−	1.44201i	−0.0664442	−	0.115085i	−0.897334	+	0.441353i	$0.854499\pi$
$158$	1.24055	+	2.14870i	0.0986929	+	0.170941i
$159$	2.71553	−	4.70343i	0.215355	−	0.373006i
$160$	3.86040			0.305191
$161$	−2.36323	+	1.18960i	−0.186248	+	0.0937538i
$162$	4.15751			0.326645
$163$	−3.83452	+	6.64158i	−0.300343	+	0.520209i	−0.976214	−	0.216811i	$-0.930434\pi$
$163$	−3.83452	+	6.64158i	−0.300343	+	0.520209i	0.675871	+	0.737020i	$0.263768\pi$
$164$	4.72909	+	8.19102i	0.369280	+	0.639611i
$165$	−31.4729	−	54.5127i	−2.45016	−	4.24381i
$166$	−0.525023	+	0.909366i	−0.0407497	+	0.0705805i
$167$	24.7486			1.91510			0.957550	−	0.288267i	$-0.0930790\pi$
$167$	24.7486			1.91510			0.957550	+	0.288267i	$0.0930790\pi$
$168$	0.405176	−	7.06951i	0.0312600	−	0.545425i
$169$	22.7507			1.75005
$170$	−1.66074	+	2.87648i	−0.127373	+	0.220616i
$171$	−2.31707	−	4.01328i	−0.177191	−	0.306904i
$172$	1.86975	+	3.23850i	0.142567	+	0.246933i
$173$	0.910837	−	1.57762i	0.0692497	−	0.119944i	−0.829322	−	0.558772i	$-0.811273\pi$
$173$	0.910837	−	1.57762i	0.0692497	−	0.119944i	0.898571	+	0.438828i	$0.144606\pi$
$174$	−1.79520			−0.136094
$175$	−1.49914	+	26.1571i	−0.113325	+	1.97729i
$176$	−6.09231			−0.459225
$177$	1.55288	−	2.68966i	0.116721	−	0.202167i
$178$	−3.44344	−	5.96421i	−0.258096	−	0.447036i
$179$	−5.70249	−	9.87700i	−0.426224	−	0.738242i	0.570310	−	0.821430i	$-0.306823\pi$
$179$	−5.70249	−	9.87700i	−0.426224	−	0.738242i	−0.996534	+	0.0831878i	$0.973490\pi$
$180$	8.03575	−	13.9183i	0.598949	−	1.03741i
$181$	0.627006			0.0466050			0.0233025	−	0.999728i	$-0.492582\pi$
$181$	0.627006			0.0466050			0.0233025	+	0.999728i	$0.492582\pi$
$182$	−14.1302	+	7.11286i	−1.04740	+	0.527240i
$183$	−21.9819			−1.62495
$184$	−0.500000	+	0.866025i	−0.0368605	+	0.0638442i
$185$	−6.60430	−	11.4390i	−0.485558	−	0.841011i
$186$	−5.66600	−	9.81381i	−0.415452	−	0.719583i
$187$	2.62090	−	4.53954i	0.191660	−	0.331964i
$188$	−4.00566			−0.292143
$189$	−6.88574	−	4.51968i	−0.500864	−	0.328758i
$190$	4.29711			0.311745
$191$	−3.54070	+	6.13267i	−0.256196	+	0.443744i	−0.965220	−	0.261440i	$-0.915803\pi$
$191$	−3.54070	+	6.13267i	−0.256196	+	0.443744i	0.709024	+	0.705184i	$0.249136\pi$
$192$	−1.33821	−	2.31784i	−0.0965766	−	0.167276i
$193$	10.5081	+	18.2006i	0.756389	+	1.31010i	0.944681	+	0.327992i	$0.106372\pi$
$193$	10.5081	+	18.2006i	0.756389	+	1.31010i	−0.188291	+	0.982113i	$0.560295\pi$
$194$	−6.44659	+	11.1658i	−0.462838	+	0.801659i
$195$	−61.7770			−4.42394
$196$	4.16969	−	5.62260i	0.297835	−	0.401615i
$197$	−0.806121			−0.0574338			−0.0287169	−	0.999588i	$-0.509142\pi$
$197$	−0.806121			−0.0574338			−0.0287169	+	0.999588i	$0.509142\pi$
$198$	−12.6817	+	21.9653i	−0.901248	+	1.56101i
$199$	−7.25800	−	12.5712i	−0.514506	−	0.891150i	−0.999858	−	0.0168316i	$-0.994642\pi$
$199$	−7.25800	−	12.5712i	−0.514506	−	0.891150i	0.485353	−	0.874319i	$-0.338691\pi$
$200$	4.95133	+	8.57596i	0.350112	+	0.606412i
$201$	0.0745470	−	0.129119i	0.00525814	−	0.00910736i
$202$	−3.14024			−0.220947
$203$	−1.48359	−	0.973803i	−0.104128	−	0.0683475i
$204$	2.30278			0.161227
$205$	−18.2561	+	31.6206i	−1.27506	+	2.20848i
$206$	−1.60924	−	2.78728i	−0.112121	−	0.194199i
$207$	2.08159	+	3.60541i	0.144680	+	0.250594i
$208$	−2.98959	+	5.17813i	−0.207291	+	0.359039i
$209$	−6.78152			−0.469088
$210$	24.4169	−	12.2910i	1.68493	−	0.848158i
$211$	24.1903			1.66533			0.832664	−	0.553778i	$-0.186815\pi$
$211$	24.1903			1.66533			0.832664	+	0.553778i	$0.186815\pi$
$212$	1.01462	−	1.75737i	0.0696841	−	0.120696i
$213$	−1.15613	−	2.00248i	−0.0792169	−	0.137208i
$214$	−0.477093	−	0.826349i	−0.0326134	−	0.0564880i
$215$	−7.21796	+	12.5019i	−0.492261	+	0.852621i
$216$	−3.11313			−0.211821
$217$	0.640981	−	11.1838i	0.0435126	−	0.759209i
$218$	12.8053			0.867286
$219$	22.6688	−	39.2634i	1.53181	−	2.65318i
$220$	−11.7594	−	20.3678i	−0.792817	−	1.37320i
$221$	−2.57224	−	4.45525i	−0.173027	−	0.299692i
$222$	−4.57876	+	7.93064i	−0.307306	+	0.532270i
$223$	10.9260			0.731659			0.365829	−	0.930682i	$-0.380785\pi$
$223$	10.9260			0.731659			0.365829	+	0.930682i	$0.380785\pi$
$224$	0.151388	−	2.64142i	0.0101150	−	0.176487i
$225$	41.2265			2.74843
$226$	1.26840	−	2.19694i	0.0843730	−	0.146138i
$227$	−12.8334	−	22.2281i	−0.851782	−	1.47533i	−0.879599	−	0.475716i	$-0.842189\pi$
$227$	−12.8334	−	22.2281i	−0.851782	−	1.47533i	0.0278172	−	0.999613i	$-0.491144\pi$
$228$	−1.48959	−	2.58005i	−0.0986507	−	0.170868i
$229$	−11.2966	+	19.5662i	−0.746499	+	1.29297i	0.202992	+	0.979180i	$0.434933\pi$
$229$	−11.2966	+	19.5662i	−0.746499	+	1.29297i	−0.949491	+	0.313794i	$0.898400\pi$
$230$	−3.86040			−0.254547
$231$	−38.5337	+	19.3971i	−2.53533	+	1.27624i
$232$	−0.670749			−0.0440368
$233$	1.75622	−	3.04187i	0.115054	−	0.199279i	−0.802747	−	0.596319i	$-0.796629\pi$
$233$	1.75622	−	3.04187i	0.115054	−	0.199279i	0.917801	+	0.397040i	$0.129963\pi$
$234$	12.4462	+	21.5574i	0.813633	+	1.40925i
$235$	−7.73172	−	13.3917i	−0.504362	−	0.873580i
$236$	0.580208	−	1.00495i	0.0377684	−	0.0654167i
$237$	6.64044			0.431343
$238$	1.90306	+	1.24914i	0.123357	+	0.0809695i
$239$	2.35218			0.152150			0.0760749	−	0.997102i	$-0.475761\pi$
$239$	2.35218			0.152150			0.0760749	+	0.997102i	$0.475761\pi$
$240$	5.16600	−	8.94778i	0.333464	−	0.577577i
$241$	11.1517	+	19.3153i	0.718345	+	1.24421i	0.961655	+	0.274261i	$0.0884332\pi$
$241$	11.1517	+	19.3153i	0.718345	+	1.24421i	−0.243311	+	0.969948i	$0.578233\pi$
$242$	13.0581	+	22.6174i	0.839409	+	1.45390i
$243$	10.2333	−	17.7246i	0.656466	−	1.13703i
$244$	−8.21322			−0.525797
$245$	26.8458	+	3.08738i	1.71512	+	0.197245i
$246$	25.3139			1.61396
$247$	−3.32780	+	5.76392i	−0.211743	+	0.366749i
$248$	−2.11702	−	3.66678i	−0.134431	−	0.232841i
$249$	1.40518	+	2.43384i	0.0890494	+	0.154238i
$250$	−9.46312	+	16.3906i	−0.598500	+	1.03663i
$251$	−13.7643			−0.868792			−0.434396	−	0.900722i	$-0.643038\pi$
$251$	−13.7643			−0.868792			−0.434396	+	0.900722i	$0.643038\pi$
$252$	−9.20827	−	6.04415i	−0.580067	−	0.380746i
$253$	6.09231			0.383020
$254$	−6.56183	+	11.3654i	−0.411726	+	0.713130i
$255$	4.44481	+	7.69864i	0.278345	+	0.482108i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	5.12954	−	8.88462i	0.319972	−	0.554207i	−0.660510	−	0.750817i	$-0.729660\pi$
$257$	5.12954	−	8.88462i	0.319972	−	0.554207i	0.980482	+	0.196610i	$0.0629932\pi$
$258$	10.0084			0.623097
$259$	−8.08594	+	4.07030i	−0.502436	+	0.252916i
$260$	−23.0820			−1.43149
$261$	−1.39622	+	2.41833i	−0.0864240	+	0.149691i
$262$	−6.57790	−	11.3933i	−0.406384	−	0.703878i
$263$	−7.35400	−	12.7375i	−0.453467	−	0.785428i	0.545132	−	0.838350i	$-0.316480\pi$
$263$	−7.35400	−	12.7375i	−0.453467	−	0.785428i	−0.998599	+	0.0529226i	$0.983146\pi$
$264$	−8.15277	+	14.1210i	−0.501768	+	0.869088i
$265$	7.83364			0.481217
$266$	0.168514	−	2.94023i	0.0103323	−	0.180277i
$267$	−18.4321			−1.12803
$268$	0.0278533	−	0.0482434i	0.00170141	−	0.00294693i
$269$	−2.94902	−	5.10786i	−0.179805	−	0.311432i	0.762009	−	0.647567i	$-0.224213\pi$
$269$	−2.94902	−	5.10786i	−0.179805	−	0.311432i	−0.941814	+	0.336135i	$0.890880\pi$
$270$	−6.00895	−	10.4078i	−0.365693	−	0.633399i
$271$	6.91465	−	11.9765i	0.420035	−	0.727522i	−0.575907	−	0.817515i	$-0.695351\pi$
$271$	6.91465	−	11.9765i	0.420035	−	0.727522i	0.995942	+	0.0899928i	$0.0286844\pi$
$272$	0.860397			0.0521692
$273$	−2.42262	+	42.2699i	−0.146624	+	2.55829i
$274$	−11.1480			−0.673477
$275$	30.1651	−	52.2474i	1.81902	−	3.15064i
$276$	1.33821	+	2.31784i	0.0805505	+	0.139518i
$277$	11.7937	+	20.4274i	0.708618	+	1.22736i	0.965370	+	0.260884i	$0.0840141\pi$
$277$	11.7937	+	20.4274i	0.708618	+	1.22736i	−0.256752	+	0.966477i	$0.582653\pi$
$278$	−0.601543	+	1.04190i	−0.0360782	+	0.0624892i
$279$	−17.6270			−1.05530
$280$	9.12300	−	4.59234i	0.545203	−	0.274445i
$281$	23.2982			1.38985			0.694926	−	0.719082i	$-0.255437\pi$
$281$	23.2982			1.38985			0.694926	+	0.719082i	$0.255437\pi$
$282$	−5.36040	+	9.28448i	−0.319207	+	0.552883i
$283$	15.9014	+	27.5421i	0.945241	+	1.63721i	0.755268	+	0.655416i	$0.227507\pi$
$283$	15.9014	+	27.5421i	0.945241	+	1.63721i	0.189973	+	0.981789i	$0.439160\pi$
$284$	−0.431972	−	0.748197i	−0.0256328	−	0.0443973i
$285$	5.75042	−	9.96002i	0.340626	−	0.589981i
$286$	36.4271			2.15398
$287$	20.9200	+	13.7315i	1.23487	+	0.810545i
$288$	−4.16317			−0.245317
$289$	8.12986	−	14.0813i	0.478227	−	0.828313i
$290$	−1.29468	−	2.24245i	−0.0760261	−	0.131681i
$291$	17.2537	+	29.8843i	1.01143	+	1.75185i
$292$	8.46984	−	14.6702i	0.495660	−	0.858508i
$293$	−17.6327			−1.03011			−0.515056	−	0.857157i	$-0.672229\pi$
$293$	−17.6327			−1.03011			−0.515056	+	0.857157i	$0.672229\pi$
$294$	−7.45239	−	17.1889i	−0.434632	−	1.00248i
$295$	4.47967			0.260816
$296$	−1.71078	+	2.96316i	−0.0994372	+	0.172230i
$297$	9.48307	+	16.4252i	0.550264	+	0.953085i
$298$	7.33201	+	12.6994i	0.424732	+	0.735657i
$299$	2.98959	−	5.17813i	0.172893	−	0.299459i
$300$	26.5036			1.53019
$301$	8.27116	+	5.42905i	0.476742	+	0.312925i
$302$	−6.11101			−0.351649
$303$	−4.20229	+	7.27858i	−0.241415	+	0.418143i
$304$	−0.556564	−	0.963997i	−0.0319211	−	0.0552890i
$305$	−15.8531	−	27.4584i	−0.907748	−	1.57227i
$306$	1.79099	−	3.10209i	0.102384	−	0.177335i
$307$	−12.2618			−0.699817			−0.349909	−	0.936784i	$-0.613787\pi$
$307$	−12.2618			−0.699817			−0.349909	+	0.936784i	$0.613787\pi$
$308$	−14.3975	+	7.24743i	−0.820375	+	0.412961i
$309$	−8.61397			−0.490032
$310$	8.17252	−	14.1552i	0.464168	−	0.803963i
$311$	−1.61030	−	2.78912i	−0.0913116	−	0.158156i	0.816752	−	0.576989i	$-0.195773\pi$
$311$	−1.61030	−	2.78912i	−0.0913116	−	0.158156i	−0.908063	+	0.418833i	$0.862439\pi$
$312$	8.00138	+	13.8588i	0.452989	+	0.784600i
$313$	10.6596	−	18.4630i	0.602516	−	1.04359i	−0.389922	−	0.920848i	$-0.627498\pi$
$313$	10.6596	−	18.4630i	0.602516	−	1.04359i	0.992439	−	0.122741i	$-0.0391686\pi$
$314$	−1.66509			−0.0939663
$315$	2.43303	−	42.4515i	0.137086	−	2.39187i
$316$	2.48110			0.139573
$317$	−8.40227	+	14.5532i	−0.471919	+	0.817387i	−0.999484	−	0.0321277i	$-0.989772\pi$
$317$	−8.40227	+	14.5532i	−0.471919	+	0.817387i	0.527565	+	0.849515i	$0.323105\pi$
$318$	−2.71553	−	4.70343i	−0.152279	−	0.263755i
$319$	2.04321	+	3.53894i	0.114398	+	0.198142i
$320$	1.93020	−	3.34320i	0.107901	−	0.186891i
$321$	−2.55379			−0.142539
$322$	−0.151388	+	2.64142i	−0.00843651	+	0.147200i
$323$	0.957732			0.0532896
$324$	2.07876	−	3.60051i	0.115486	−	0.200028i
$325$	−29.6049	−	51.2773i	−1.64219	−	2.84435i
$326$	3.83452	+	6.64158i	0.212374	+	0.367843i
$327$	17.1362	−	29.6807i	0.947632	−	1.64135i
$328$	9.45817			0.522240
$329$	−9.46629	+	4.76515i	−0.521893	+	0.262711i
$330$	−62.9458			−3.46505
$331$	−4.79448	+	8.30429i	−0.263529	+	0.456445i	−0.967177	−	0.254103i	$-0.918220\pi$
$331$	−4.79448	+	8.30429i	−0.263529	+	0.456445i	0.703648	+	0.710548i	$0.251553\pi$
$332$	0.525023	+	0.909366i	0.0288144	+	0.0499079i
$333$	7.12228	+	12.3362i	0.390299	+	0.676017i
$334$	12.3743	−	21.4329i	0.677090	−	1.17275i
$335$	0.215050			0.0117494
$336$	−5.91979	−	3.88565i	−0.322951	−	0.211980i
$337$	−7.98011			−0.434704			−0.217352	−	0.976093i	$-0.569742\pi$
$337$	−7.98011			−0.434704			−0.217352	+	0.976093i	$0.569742\pi$
$338$	11.3753	−	19.7027i	0.618737	−	1.07168i
$339$	−3.39477	−	5.87991i	−0.184379	−	0.319353i
$340$	1.66074	+	2.87648i	0.0900661	+	0.155999i
$341$	−12.8975	+	22.3392i	−0.698440	+	1.20973i
$342$	−4.63414			−0.250586
$343$	3.16527	−	18.2478i	0.170908	−	0.985287i
$344$	3.73949			0.201620
$345$	−5.16600	+	8.94778i	−0.278128	+	0.481732i
$346$	−0.910837	−	1.57762i	−0.0489669	−	0.0848132i
$347$	10.9079	+	18.8931i	0.585568	+	1.01423i	0.994804	+	0.101806i	$0.0324620\pi$
$347$	10.9079	+	18.8931i	0.585568	+	1.01423i	−0.409236	+	0.912429i	$0.634205\pi$
$348$	−0.897600	+	1.55469i	−0.0481164	+	0.0833400i
$349$	11.6542			0.623833			0.311917	−	0.950109i	$-0.399029\pi$
$349$	11.6542			0.623833			0.311917	+	0.950109i	$0.399029\pi$
$350$	21.9031	+	14.3768i	1.17077	+	0.768474i
$351$	18.6140			0.993540
$352$	−3.04616	+	5.27610i	−0.162361	+	0.281217i
$353$	−1.85690	−	3.21625i	−0.0988330	−	0.171184i	0.812369	−	0.583144i	$-0.198178\pi$
$353$	−1.85690	−	3.21625i	−0.0988330	−	0.171184i	−0.911202	+	0.411960i	$0.864844\pi$
$354$	−1.55288	−	2.68966i	−0.0825344	−	0.142954i
$355$	1.66758	−	2.88834i	0.0885061	−	0.153297i
$356$	−6.88687			−0.365004
$357$	5.44198	−	2.73939i	0.288020	−	0.144984i
$358$	−11.4050			−0.602772
$359$	−5.79909	+	10.0443i	−0.306064	+	0.530119i	−0.977498	−	0.210946i	$-0.932346\pi$
$359$	−5.79909	+	10.0443i	−0.306064	+	0.530119i	0.671434	+	0.741065i	$0.265679\pi$
$360$	−8.03575	−	13.9183i	−0.423521	−	0.733560i
$361$	8.88047	+	15.3814i	0.467393	+	0.809549i
$362$	0.313503	−	0.543003i	0.0164773	−	0.0285396i
$363$	69.8979			3.66869
$364$	−0.905176	+	15.7935i	−0.0474441	+	0.827805i
$365$	65.3939			3.42287
$366$	−10.9910	+	19.0369i	−0.574507	+	0.995076i
$367$	1.82780	+	3.16584i	0.0954103	+	0.165255i	0.909780	−	0.415091i	$-0.136250\pi$
$367$	1.82780	+	3.16584i	0.0954103	+	0.165255i	−0.814369	+	0.580347i	$0.802917\pi$
$368$	0.500000	+	0.866025i	0.0260643	+	0.0451447i
$369$	19.6880	−	34.1006i	1.02492	−	1.77521i
$370$	−13.2086			−0.686682
$371$	0.307201	−	5.36005i	0.0159491	−	0.278280i
$372$	−11.3320			−0.587537
$373$	−1.91307	+	3.31354i	−0.0990551	+	0.171569i	−0.911294	−	0.411757i	$-0.864915\pi$
$373$	−1.91307	+	3.31354i	−0.0990551	+	0.171569i	0.812239	+	0.583325i	$0.198249\pi$
$374$	−2.62090	−	4.53954i	−0.135524	−	0.234734i
$375$	25.3272	+	43.8680i	1.30789	+	2.26533i
$376$	−2.00283	+	3.46900i	−0.103288	+	0.178900i
$377$	4.01053			0.206553
$378$	−7.35703	+	3.70338i	−0.378405	+	0.190482i
$379$	−7.57829			−0.389270			−0.194635	−	0.980876i	$-0.562352\pi$
$379$	−7.57829			−0.389270			−0.194635	+	0.980876i	$0.562352\pi$
$380$	2.14856	−	3.72141i	0.110219	−	0.190904i
$381$	17.5622	+	30.4185i	0.899736	+	1.55839i
$382$	3.54070	+	6.13267i	0.181158	+	0.313774i
$383$	−3.22264	+	5.58178i	−0.164669	+	0.285216i	−0.936538	−	0.350567i	$-0.885989\pi$
$383$	−3.22264	+	5.58178i	−0.164669	+	0.285216i	0.771868	+	0.635782i	$0.219322\pi$
$384$	−2.67641			−0.136580
$385$	−52.0197	−	34.1448i	−2.65117	−	1.74018i
$386$	21.0162			1.06970
$387$	7.78408	−	13.4824i	0.395687	−	0.685350i
$388$	6.44659	+	11.1658i	0.327276	+	0.566858i
$389$	−6.92948	−	12.0022i	−0.351339	−	0.608537i	0.635146	−	0.772392i	$-0.280940\pi$
$389$	−6.92948	−	12.0022i	−0.351339	−	0.608537i	−0.986484	+	0.163856i	$0.947607\pi$
$390$	−30.8885	+	53.5004i	−1.56410	+	2.70910i
$391$	−0.860397			−0.0435121
$392$	−2.78447	−	6.42236i	−0.140637	−	0.324378i
$393$	−35.2103			−1.77613
$394$	−0.403061	+	0.698121i	−0.0203059	+	0.0351709i
$395$	4.78902	+	8.29482i	0.240962	+	0.417358i
$396$	12.6817	+	21.9653i	0.637278	+	1.10380i
$397$	−13.7830	+	23.8729i	−0.691750	+	1.19815i	0.279514	+	0.960142i	$0.409827\pi$
$397$	−13.7830	+	23.8729i	−0.691750	+	1.19815i	−0.971264	+	0.238004i	$0.923507\pi$
$398$	−14.5160			−0.727621
$399$	−6.58948	−	4.32522i	−0.329887	−	0.216532i
$400$	9.90267			0.495133
$401$	−16.9164	+	29.3001i	−0.844766	+	1.46318i	0.0410584	+	0.999157i	$0.486927\pi$
$401$	−16.9164	+	29.3001i	−0.844766	+	1.46318i	−0.885824	+	0.464021i	$0.846406\pi$
$402$	−0.0745470	−	0.129119i	−0.00371806	−	0.00643988i
$403$	12.6580	+	21.9244i	0.630541	+	1.09213i
$404$	−1.57012	+	2.71953i	−0.0781165	+	0.135302i
$405$	16.0496			0.797513
$406$	−1.58513	+	0.797925i	−0.0786688	+	0.0396003i
$407$	20.8452			1.03326
$408$	1.15139	−	1.99426i	0.0570022	−	0.0987307i
$409$	−9.43072	−	16.3345i	−0.466319	−	0.807688i	0.532941	−	0.846152i	$-0.321087\pi$
$409$	−9.43072	−	16.3345i	−0.466319	−	0.807688i	−0.999260	+	0.0384641i	$0.987753\pi$
$410$	18.2561	+	31.6206i	0.901607	+	1.56163i
$411$	−14.9183	+	25.8393i	−0.735867	+	1.27456i
$412$	−3.21848			−0.158563
$413$	0.175673	−	3.06514i	0.00864430	−	0.150826i
$414$	4.16317			0.204609
$415$	−2.02680	+	3.51051i	−0.0994915	+	0.172324i
$416$	2.98959	+	5.17813i	0.146577	+	0.253879i
$417$	1.60998	+	2.78856i	0.0788409	+	0.136556i
$418$	−3.39076	+	5.87297i	−0.165848	+	0.287256i
$419$	−35.1574			−1.71755			−0.858775	−	0.512353i	$-0.828774\pi$
$419$	−35.1574			−1.71755			−0.858775	+	0.512353i	$0.828774\pi$
$420$	1.56414	−	27.2911i	0.0763222	−	1.33167i
$421$	−28.1241			−1.37068			−0.685341	−	0.728222i	$-0.740347\pi$
$421$	−28.1241			−1.37068			−0.685341	+	0.728222i	$0.740347\pi$
$422$	12.0951	−	20.9494i	0.588782	−	1.01980i
$423$	8.33813	+	14.4421i	0.405414	+	0.702197i
$424$	−1.01462	−	1.75737i	−0.0492741	−	0.0853452i
$425$	−4.26011	+	7.37873i	−0.206646	+	0.357921i
$426$	−2.31227			−0.112030
$427$	−19.4097	+	9.77047i	−0.939301	+	0.472826i
$428$	−0.954185			−0.0461223
$429$	48.7469	−	84.4321i	2.35352	−	4.07642i
$430$	7.21796	+	12.5019i	0.348081	+	0.602894i
$431$	2.88793	+	5.00204i	0.139107	+	0.240940i	0.927159	−	0.374669i	$-0.122244\pi$
$431$	2.88793	+	5.00204i	0.139107	+	0.240940i	−0.788052	+	0.615609i	$0.788910\pi$
$432$	−1.55656	+	2.69605i	−0.0748902	+	0.129714i
$433$	−28.9576			−1.39161			−0.695806	−	0.718229i	$-0.744953\pi$
$433$	−28.9576			−1.39161			−0.695806	+	0.718229i	$0.744953\pi$
$434$	−9.36500	−	6.14703i	−0.449534	−	0.295067i
$435$	−6.93018			−0.332277
$436$	6.40267	−	11.0897i	0.306632	−	0.531102i
$437$	0.556564	+	0.963997i	0.0266241	+	0.0461142i
$438$	−22.6688	−	39.2634i	−1.08316	−	1.87608i
$439$	−8.40340	+	14.5551i	−0.401073	+	0.694678i	−0.993856	−	0.110684i	$-0.964696\pi$
$439$	−8.40340	+	14.5551i	−0.401073	+	0.694678i	0.592783	+	0.805362i	$0.298029\pi$
$440$	−23.5187			−1.12121
$441$	−28.9514	−	3.32952i	−1.37864	−	0.158549i
$442$	−5.14447			−0.244698
$443$	−5.00824	+	8.67452i	−0.237949	+	0.412139i	−0.960126	−	0.279569i	$-0.909808\pi$
$443$	−5.00824	+	8.67452i	−0.237949	+	0.412139i	0.722177	+	0.691708i	$0.243142\pi$
$444$	4.57876	+	7.93064i	0.217298	+	0.376371i
$445$	−13.2930	−	23.0242i	−0.630150	−	1.09145i
$446$	5.46300	−	9.46219i	0.258680	−	0.448048i
$447$	39.2469			1.85632
$448$	−2.21184	−	1.45181i	−0.104500	−	0.0685918i
$449$	−36.6615			−1.73016			−0.865082	−	0.501631i	$-0.832734\pi$
$449$	−36.6615			−1.73016			−0.865082	+	0.501631i	$0.832734\pi$
$450$	20.6133	−	35.7032i	0.971718	−	1.68307i
$451$	−28.8111	−	49.9022i	−1.35666	−	2.34980i
$452$	−1.26840	−	2.19694i	−0.0596607	−	0.103335i
$453$	−8.17779	+	14.1643i	−0.384226	+	0.665499i
$454$	−25.6668			−1.20460
$455$	−54.5481	+	27.4584i	−2.55725	+	1.28727i
$456$	−2.97919			−0.139513
$457$	13.6998	−	23.7287i	0.640849	−	1.10998i	−0.344395	−	0.938825i	$-0.611916\pi$
$457$	13.6998	−	23.7287i	0.640849	−	1.10998i	0.985244	−	0.171158i	$-0.0547507\pi$
$458$	11.2966	+	19.5662i	0.527854	+	0.914271i
$459$	−1.33926	−	2.31967i	−0.0625114	−	0.108273i
$460$	−1.93020	+	3.34320i	−0.0899960	+	0.155878i
$461$	−21.7137			−1.01131			−0.505653	−	0.862737i	$-0.668748\pi$
$461$	−21.7137			−1.01131			−0.505653	+	0.862737i	$0.668748\pi$
$462$	−2.46846	+	43.0697i	−0.114843	+	2.00378i
$463$	39.3093			1.82686			0.913430	−	0.406996i	$-0.133424\pi$
$463$	39.3093			1.82686			0.913430	+	0.406996i	$0.133424\pi$
$464$	−0.335374	+	0.580886i	−0.0155694	+	0.0269669i
$465$	−21.8730	−	37.8852i	−1.01434	−	1.75688i
$466$	−1.75622	−	3.04187i	−0.0813555	−	0.140912i
$467$	11.0602	−	19.1568i	0.511804	−	0.886470i	−0.488102	−	0.872786i	$-0.662311\pi$
$467$	11.0602	−	19.1568i	0.511804	−	0.886470i	0.999906	−	0.0136841i	$-0.00435591\pi$
$468$	24.8924			1.15065
$469$	0.00843331	−	0.147145i	0.000389414	−	0.00679450i
$470$	−15.4634			−0.713275
$471$	−2.22823	+	3.85941i	−0.102671	+	0.177832i
$472$	−0.580208	−	1.00495i	−0.0267063	−	0.0462566i
$473$	−11.3911	−	19.7299i	−0.523762	−	0.907183i
$474$	3.32022	−	5.75079i	0.152503	−	0.264143i
$475$	11.0229			0.505767
$476$	2.03331	−	1.02353i	0.0931968	−	0.0469134i
$477$	−8.44804			−0.386809
$478$	1.17609	−	2.03705i	0.0537931	−	0.0931724i
$479$	−2.27229	−	3.93573i	−0.103824	−	0.179828i	0.809433	−	0.587212i	$-0.199774\pi$
$479$	−2.27229	−	3.93573i	−0.103824	−	0.179828i	−0.913257	+	0.407384i	$0.866441\pi$
$480$	−5.16600	−	8.94778i	−0.235795	−	0.408408i
$481$	10.2291	−	17.7173i	0.466406	−	0.807839i
$482$	22.3034			1.01589
$483$	5.91979	+	3.88565i	0.269360	+	0.176803i
$484$	26.1163			1.18710
$485$	−24.8864	+	43.1045i	−1.13003	+	1.95727i
$486$	−10.2333	−	17.7246i	−0.464192	−	0.804004i
$487$	13.4897	+	23.3649i	0.611277	+	1.05876i	0.991025	+	0.133673i	$0.0426773\pi$
$487$	13.4897	+	23.3649i	0.611277	+	1.05876i	−0.379748	+	0.925090i	$0.623989\pi$
$488$	−4.10661	+	7.11286i	−0.185897	+	0.321984i
$489$	20.5255			0.928194
$490$	16.0967	−	21.7055i	0.727173	−	0.980554i
$491$	33.2684			1.50138			0.750690	−	0.660654i	$-0.229721\pi$
$491$	33.2684			1.50138			0.750690	+	0.660654i	$0.229721\pi$
$492$	12.6570	−	21.9225i	0.570620	−	0.988344i
$493$	−0.288555	−	0.499792i	−0.0129959	−	0.0225095i
$494$	3.32780	+	5.76392i	0.149725	+	0.259331i
$495$	−48.9563	+	84.7948i	−2.20042	+	3.81124i
$496$	−4.23403			−0.190114
$497$	−1.91090	−	1.25428i	−0.0857158	−	0.0562624i
$498$	2.81035			0.125935
$499$	−9.86704	+	17.0902i	−0.441709	+	0.765063i	−0.997816	−	0.0660478i	$-0.978961\pi$
$499$	−9.86704	+	17.0902i	−0.441709	+	0.765063i	0.556107	+	0.831111i	$0.312294\pi$
$500$	9.46312	+	16.3906i	0.423203	+	0.733010i
$501$	−33.1186	−	57.3632i	−1.47963	−	2.56280i
$502$	−6.88213	+	11.9202i	−0.307164	+	0.532024i
$503$	−20.8367			−0.929062			−0.464531	−	0.885557i	$-0.653777\pi$
$503$	−20.8367			−0.929062			−0.464531	+	0.885557i	$0.653777\pi$
$504$	−9.83853	+	4.95252i	−0.438243	+	0.220603i
$505$	−12.1226			−0.539448
$506$	3.04616	−	5.27610i	0.135418	−	0.234551i
$507$	−30.4451	−	52.7324i	−1.35211	−	2.34193i
$508$	6.56183	+	11.3654i	0.291134	+	0.504259i
$509$	8.24515	−	14.2810i	0.365460	−	0.632995i	−0.623390	−	0.781911i	$-0.714245\pi$
$509$	8.24515	−	14.2810i	0.365460	−	0.632995i	0.988850	+	0.148916i	$0.0475784\pi$
$510$	8.88963			0.393639
$511$	2.56446	−	44.7447i	0.113445	−	1.97939i
$512$	−1.00000			−0.0441942
$513$	−1.73265	+	3.00104i	−0.0764985	+	0.132499i
$514$	−5.12954	−	8.88462i	−0.226254	−	0.391884i
$515$	−6.21230	−	10.7600i	−0.273747	−	0.474143i
$516$	5.00421	−	8.66754i	0.220298	−	0.381567i
$517$	24.4037			1.07328
$518$	−0.517983	+	9.03778i	−0.0227589	+	0.397097i
$519$	−4.87555			−0.214013
$520$	−11.5410	+	19.9896i	−0.506107	+	0.876603i
$521$	14.9196	+	25.8415i	0.653638	+	1.13213i	0.982233	+	0.187664i	$0.0600916\pi$
$521$	14.9196	+	25.8415i	0.653638	+	1.13213i	−0.328595	+	0.944471i	$0.606575\pi$
$522$	1.39622	+	2.41833i	0.0611110	+	0.105847i
$523$	−15.8845	+	27.5127i	−0.694580	+	1.20305i	0.275742	+	0.961232i	$0.411076\pi$
$523$	−15.8845	+	27.5127i	−0.694580	+	1.20305i	−0.970322	+	0.241816i	$0.922257\pi$
$524$	−13.1558			−0.574714
$525$	62.6340	−	31.5287i	2.73357	−	1.37603i
$526$	−14.7080			−0.641299
$527$	1.82147	−	3.15489i	0.0793447	−	0.137429i
$528$	8.15277	+	14.1210i	0.354804	+	0.614538i
$529$	−0.500000	−	0.866025i	−0.0217391	−	0.0376533i
$530$	3.91682	−	6.78413i	0.170136	−	0.294684i
$531$	−4.83102			−0.209648
$532$	−2.46206	−	1.61605i	−0.106744	−	0.0700648i
$533$	−56.5522			−2.44955
$534$	−9.21605	+	15.9627i	−0.398817	+	0.690772i
$535$	−1.84177	−	3.19003i	−0.0796265	−	0.137917i
$536$	−0.0278533	−	0.0482434i	−0.00120308	−	0.00208380i
$537$	−15.2622	+	26.4349i	−0.658613	+	1.14075i
$538$	−5.89805			−0.254283
$539$	−25.4031	+	34.2547i	−1.09419	+	1.47545i
$540$	−12.0179			−0.517168
$541$	8.47953	−	14.6870i	0.364563	−	0.631442i	−0.624143	−	0.781310i	$-0.714552\pi$
$541$	8.47953	−	14.6870i	0.364563	−	0.631442i	0.988706	+	0.149868i	$0.0478849\pi$
$542$	−6.91465	−	11.9765i	−0.297010	−	0.514436i
$543$	−0.839062	−	1.45330i	−0.0360076	−	0.0623670i
$544$	0.430199	−	0.745126i	0.0184446	−	0.0319470i
$545$	49.4337			2.11751
$546$	35.3955	+	23.2330i	1.51479	+	0.994282i
$547$	29.7635			1.27259			0.636297	−	0.771444i	$-0.280465\pi$
$547$	29.7635			1.27259			0.636297	+	0.771444i	$0.280465\pi$
$548$	−5.57401	+	9.65447i	−0.238110	+	0.412418i
$549$	17.0965	+	29.6120i	0.729662	+	1.26381i
$550$	−30.1651	−	52.2474i	−1.28624	−	2.22784i
$551$	−0.373315	+	0.646600i	−0.0159037	+	0.0275461i
$552$	2.67641			0.113916
$553$	5.86341	−	2.95152i	0.249337	−	0.125512i
$554$	23.5875			1.00214
$555$	−17.6758	+	30.6154i	−0.750297	+	1.29955i
$556$	0.601543	+	1.04190i	0.0255111	+	0.0441865i
$557$	−23.1684	−	40.1289i	−0.981678	−	1.70032i	−0.655857	−	0.754885i	$-0.727693\pi$
$557$	−23.1684	−	40.1289i	−0.981678	−	1.70032i	−0.325821	−	0.945431i	$-0.605641\pi$
$558$	−8.81350	+	15.2654i	−0.373105	+	0.646237i
$559$	−22.3591			−0.945690
$560$	0.584417	−	10.1969i	0.0246961	−	0.430898i
$561$	−14.0292			−0.592315
$562$	11.6491	−	20.1768i	0.491387	−	0.851107i
$563$	−8.18799	−	14.1820i	−0.345083	−	0.597701i	0.640286	−	0.768137i	$-0.278816\pi$
$563$	−8.18799	−	14.1820i	−0.345083	−	0.597701i	−0.985369	+	0.170436i	$0.945483\pi$
$564$	5.36040	+	9.28448i	0.225713	+	0.390947i
$565$	4.89654	−	8.48106i	0.205999	−	0.356801i
$566$	31.8028			1.33677
$567$	0.629397	−	10.9817i	0.0264322	−	0.461189i
$568$	−0.863943			−0.0362503
$569$	11.7859	−	20.4137i	0.494089	−	0.855786i	−0.505888	−	0.862599i	$-0.668835\pi$
$569$	11.7859	−	20.4137i	0.494089	−	0.855786i	0.999977	+	0.00681257i	$0.00216853\pi$
$570$	−5.75042	−	9.96002i	−0.240859	−	0.417179i
$571$	5.81180	+	10.0663i	0.243216	+	0.421263i	0.961629	−	0.274354i	$-0.0884641\pi$
$571$	5.81180	+	10.0663i	0.243216	+	0.421263i	−0.718412	+	0.695618i	$0.755131\pi$
$572$	18.2135	−	31.5468i	0.761546	−	1.31904i
$573$	18.9527			0.791761
$574$	22.3518	−	11.2515i	0.932947	−	0.469627i
$575$	−9.90267			−0.412970
$576$	−2.08159	+	3.60541i	−0.0867328	+	0.150226i
$577$	−13.3214	−	23.0733i	−0.554577	−	0.960556i	−0.997936	−	0.0642117i	$-0.979547\pi$
$577$	−13.3214	−	23.0733i	−0.554577	−	0.960556i	0.443359	−	0.896344i	$-0.353787\pi$
$578$	−8.12986	−	14.0813i	−0.338158	−	0.585706i
$579$	28.1240	−	48.7122i	1.16879	−	2.02441i
$580$	−2.58936			−0.107517
$581$	2.32253	+	1.52447i	0.0963549	+	0.0632457i
$582$	34.5074			1.43038
$583$	−6.18136	+	10.7064i	−0.256006	+	0.443415i
$584$	−8.46984	−	14.6702i	−0.350484	−	0.607057i
$585$	48.0472	+	83.2203i	1.98651	+	3.44073i
$586$	−8.81633	+	15.2703i	−0.364199	+	0.630812i
$587$	−12.6846			−0.523549			−0.261774	−	0.965129i	$-0.584308\pi$
$587$	−12.6846			−0.523549			−0.261774	+	0.965129i	$0.584308\pi$
$588$	−18.6122	−	2.14048i	−0.767554	−	0.0882718i
$589$	−4.71302			−0.194196
$590$	2.23983	−	3.87951i	0.0922125	−	0.159717i
$591$	1.07876	+	1.86846i	0.0443741	+	0.0768582i
$592$	1.71078	+	2.96316i	0.0703127	+	0.121785i
$593$	−4.84618	+	8.39382i	−0.199009	+	0.344693i	−0.948207	−	0.317652i	$-0.897106\pi$
$593$	−4.84618	+	8.39382i	−0.199009	+	0.344693i	0.749199	+	0.662345i	$0.230439\pi$
$594$	18.9661			0.778191
$595$	7.34657	+	4.82216i	0.301180	+	0.197689i
$596$	14.6640			0.600661
$597$	−19.4254	+	33.6457i	−0.795028	+	1.37703i
$598$	−2.98959	−	5.17813i	−0.122254	−	0.211749i
$599$	5.41150	+	9.37299i	0.221108	+	0.382970i	0.955145	−	0.296140i	$-0.0956994\pi$
$599$	5.41150	+	9.37299i	0.221108	+	0.382970i	−0.734037	+	0.679110i	$0.762366\pi$
$600$	13.2518	−	22.9528i	0.541002	−	0.937044i
$601$	28.6724			1.16957			0.584786	−	0.811187i	$-0.301178\pi$
$601$	28.6724			1.16957			0.584786	+	0.811187i	$0.301178\pi$
$602$	8.83727	−	4.44851i	0.360180	−	0.181308i
$603$	−0.231917			−0.00944437
$604$	−3.05551	+	5.29229i	−0.124327	+	0.215340i
$605$	50.4096	+	87.3120i	2.04944	+	3.54974i
$606$	4.20229	+	7.27858i	0.170706	+	0.295672i
$607$	−7.91578	+	13.7105i	−0.321292	+	0.556494i	−0.980755	−	0.195243i	$-0.937450\pi$
$607$	−7.91578	+	13.7105i	−0.321292	+	0.556494i	0.659463	+	0.751737i	$0.270784\pi$
$608$	−1.11313			−0.0451433
$609$	−0.271771	+	4.74187i	−0.0110127	+	0.192150i
$610$	−31.7063			−1.28375
$611$	11.9753	−	20.7418i	0.484469	−	0.839124i
$612$	−1.79099	−	3.10209i	−0.0723965	−	0.125394i
$613$	−6.22222	−	10.7772i	−0.251313	−	0.435287i	0.712574	−	0.701597i	$-0.247529\pi$
$613$	−6.22222	−	10.7772i	−0.251313	−	0.435287i	−0.963888	+	0.266309i	$0.914196\pi$
$614$	−6.13089	+	10.6190i	−0.247423	+	0.428549i
$615$	97.7219			3.94053
$616$	−0.922302	+	16.0923i	−0.0371606	+	0.648379i
$617$	−24.1914			−0.973908			−0.486954	−	0.873428i	$-0.661892\pi$
$617$	−24.1914			−0.973908			−0.486954	+	0.873428i	$0.661892\pi$
$618$	−4.30698	+	7.45992i	−0.173252	+	0.300082i
$619$	13.6142	+	23.5805i	0.547200	+	0.947779i	0.998465	+	0.0553885i	$0.0176397\pi$
$619$	13.6142	+	23.5805i	0.547200	+	0.947779i	−0.451265	+	0.892390i	$0.649027\pi$
$620$	−8.17252	−	14.1552i	−0.328216	−	0.568487i
$621$	1.55656	−	2.69605i	0.0624628	−	0.108189i
$622$	−3.22059			−0.129134
$623$	−16.2752	+	8.19264i	−0.652054	+	0.328231i
$624$	16.0028			0.640623
$625$	−11.7747	+	20.3944i	−0.470989	+	0.815777i
$626$	−10.6596	−	18.4630i	−0.426043	−	0.737929i
$627$	9.07507	+	15.7185i	0.362423	+	0.627736i
$628$	−0.832544	+	1.44201i	−0.0332221	+	0.0575424i
$629$	−2.94390			−0.117381
$630$	−35.5476	−	23.3328i	−1.41625	−	0.929602i
$631$	17.2260			0.685757			0.342878	−	0.939380i	$-0.388598\pi$
$631$	17.2260			0.685757			0.342878	+	0.939380i	$0.388598\pi$
$632$	1.24055	−	2.14870i	0.0493464	−	0.0854706i
$633$	−32.3716	−	56.0692i	−1.28665	−	2.22855i
$634$	8.40227	+	14.5532i	0.333697	+	0.577980i
$635$	−25.3313	+	43.8750i	−1.00524	+	1.74113i
$636$	−5.43106			−0.215355
$637$	16.6489	+	38.4005i	0.659653	+	1.52148i
$638$	4.08641			0.161783
$639$	−1.79837	+	3.11487i	−0.0711425	+	0.123222i
$640$	−1.93020	−	3.34320i	−0.0762978	−	0.132152i
$641$	1.17161	+	2.02928i	0.0462757	+	0.0801518i	0.888235	−	0.459388i	$-0.151931\pi$
$641$	1.17161	+	2.02928i	0.0462757	+	0.0801518i	−0.841960	+	0.539540i	$0.818598\pi$
$642$	−1.27690	+	2.21165i	−0.0503951	+	0.0872868i
$643$	33.8089			1.33329			0.666646	−	0.745374i	$-0.267729\pi$
$643$	33.8089			1.33329			0.666646	+	0.745374i	$0.267729\pi$
$644$	2.21184	+	1.45181i	0.0871587	+	0.0572095i
$645$	38.6365			1.52131
$646$	0.478866	−	0.829420i	0.0188407	−	0.0326331i
$647$	13.5918	+	23.5416i	0.534348	+	0.925518i	0.999195	+	0.0401265i	$0.0127761\pi$
$647$	13.5918	+	23.5416i	0.534348	+	0.925518i	−0.464847	+	0.885391i	$0.653891\pi$
$648$	−2.07876	−	3.60051i	−0.0816612	−	0.141441i
$649$	−3.53481	+	6.12247i	−0.138753	+	0.240328i
$650$	−59.2099			−2.32240
$651$	−26.7801	+	13.4806i	−1.04960	+	0.528346i
$652$	7.66903			0.300343
$653$	10.8258	−	18.7509i	0.423647	−	0.733777i	−0.572646	−	0.819803i	$-0.694083\pi$
$653$	10.8258	−	18.7509i	0.423647	−	0.733777i	0.996293	+	0.0860250i	$0.0274165\pi$
$654$	−17.1362	−	29.6807i	−0.670077	−	1.16061i
$655$	−25.3933	−	43.9825i	−0.992198	−	1.71854i
$656$	4.72909	−	8.19102i	0.184640	−	0.319805i
$657$	−70.5228			−2.75136
$658$	−0.606408	+	10.5806i	−0.0236403	+	0.412476i
$659$	3.19097			0.124303			0.0621513	−	0.998067i	$-0.480204\pi$
$659$	3.19097			0.124303			0.0621513	+	0.998067i	$0.480204\pi$
$660$	−31.4729	+	54.5127i	−1.22508	+	2.12190i
$661$	−7.52548	−	13.0345i	−0.292707	−	0.506984i	0.681742	−	0.731593i	$-0.261223\pi$
$661$	−7.52548	−	13.0345i	−0.292707	−	0.506984i	−0.974449	+	0.224609i	$0.927890\pi$
$662$	4.79448	+	8.30429i	0.186343	+	0.322755i
$663$	−6.88436	+	11.9241i	−0.267366	+	0.463092i
$664$	1.05005			0.0407497
$665$	0.650531	−	11.3505i	0.0252265	−	0.440152i
$666$	14.2446			0.551966
$667$	0.335374	−	0.580886i	0.0129858	−	0.0224920i
$668$	−12.3743	−	21.4329i	−0.478775	−	0.829263i
$669$	−14.6212	−	25.3247i	−0.565289	−	0.979110i
$670$	0.107525	−	0.186239i	0.00415405	−	0.00719503i
$671$	50.0375			1.93168
$672$	−6.32497	+	3.18386i	−0.243991	+	0.122820i
$673$	−34.3972			−1.32591			−0.662957	−	0.748657i	$-0.730699\pi$
$673$	−34.3972			−1.32591			−0.662957	+	0.748657i	$0.730699\pi$
$674$	−3.99005	+	6.91098i	−0.153691	+	0.266201i
$675$	−15.4141	−	26.6981i	−0.593290	−	1.02761i
$676$	−11.3753	−	19.7027i	−0.437513	−	0.757794i
$677$	−11.9979	+	20.7810i	−0.461116	+	0.798677i	−0.999017	−	0.0443313i	$-0.985884\pi$
$677$	−11.9979	+	20.7810i	−0.461116	+	0.798677i	0.537900	+	0.843008i	$0.319218\pi$
$678$	−6.78954			−0.260751
$679$	28.5176	+	18.7185i	1.09441	+	0.718350i
$680$	3.32147			0.127373
$681$	−34.3474	+	59.4914i	−1.31620	+	2.27972i
$682$	12.8975	+	22.3392i	0.493872	+	0.855411i
$683$	−22.5563	−	39.0687i	−0.863095	−	1.49492i	−0.868927	−	0.494941i	$-0.835190\pi$
$683$	−22.5563	−	39.0687i	−0.863095	−	1.49492i	0.00583208	−	0.999983i	$-0.498144\pi$
$684$	−2.31707	+	4.01328i	−0.0885954	+	0.153452i
$685$	−43.0358			−1.64431
$686$	−14.2204	−	11.8651i	−0.542937	−	0.453011i
$687$	60.4686			2.30702
$688$	1.86975	−	3.23850i	0.0712834	−	0.123466i
$689$	6.06658	+	10.5076i	0.231118	+	0.400308i
$690$	5.16600	+	8.94778i	0.196666	+	0.340636i
$691$	9.34571	−	16.1872i	0.355527	−	0.615792i	−0.631681	−	0.775229i	$-0.717635\pi$
$691$	9.34571	−	16.1872i	0.355527	−	0.615792i	0.987208	+	0.159437i	$0.0509679\pi$
$692$	−1.82167			−0.0692497
$693$	56.0997	+	36.8229i	2.13105	+	1.39879i
$694$	21.8159			0.828119
$695$	−2.32220	+	4.02216i	−0.0880859	+	0.152569i
$696$	0.897600	+	1.55469i	0.0340234	+	0.0589303i
$697$	4.06889	+	7.04753i	0.154120	+	0.266944i
$698$	5.82708	−	10.0928i	0.220558	−	0.382018i
$699$	−9.40075			−0.355569
$700$	23.4023	−	11.7802i	0.884522	−	0.445251i
$701$	27.0349			1.02109			0.510547	−	0.859850i	$-0.329443\pi$
$701$	27.0349			1.02109			0.510547	+	0.859850i	$0.329443\pi$
$702$	9.30698	−	16.1202i	0.351269	−	0.608417i
$703$	1.90432	+	3.29838i	0.0718227	+	0.124401i
$704$	3.04616	+	5.27610i	0.114806	+	0.198850i
$705$	−20.6933	+	35.8418i	−0.779353	+	1.34988i
$706$	−3.71381			−0.139771
$707$	−0.475395	+	8.29469i	−0.0178791	+	0.311954i
$708$	−3.10575			−0.116721
$709$	−4.74095	+	8.21156i	−0.178050	+	0.308392i	−0.941213	−	0.337815i	$-0.890312\pi$
$709$	−4.74095	+	8.21156i	−0.178050	+	0.308392i	0.763163	+	0.646207i	$0.223646\pi$
$710$	−1.66758	−	2.88834i	−0.0625832	−	0.108397i
$711$	−5.16463	−	8.94539i	−0.193689	−	0.335478i
$712$	−3.44344	+	5.96421i	−0.129048	+	0.223518i
$713$	4.23403			0.158566
$714$	0.348612	−	6.08259i	0.0130465	−	0.227635i
$715$	140.623			5.25900
$716$	−5.70249	+	9.87700i	−0.213112	+	0.369121i
$717$	−3.14770	−	5.45198i	−0.117553	−	0.203608i
$718$	5.79909	+	10.0443i	0.216420	+	0.374850i
$719$	15.1886	−	26.3075i	0.566441	−	0.981104i	−0.430474	−	0.902603i	$-0.641653\pi$
$719$	15.1886	−	26.3075i	0.566441	−	0.981104i	0.996914	−	0.0785006i	$-0.0250132\pi$
$720$	−16.0715			−0.598949
$721$	−7.60600	+	3.82871i	−0.283262	+	0.142589i
$722$	17.7609			0.660994
$723$	29.8465	−	51.6957i	1.11001	−	1.92259i
$724$	−0.313503	−	0.543003i	−0.0116512	−	0.0201805i
$725$	−3.32110	−	5.75232i	−0.123343	−	0.213636i
$726$	34.9489	−	60.5334i	1.29708	−	2.24660i
$727$	−36.5415			−1.35525			−0.677625	−	0.735407i	$-0.736991\pi$
$727$	−36.5415			−1.35525			−0.677625	+	0.735407i	$0.736991\pi$
$728$	13.2250	+	8.68067i	0.490151	+	0.321727i
$729$	−42.3045			−1.56683
$730$	32.6969	−	56.6327i	1.21017	−	2.09607i
$731$	1.60872	+	2.78639i	0.0595008	+	0.103058i
$732$	10.9910	+	19.0369i	0.406238	+	0.703625i
$733$	−14.0285	+	24.2981i	−0.518155	+	0.897471i	0.481622	+	0.876379i	$0.340048\pi$
$733$	−14.0285	+	24.2981i	−0.518155	+	0.897471i	−0.999778	+	0.0210921i	$0.993286\pi$
$734$	3.65560			0.134931
$735$	−28.7692	−	66.3559i	−1.06117	−	2.44757i
$736$	1.00000			0.0368605
$737$	−0.169691	+	0.293914i	−0.00625066	+	0.0108265i
$738$	−19.6880	−	34.1006i	−0.724725	−	1.25526i
$739$	0.950692	+	1.64665i	0.0349718	+	0.0605729i	0.882982	−	0.469408i	$-0.155533\pi$
$739$	0.950692	+	1.64665i	0.0349718	+	0.0605729i	−0.848010	+	0.529981i	$0.822199\pi$
$740$	−6.60430	+	11.4390i	−0.242779	+	0.420505i
$741$	17.8131			0.654381
$742$	−4.48833	−	2.94607i	−0.164772	−	0.108153i
$743$	−14.2220			−0.521755			−0.260878	−	0.965372i	$-0.584012\pi$
$743$	−14.2220			−0.521755			−0.260878	+	0.965372i	$0.584012\pi$
$744$	−5.66600	+	9.81381i	−0.207726	+	0.359792i
$745$	28.3045	+	49.0248i	1.03700	+	1.79613i
$746$	1.91307	+	3.31354i	0.0700426	+	0.121317i
$747$	2.18576	−	3.78585i	0.0799728	−	0.138517i
$748$	−5.24181			−0.191660
$749$	−2.25496	+	1.13510i	−0.0823944	+	0.0414757i
$750$	50.6544			1.84964
$751$	−8.26840	+	14.3213i	−0.301718	+	0.522591i	−0.976525	−	0.215403i	$-0.930894\pi$
$751$	−8.26840	+	14.3213i	−0.301718	+	0.522591i	0.674807	+	0.737994i	$0.264227\pi$
$752$	2.00283	+	3.46900i	0.0730357	+	0.126502i
$753$	18.4194	+	31.9033i	0.671240	+	1.16262i
$754$	2.00527	−	3.47322i	0.0730275	−	0.126487i
$755$	−23.5909			−0.858562
$756$	−0.471290	+	8.22307i	−0.0171406	+	0.299070i
$757$	12.5780			0.457155			0.228578	−	0.973526i	$-0.426593\pi$
$757$	12.5780			0.457155			0.228578	+	0.973526i	$0.426593\pi$
$758$	−3.78914	+	6.56299i	−0.137628	+	0.238378i
$759$	−8.15277	−	14.1210i	−0.295927	−	0.512560i
$760$	−2.14856	−	3.72141i	−0.0779364	−	0.134990i
$761$	14.2745	−	24.7242i	0.517451	−	0.896252i	−0.482343	−	0.875982i	$-0.660214\pi$
$761$	14.2745	−	24.7242i	0.517451	−	0.896252i	0.999795	−	0.0202695i	$-0.00645243\pi$
$762$	35.1243			1.27242
$763$	1.93857	−	33.8242i	0.0701810	−	1.22452i
$764$	7.08139			0.256196
$765$	6.91394	−	11.9753i	0.249974	−	0.432967i
$766$	3.22264	+	5.58178i	0.116439	+	0.201678i
$767$	3.46917	+	6.00879i	0.125265	+	0.216965i
$768$	−1.33821	+	2.31784i	−0.0482883	+	0.0836378i
$769$	−2.48636			−0.0896605			−0.0448302	−	0.998995i	$-0.514275\pi$
$769$	−2.48636			−0.0896605			−0.0448302	+	0.998995i	$0.514275\pi$
$770$	−55.5802	+	27.9780i	−2.00297	+	1.00826i
$771$	−27.4575			−0.988858
$772$	10.5081	−	18.2006i	0.378195	−	0.655052i
$773$	−1.51521	−	2.62442i	−0.0544984	−	0.0943939i	0.837489	−	0.546454i	$-0.184023\pi$
$773$	−1.51521	−	2.62442i	−0.0544984	−	0.0943939i	−0.891988	+	0.452060i	$0.850689\pi$
$774$	−7.78408	−	13.4824i	−0.279793	−	0.484615i
$775$	20.9641	−	36.3109i	0.753053	−	1.30433i
$776$	12.8932			0.462838
$777$	20.2549	+	13.2950i	0.726642	+	0.476956i
$778$	−13.8590			−0.496868
$779$	5.26408	−	9.11765i	0.188605	−	0.326674i
$780$	30.8885	+	53.5004i	1.10599	+	1.91562i
$781$	2.63171	+	4.55825i	0.0941699	+	0.163107i
$782$	−0.430199	+	0.745126i	−0.0153839	+	0.0266456i
$783$	2.08813			0.0746236
$784$	−6.95416	−	0.799757i	−0.248363	−	0.0285627i
$785$	−6.42790			−0.229422
$786$	−17.6052	+	30.4930i	−0.627955	+	1.08765i
$787$	−23.8794	−	41.3604i	−0.851209	−	1.47434i	−0.880117	−	0.474756i	$-0.842536\pi$
$787$	−23.8794	−	41.3604i	−0.851209	−	1.47434i	0.0289080	−	0.999582i	$-0.490797\pi$
$788$	0.403061	+	0.698121i	0.0143584	+	0.0248695i
$789$	−19.6823	+	34.0908i	−0.700709	+	1.21366i
$790$	9.57803			0.340771
$791$	−5.61101	−	3.68297i	−0.199505	−	0.130951i
$792$	25.3634			0.901248
$793$	24.5542	−	42.5291i	0.871944	−	1.51025i
$794$	13.7830	+	23.8729i	0.489141	+	0.847217i
$795$	−10.4830	−	18.1571i	−0.371794	−	0.643967i
$796$	−7.25800	+	12.5712i	−0.257253	+	0.445575i
$797$	−25.2116			−0.893040			−0.446520	−	0.894774i	$-0.647337\pi$
$797$	−25.2116			−0.893040			−0.446520	+	0.894774i	$0.647337\pi$
$798$	−7.04050	+	3.54405i	−0.249231	+	0.125458i
$799$	−3.44646			−0.121927
$800$	4.95133	−	8.57596i	0.175056	−	0.303206i
$801$	14.3356	+	24.8300i	0.506524	+	0.877326i
$802$	16.9164	+	29.3001i	0.597340	+	1.03462i
$803$	−51.6009	+	89.3754i	−1.82096	+	3.15399i
$804$	−0.149094			−0.00525814
$805$	−0.584417	+	10.1969i	−0.0205980	+	0.359394i
$806$	25.3161			0.891720
$807$	−7.89280	+	13.6707i	−0.277840	+	0.481232i
$808$	1.57012	+	2.71953i	0.0552367	+	0.0956728i
$809$	−3.94272	−	6.82899i	−0.138619	−	0.240095i	0.788355	−	0.615220i	$-0.210933\pi$
$809$	−3.94272	−	6.82899i	−0.138619	−	0.240095i	−0.926974	+	0.375126i	$0.877600\pi$
$810$	8.02482	−	13.8994i	0.281964	−	0.488375i
$811$	−4.28998			−0.150641			−0.0753207	−	0.997159i	$-0.523998\pi$
$811$	−4.28998			−0.150641			−0.0753207	+	0.997159i	$0.523998\pi$
$812$	−0.101543	+	1.77173i	−0.00356347	+	0.0621754i
$813$	−37.0129			−1.29810
$814$	10.4226	−	18.0525i	0.365313	−	0.632740i
$815$	14.8028	+	25.6391i	0.518518	+	0.898100i
$816$	−1.15139	−	1.99426i	−0.0403066	−	0.0698131i
$817$	2.08127	−	3.60486i	0.0728143	−	0.126118i
$818$	−18.8614			−0.659475
$819$	58.8264	−	29.6120i	2.05556	−	1.03473i
$820$	36.5123			1.27506
$821$	−12.1131	+	20.9806i	−0.422751	+	0.732227i	−0.996207	−	0.0870095i	$-0.972269\pi$
$821$	−12.1131	+	20.9806i	−0.422751	+	0.732227i	0.573456	+	0.819236i	$0.305602\pi$
$822$	14.9183	+	25.8393i	0.520337	+	0.901250i
$823$	−0.876466	−	1.51808i	−0.0305517	−	0.0529170i	0.850345	−	0.526225i	$-0.176393\pi$
$823$	−0.876466	−	1.51808i	−0.0305517	−	0.0529170i	−0.880897	+	0.473308i	$0.843060\pi$
$824$	−1.60924	+	2.78728i	−0.0560605	+	0.0970996i
$825$	−161.468			−5.62160
$826$	−2.56666	−	1.68471i	−0.0893054	−	0.0586185i
$827$	−32.8224			−1.14135			−0.570674	−	0.821177i	$-0.693318\pi$
$827$	−32.8224			−1.14135			−0.570674	+	0.821177i	$0.693318\pi$
$828$	2.08159	−	3.60541i	0.0723401	−	0.125297i
$829$	−1.91748	−	3.32118i	−0.0665969	−	0.115349i	0.830804	−	0.556565i	$-0.187881\pi$
$829$	−1.91748	−	3.32118i	−0.0665969	−	0.115349i	−0.897401	+	0.441215i	$0.854547\pi$
$830$	2.02680	+	3.51051i	0.0703511	+	0.121852i
$831$	31.5649	−	54.6720i	1.09497	−	1.89655i
$832$	5.97919			0.207291
$833$	3.58759	−	4.83767i	0.124303	−	0.167615i
$834$	3.21995			0.111498
$835$	47.7696	−	82.7394i	1.65314	−	2.86332i
$836$	3.39076	+	5.87297i	0.117272	+	0.203121i
$837$	6.59054	+	11.4152i	0.227802	+	0.394565i
$838$	−17.5787	+	30.4472i	−0.607245	+	1.05178i
$839$	−9.38392			−0.323969			−0.161984	−	0.986793i	$-0.551789\pi$
$839$	−9.38392			−0.323969			−0.161984	+	0.986793i	$0.551789\pi$
$840$	−22.8527	−	15.0002i	−0.788495	−	0.517554i
$841$	−28.5501			−0.984486
$842$	−14.0620	+	24.3562i	−0.484610	+	0.839368i
$843$	−31.1777	−	54.0014i	−1.07382	−	1.85991i
$844$	−12.0951	−	20.9494i	−0.416332	−	0.721108i
$845$	43.9133	−	76.0601i	1.51066	−	2.61655i
$846$	16.6763			0.573342
$847$	61.7187	−	31.0680i	2.12068	−	1.06751i
$848$	−2.02923			−0.0696841
$849$	42.5587	−	73.7138i	1.46061	−	2.52985i
$850$	4.26011	+	7.37873i	0.146121	+	0.253088i
$851$	−1.71078	−	2.96316i	−0.0586449	−	0.101576i
$852$	−1.15613	+	2.00248i	−0.0396085	+	0.0686039i
$853$	47.5099			1.62671			0.813354	−	0.581769i	$-0.197639\pi$
$853$	47.5099			1.62671			0.813354	+	0.581769i	$0.197639\pi$
$854$	−1.24338	+	21.6945i	−0.0425476	+	0.742372i
$855$	−17.8896			−0.611812
$856$	−0.477093	+	0.826349i	−0.0163067	+	0.0282440i
$857$	4.30850	+	7.46255i	0.147176	+	0.254916i	0.930183	−	0.367097i	$-0.119648\pi$
$857$	4.30850	+	7.46255i	0.147176	+	0.254916i	−0.783007	+	0.622013i	$0.786315\pi$
$858$	−48.7469	−	84.4321i	−1.66419	−	2.88246i
$859$	5.58665	−	9.67637i	0.190614	−	0.330153i	−0.754840	−	0.655909i	$-0.772285\pi$
$859$	5.58665	−	9.67637i	0.190614	−	0.330153i	0.945454	+	0.325756i	$0.105619\pi$
$860$	14.4359			0.492261
$861$	3.83222	−	66.8647i	0.130602	−	2.27874i
$862$	5.77586			0.196727
$863$	2.19553	−	3.80276i	0.0747366	−	0.129448i	−0.826235	−	0.563325i	$-0.809522\pi$
$863$	2.19553	−	3.80276i	0.0747366	−	0.129448i	0.900972	+	0.433878i	$0.142855\pi$
$864$	1.55656	+	2.69605i	0.0529554	+	0.0917214i
$865$	−3.51619	−	6.09023i	−0.119554	−	0.207074i
$866$	−14.4788	+	25.0780i	−0.492009	+	0.852185i
$867$	−43.5177			−1.47794
$868$	−10.0060	+	5.03682i	−0.339625	+	0.170961i
$869$	−15.1156			−0.512763
$870$	−3.46509	+	6.00171i	−0.117478	+	0.203477i
$871$	0.166540	+	0.288456i	0.00564300	+	0.00977397i
$872$	−6.40267	−	11.0897i	−0.216822	−	0.375546i
$873$	26.8383	−	46.4852i	0.908337	−	1.57329i
$874$	1.11313			0.0376521
$875$	41.8618	+	27.4774i	1.41519	+	0.928905i
$876$	−45.3375			−1.53181
$877$	7.68898	−	13.3177i	0.259638	−	0.449707i	−0.706507	−	0.707706i	$-0.749730\pi$
$877$	7.68898	−	13.3177i	0.259638	−	0.449707i	0.966145	+	0.258000i	$0.0830633\pi$
$878$	8.40340	+	14.5551i	0.283601	+	0.491212i
$879$	23.5961	+	40.8697i	0.795878	+	1.37850i
$880$	−11.7594	+	20.3678i	−0.396408	+	0.686600i
$881$	30.7005			1.03433			0.517163	−	0.855887i	$-0.326988\pi$
$881$	30.7005			1.03433			0.517163	+	0.855887i	$0.326988\pi$
$882$	−17.3591	+	23.4079i	−0.584513	+	0.788184i
$883$	−14.0021			−0.471209			−0.235604	−	0.971849i	$-0.575707\pi$
$883$	−14.0021			−0.471209			−0.235604	+	0.971849i	$0.575707\pi$
$884$	−2.57224	+	4.45525i	−0.0865137	+	0.149846i
$885$	−5.99472	−	10.3832i	−0.201510	−	0.349026i
$886$	5.00824	+	8.67452i	0.168255	+	0.291426i
$887$	−20.7021	+	35.8572i	−0.695110	+	1.20397i	0.275034	+	0.961435i	$0.411311\pi$
$887$	−20.7021	+	35.8572i	−0.695110	+	1.20397i	−0.970144	+	0.242531i	$0.922022\pi$
$888$	9.15751			0.307306
$889$	29.0274	+	19.0531i	0.973549	+	0.639021i
$890$	−26.5861			−0.891167
$891$	−12.6644	+	21.9354i	−0.424274	+	0.734865i
$892$	−5.46300	−	9.46219i	−0.182915	−	0.316818i
$893$	2.22941	+	3.86144i	0.0746042	+	0.129218i
$894$	19.6235	−	33.9888i	0.656307	−	1.13676i
$895$	−44.0278			−1.47169
$896$	−2.36323	+	1.18960i	−0.0789499	+	0.0397418i
$897$	−16.0028			−0.534316
$898$	−18.3308	+	31.7498i	−0.611705	+	1.05950i
$899$	1.41999	+	2.45949i	0.0473592	+	0.0820285i
$900$	−20.6133	−	35.7032i	−0.687108	−	1.19011i
$901$	0.872972	−	1.51203i	0.0290829	−	0.0503731i
$902$	−57.6221			−1.91861
$903$	1.51515	−	26.4364i	0.0504211	−	0.879748i
$904$	−2.53681			−0.0843730
$905$	1.21025	−	2.09621i	0.0402299	−	0.0696803i
$906$	8.17779	+	14.1643i	0.271689	+	0.470579i
$907$	−24.4059	−	42.2723i	−0.810386	−	1.40363i	−0.912594	−	0.408867i	$-0.865924\pi$
$907$	−24.4059	−	42.2723i	−0.810386	−	1.40363i	0.102208	−	0.994763i	$-0.467409\pi$
$908$	−12.8334	+	22.2281i	−0.425891	+	0.737665i
$909$	13.0734			0.433616
$910$	−3.49434	+	60.9693i	−0.115836	+	2.02111i
$911$	11.6605			0.386329			0.193164	−	0.981166i	$-0.438125\pi$
$911$	11.6605			0.386329			0.193164	+	0.981166i	$0.438125\pi$
$912$	−1.48959	+	2.58005i	−0.0493254	+	0.0854340i
$913$	−3.19860	−	5.54014i	−0.105858	−	0.183352i
$914$	−13.6998	−	23.7287i	−0.453148	−	0.784876i
$915$	−42.4295	+	73.4901i	−1.40268	+	2.42951i
$916$	22.5932			0.746499
$917$	−31.0901	+	15.6502i	−1.02669	+	0.516814i
$918$	−2.67853			−0.0884045
$919$	−2.84767	+	4.93232i	−0.0939361	+	0.162702i	−0.909164	−	0.416438i	$-0.863278\pi$
$919$	−2.84767	+	4.93232i	−0.0939361	+	0.162702i	0.815228	+	0.579140i	$0.196612\pi$
$920$	1.93020	+	3.34320i	0.0636368	+	0.110222i
$921$	16.4088	+	28.4209i	0.540688	+	0.936499i
$922$	−10.8568	+	18.8046i	−0.357551	+	0.619296i
$923$	5.16568			0.170030
$924$	36.0652	+	23.6726i	1.18646	+	0.778771i
$925$	−33.8826			−1.11405
$926$	19.6547	−	34.0429i	0.645892	−	1.11872i
$927$	6.69954	+	11.6039i	0.220042	+	0.381124i
$928$	0.335374	+	0.580886i	0.0110092	+	0.0190685i
$929$	2.61603	−	4.53110i	0.0858293	−	0.148661i	−0.819915	−	0.572485i	$-0.805979\pi$
$929$	2.61603	−	4.53110i	0.0858293	−	0.148661i	0.905744	+	0.423825i	$0.139313\pi$
$930$	−43.7460			−1.43449
$931$	−7.74087	−	0.890231i	−0.253697	−	0.0291761i
$932$	−3.51245			−0.115054
$933$	−4.30982	+	7.46482i	−0.141097	+	0.244387i
$934$	−11.0602	−	19.1568i	−0.361900	−	0.626829i
$935$	−10.1177	−	17.5244i	−0.330885	−	0.573110i
$936$	12.4462	−	21.5574i	0.406817	−	0.704627i
$937$	−17.8841			−0.584249			−0.292124	−	0.956380i	$-0.594362\pi$
$937$	−17.8841			−0.584249			−0.292124	+	0.956380i	$0.594362\pi$
$938$	−0.123214	−	0.0808757i	−0.00402309	−	0.00264069i
$939$	−57.0590			−1.86205
$940$	−7.73172	+	13.3917i	−0.252181	+	0.436790i
$941$	−12.3455	−	21.3830i	−0.402451	−	0.697066i	0.591570	−	0.806254i	$-0.298508\pi$
$941$	−12.3455	−	21.3830i	−0.402451	−	0.697066i	−0.994021	+	0.109187i	$0.965175\pi$
$942$	2.22823	+	3.85941i	0.0725996	+	0.125746i
$943$	−4.72909	+	8.19102i	−0.154000	+	0.266736i
$944$	−1.16042			−0.0377684
$945$	−28.4011	+	14.2965i	−0.923886	+	0.465066i
$946$	−22.7822			−0.740712
$947$	−28.0570	+	48.5961i	−0.911730	+	1.57916i	−0.100109	+	0.994976i	$0.531919\pi$
$947$	−28.0570	+	48.5961i	−0.911730	+	1.57916i	−0.811620	+	0.584186i	$0.801414\pi$
$948$	−3.32022	−	5.75079i	−0.107836	−	0.186777i
$949$	50.6427	+	87.7158i	1.64393	+	2.84737i
$950$	5.51146	−	9.54614i	0.178816	−	0.309718i
$951$	44.9758			1.45844
$952$	0.130254	−	2.27267i	0.00422154	−	0.0736576i
$953$	−16.8019			−0.544268			−0.272134	−	0.962259i	$-0.587729\pi$
$953$	−16.8019			−0.544268			−0.272134	+	0.962259i	$0.587729\pi$
$954$	−4.22402	+	7.31622i	−0.136758	+	0.236871i
$955$	13.6685	+	23.6745i	0.442302	+	0.766090i
$956$	−1.17609	−	2.03705i	−0.0380375	−	0.0658828i
$957$	5.46846	−	9.47165i	0.176770	−	0.306175i
$958$	−4.54458			−0.146829
$959$	−1.68767	+	29.4466i	−0.0544979	+	0.950879i
$960$	−10.3320			−0.333464
$961$	6.53649	−	11.3215i	0.210854	−	0.365211i
$962$	−10.2291	−	17.7173i	−0.329799	−	0.571229i
$963$	1.98622	+	3.44023i	0.0640050	+	0.110860i
$964$	11.1517	−	19.3153i	0.359172	−	0.622105i
$965$	81.1309			2.61169
$966$	6.32497	−	3.18386i	0.203502	−	0.102439i
$967$	−16.5124			−0.531005			−0.265502	−	0.964110i	$-0.585538\pi$
$967$	−16.5124			−0.531005			−0.265502	+	0.964110i	$0.585538\pi$
$968$	13.0581	−	22.6174i	0.419705	−	0.726950i
$969$	−1.28164	−	2.21987i	−0.0411723	−	0.0713124i
$970$	24.8864	+	43.1045i	0.799054	+	1.38400i
$971$	−15.5960	+	27.0131i	−0.500500	+	0.866891i	0.499500	+	0.866314i	$0.333517\pi$
$971$	−15.5960	+	27.0131i	−0.500500	+	0.866891i	−1.00000		0.000577094i	$0.999816\pi$
$972$	−20.4666			−0.656466
$973$	2.66103	+	1.74666i	0.0853089	+	0.0559953i
$974$	26.9794			0.864477
$975$	−79.2350	+	137.239i	−2.53755	+	4.39517i
$976$	4.10661	+	7.11286i	0.131449	+	0.227677i
$977$	2.74471	+	4.75398i	0.0878112	+	0.152093i	0.906586	−	0.422022i	$-0.138679\pi$
$977$	2.74471	+	4.75398i	0.0878112	+	0.152093i	−0.818774	+	0.574115i	$0.805346\pi$
$978$	10.2627	−	17.7756i	0.328166	−	0.568401i
$979$	41.9570			1.34095
$980$	−10.7492	−	24.7929i	−0.343370	−	0.791979i
$981$	−53.3108			−1.70208
$982$	16.6342	−	28.8113i	0.530818	−	0.919404i
$983$	9.35356	+	16.2008i	0.298332	+	0.516726i	0.975755	−	0.218868i	$-0.0702363\pi$
$983$	9.35356	+	16.2008i	0.298332	+	0.516726i	−0.677422	+	0.735594i	$0.736903\pi$
$984$	−12.6570	−	21.9225i	−0.403490	−	0.698864i
$985$	−1.55597	+	2.69503i	−0.0495775	+	0.0858707i
$986$	−0.577110			−0.0183789
$987$	23.7127	+	15.5646i	0.754783	+	0.495427i
$988$	6.65560			0.211743
$989$	−1.86975	+	3.23850i	−0.0594545	+	0.102978i
$990$	48.9563	+	84.7948i	1.55593	+	2.69496i
$991$	16.4453	+	28.4841i	0.522403	+	0.904829i	0.999660	+	0.0260650i	$0.00829769\pi$
$991$	16.4453	+	28.4841i	0.522403	+	0.904829i	−0.477257	+	0.878764i	$0.658369\pi$
$992$	−2.11702	+	3.66678i	−0.0672153	+	0.116420i
$993$	25.6640			0.814423
$994$	−2.04169	+	1.02775i	−0.0647586	+	0.0325982i
$995$	−56.0375			−1.77651
$996$	1.40518	−	2.43384i	0.0445247	−	0.0771190i
$997$	14.7515	+	25.5504i	0.467185	+	0.809189i	0.999297	−	0.0374852i	$-0.0119347\pi$
$997$	14.7515	+	25.5504i	0.467185	+	0.809189i	−0.532112	+	0.846674i	$0.678601\pi$
$998$	9.86704	+	17.0902i	0.312336	+	0.540981i
$999$	5.32588	−	9.22470i	0.168503	−	0.291857i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.e.d.93.1	✓	8
7.2	even	3		2254.2.a.u.1.4		4
7.4	even	3	inner	322.2.e.d.277.1	yes	8
7.5	odd	6		2254.2.a.r.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.e.d.93.1	✓	8	1.1	even	1	trivial
322.2.e.d.277.1	yes	8	7.4	even	3	inner
2254.2.a.r.1.1		4	7.5	odd	6
2254.2.a.u.1.4		4	7.2	even	3

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:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.33821 - 2.31784i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.93020 - 3.34320i) q^{5} -2.67641 q^{6} +(-2.21184 - 1.45181i) q^{7} -1.00000 q^{8} +(-2.08159 + 3.60541i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.33821 - 2.31784i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.93020 - 3.34320i) q^{5} -2.67641 q^{6} +(-2.21184 - 1.45181i) q^{7} -1.00000 q^{8} +(-2.08159 + 3.60541i) q^{9} +(-1.93020 - 3.34320i) q^{10} +(3.04616 + 5.27610i) q^{11} +(-1.33821 + 2.31784i) q^{12} +5.97919 q^{13} +(-2.36323 + 1.18960i) q^{14} -10.3320 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.430199 - 0.745126i) q^{17} +(2.08159 + 3.60541i) q^{18} +(-0.556564 + 0.963997i) q^{19} -3.86040 q^{20} +(-0.405176 + 7.06951i) q^{21} +6.09231 q^{22} +(0.500000 - 0.866025i) q^{23} +(1.33821 + 2.31784i) q^{24} +(-4.95133 - 8.57596i) q^{25} +(2.98959 - 5.17813i) q^{26} +3.11313 q^{27} +(-0.151388 + 2.64142i) q^{28} +0.670749 q^{29} +(-5.16600 + 8.94778i) q^{30} +(2.11702 + 3.66678i) q^{31} +(0.500000 + 0.866025i) q^{32} +(8.15277 - 14.1210i) q^{33} -0.860397 q^{34} +(-9.12300 + 4.59234i) q^{35} +4.16317 q^{36} +(1.71078 - 2.96316i) q^{37} +(0.556564 + 0.963997i) q^{38} +(-8.00138 - 13.8588i) q^{39} +(-1.93020 + 3.34320i) q^{40} -9.45817 q^{41} +(5.91979 + 3.88565i) q^{42} -3.73949 q^{43} +(3.04616 - 5.27610i) q^{44} +(8.03575 + 13.9183i) q^{45} +(-0.500000 - 0.866025i) q^{46} +(2.00283 - 3.46900i) q^{47} +2.67641 q^{48} +(2.78447 + 6.42236i) q^{49} -9.90267 q^{50} +(-1.15139 + 1.99426i) q^{51} +(-2.98959 - 5.17813i) q^{52} +(1.01462 + 1.75737i) q^{53} +(1.55656 - 2.69605i) q^{54} +23.5187 q^{55} +(2.21184 + 1.45181i) q^{56} +2.97919 q^{57} +(0.335374 - 0.580886i) q^{58} +(0.580208 + 1.00495i) q^{59} +(5.16600 + 8.94778i) q^{60} +(4.10661 - 7.11286i) q^{61} +4.23403 q^{62} +(9.83853 - 4.95252i) q^{63} +1.00000 q^{64} +(11.5410 - 19.9896i) q^{65} +(-8.15277 - 14.1210i) q^{66} +(0.0278533 + 0.0482434i) q^{67} +(-0.430199 + 0.745126i) q^{68} -2.67641 q^{69} +(-0.584417 + 10.1969i) q^{70} +0.863943 q^{71} +(2.08159 - 3.60541i) q^{72} +(8.46984 + 14.6702i) q^{73} +(-1.71078 - 2.96316i) q^{74} +(-13.2518 + 22.9528i) q^{75} +1.11313 q^{76} +(0.922302 - 16.0923i) q^{77} -16.0028 q^{78} +(-1.24055 + 2.14870i) q^{79} +(1.93020 + 3.34320i) q^{80} +(2.07876 + 3.60051i) q^{81} +(-4.72909 + 8.19102i) q^{82} -1.05005 q^{83} +(6.32497 - 3.18386i) q^{84} -3.32147 q^{85} +(-1.86975 + 3.23850i) q^{86} +(-0.897600 - 1.55469i) q^{87} +(-3.04616 - 5.27610i) q^{88} +(3.44344 - 5.96421i) q^{89} +16.0715 q^{90} +(-13.2250 - 8.68067i) q^{91} -1.00000 q^{92} +(5.66600 - 9.81381i) q^{93} +(-2.00283 - 3.46900i) q^{94} +(2.14856 + 3.72141i) q^{95} +(1.33821 - 2.31784i) q^{96} -12.8932 q^{97} +(6.95416 + 0.799757i) q^{98} -25.3634 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - q^{3} - 4 q^{4} + 5 q^{5} - 2 q^{6} - 3 q^{7} - 8 q^{8} + q^{9}+O(q^{10}) \) 8 * q + 4 * q^2 - q^3 - 4 * q^4 + 5 * q^5 - 2 * q^6 - 3 * q^7 - 8 * q^8 + q^9	\( 8 q + 4 q^{2} - q^{3} - 4 q^{4} + 5 q^{5} - 2 q^{6} - 3 q^{7} - 8 q^{8} + q^{9} - 5 q^{10} + 2 q^{11} - q^{12} + 14 q^{13} + 3 q^{14} - 10 q^{15} - 4 q^{16} + 7 q^{17} - q^{18} + q^{19} - 10 q^{20} - 5 q^{21} + 4 q^{22} + 4 q^{23} + q^{24} - 19 q^{25} + 7 q^{26} + 14 q^{27} + 6 q^{28} - 12 q^{29} - 5 q^{30} + 4 q^{31} + 4 q^{32} + 13 q^{33} + 14 q^{34} - 14 q^{35} - 2 q^{36} - q^{38} - 19 q^{39} - 5 q^{40} - 30 q^{41} + 20 q^{42} - 24 q^{43} + 2 q^{44} + 25 q^{45} - 4 q^{46} + 15 q^{47} + 2 q^{48} + 17 q^{49} - 38 q^{50} - 2 q^{51} - 7 q^{52} - 21 q^{53} + 7 q^{54} + 24 q^{55} + 3 q^{56} - 10 q^{57} - 6 q^{58} + 32 q^{59} + 5 q^{60} + 3 q^{61} + 8 q^{62} + 25 q^{63} + 8 q^{64} + 6 q^{65} - 13 q^{66} - 13 q^{67} + 7 q^{68} - 2 q^{69} + 14 q^{70} - 14 q^{71} - q^{72} + 16 q^{73} - 6 q^{75} - 2 q^{76} + 23 q^{77} - 38 q^{78} - 3 q^{79} + 5 q^{80} - 15 q^{82} + 16 q^{83} + 25 q^{84} - 48 q^{85} - 12 q^{86} + 9 q^{87} - 2 q^{88} + 33 q^{89} + 50 q^{90} - 18 q^{91} - 8 q^{92} + 9 q^{93} - 15 q^{94} + 11 q^{95} + q^{96} - 24 q^{97} + 34 q^{98} - 70 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 - q^3 - 4 * q^4 + 5 * q^5 - 2 * q^6 - 3 * q^7 - 8 * q^8 + q^9 - 5 * q^10 + 2 * q^11 - q^12 + 14 * q^13 + 3 * q^14 - 10 * q^15 - 4 * q^16 + 7 * q^17 - q^18 + q^19 - 10 * q^20 - 5 * q^21 + 4 * q^22 + 4 * q^23 + q^24 - 19 * q^25 + 7 * q^26 + 14 * q^27 + 6 * q^28 - 12 * q^29 - 5 * q^30 + 4 * q^31 + 4 * q^32 + 13 * q^33 + 14 * q^34 - 14 * q^35 - 2 * q^36 - q^38 - 19 * q^39 - 5 * q^40 - 30 * q^41 + 20 * q^42 - 24 * q^43 + 2 * q^44 + 25 * q^45 - 4 * q^46 + 15 * q^47 + 2 * q^48 + 17 * q^49 - 38 * q^50 - 2 * q^51 - 7 * q^52 - 21 * q^53 + 7 * q^54 + 24 * q^55 + 3 * q^56 - 10 * q^57 - 6 * q^58 + 32 * q^59 + 5 * q^60 + 3 * q^61 + 8 * q^62 + 25 * q^63 + 8 * q^64 + 6 * q^65 - 13 * q^66 - 13 * q^67 + 7 * q^68 - 2 * q^69 + 14 * q^70 - 14 * q^71 - q^72 + 16 * q^73 - 6 * q^75 - 2 * q^76 + 23 * q^77 - 38 * q^78 - 3 * q^79 + 5 * q^80 - 15 * q^82 + 16 * q^83 + 25 * q^84 - 48 * q^85 - 12 * q^86 + 9 * q^87 - 2 * q^88 + 33 * q^89 + 50 * q^90 - 18 * q^91 - 8 * q^92 + 9 * q^93 - 15 * q^94 + 11 * q^95 + q^96 - 24 * q^97 + 34 * q^98 - 70 * q^99

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