LMFDB - Embedded newform 322.2.e.a.277.2

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:	8.0.310217769.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 4x^{6} - 2x^{5} + 15x^{4} - 4x^{3} + 5x^{2} + x + 1 $ x^8 + 4x^6 - 2x^5 + 15x^4 - 4x^3 + 5*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			277.2
Root			$0.346911 - 0.600868i$ of defining polynomial
Character	$\chi$	$=$	322.277
Dual form			322.2.e.a.93.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.873734 + 1.51335i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.13304 - 3.69453i) q^{5} +1.74747 q^{6} +(1.89234 + 1.84906i) q^{7} +1.00000 q^{8} +(-0.0268230 - 0.0464588i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.873734 + 1.51335i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.13304 - 3.69453i) q^{5} +1.74747 q^{6} +(1.89234 + 1.84906i) q^{7} +1.00000 q^{8} +(-0.0268230 - 0.0464588i) q^{9} +(-2.13304 + 3.69453i) q^{10} +(-1.59438 + 2.76155i) q^{11} +(-0.873734 - 1.51335i) q^{12} -4.60948 q^{13} +(0.655163 - 2.56335i) q^{14} +7.45484 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.57939 + 2.73559i) q^{17} +(-0.0268230 + 0.0464588i) q^{18} +(2.26815 + 3.92856i) q^{19} +4.26608 q^{20} +(-4.45169 + 1.24819i) q^{21} +3.18876 q^{22} +(0.500000 + 0.866025i) q^{23} +(-0.873734 + 1.51335i) q^{24} +(-6.59971 + 11.4310i) q^{25} +(2.30474 + 3.99192i) q^{26} -5.14866 q^{27} +(-2.54751 + 0.714287i) q^{28} -3.70737 q^{29} +(-3.72742 - 6.45608i) q^{30} +(-1.61805 + 2.80255i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.78613 - 4.82572i) q^{33} +3.15879 q^{34} +(2.79498 - 10.9355i) q^{35} +0.0536460 q^{36} +(3.62328 + 6.27570i) q^{37} +(2.26815 - 3.92856i) q^{38} +(4.02746 - 6.97576i) q^{39} +(-2.13304 - 3.69453i) q^{40} +5.11454 q^{41} +(3.30681 + 3.23118i) q^{42} -2.29605 q^{43} +(-1.59438 - 2.76155i) q^{44} +(-0.114429 + 0.198197i) q^{45} +(0.500000 - 0.866025i) q^{46} +(-2.84899 - 4.93459i) q^{47} +1.74747 q^{48} +(0.161936 + 6.99813i) q^{49} +13.1994 q^{50} +(-2.75994 - 4.78036i) q^{51} +(2.30474 - 3.99192i) q^{52} +(6.09971 - 10.5650i) q^{53} +(2.57433 + 4.45887i) q^{54} +13.6035 q^{55} +(1.89234 + 1.84906i) q^{56} -7.92705 q^{57} +(1.85368 + 3.21068i) q^{58} +(-0.459266 + 0.795473i) q^{59} +(-3.72742 + 6.45608i) q^{60} +(-6.74448 - 11.6818i) q^{61} +3.23611 q^{62} +(0.0351469 - 0.137513i) q^{63} +1.00000 q^{64} +(9.83220 + 17.0299i) q^{65} +(-2.78613 + 4.82572i) q^{66} +(-2.37788 + 4.11861i) q^{67} +(-1.57939 - 2.73559i) q^{68} -1.74747 q^{69} +(-10.8679 + 3.04721i) q^{70} +3.61960 q^{71} +(-0.0268230 - 0.0464588i) q^{72} +(6.68525 - 11.5792i) q^{73} +(3.62328 - 6.27570i) q^{74} +(-11.5328 - 19.9754i) q^{75} -4.53631 q^{76} +(-8.12339 + 2.27769i) q^{77} -8.05492 q^{78} +(3.71036 + 6.42653i) q^{79} +(-2.13304 + 3.69453i) q^{80} +(4.57903 - 7.93111i) q^{81} +(-2.55727 - 4.42932i) q^{82} -9.36524 q^{83} +(1.14488 - 4.47937i) q^{84} +13.4756 q^{85} +(1.14803 + 1.98844i) q^{86} +(3.23926 - 5.61056i) q^{87} +(-1.59438 + 2.76155i) q^{88} +(2.61155 + 4.52334i) q^{89} +0.228858 q^{90} +(-8.72272 - 8.52321i) q^{91} -1.00000 q^{92} +(-2.82750 - 4.89737i) q^{93} +(-2.84899 + 4.93459i) q^{94} +(9.67612 - 16.7595i) q^{95} +(-0.873734 - 1.51335i) q^{96} -5.74459 q^{97} +(5.97959 - 3.63930i) q^{98} +0.171064 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 3 q^{3} - 4 q^{4} - 7 q^{5} + 6 q^{6} - q^{7} + 8 q^{8} + q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 - 3 * q^3 - 4 * q^4 - 7 * q^5 + 6 * q^6 - q^7 + 8 * q^8 + q^9	\( 8 q - 4 q^{2} - 3 q^{3} - 4 q^{4} - 7 q^{5} + 6 q^{6} - q^{7} + 8 q^{8} + q^{9} - 7 q^{10} - 2 q^{11} - 3 q^{12} + 2 q^{13} - q^{14} + 18 q^{15} - 4 q^{16} - 5 q^{17} + q^{18} - 11 q^{19} + 14 q^{20} + q^{21} + 4 q^{22} + 4 q^{23} - 3 q^{24} - 3 q^{25} - q^{26} + 6 q^{27} + 2 q^{28} + 4 q^{29} - 9 q^{30} - 6 q^{31} - 4 q^{32} - 15 q^{33} + 10 q^{34} - 8 q^{35} - 2 q^{36} + 8 q^{37} - 11 q^{38} - 3 q^{39} - 7 q^{40} + 18 q^{41} - 2 q^{42} + 8 q^{43} - 2 q^{44} - 3 q^{45} + 4 q^{46} - 11 q^{47} + 6 q^{48} - 19 q^{49} + 6 q^{50} + 18 q^{51} - q^{52} - q^{53} - 3 q^{54} + 20 q^{55} - q^{56} + 6 q^{57} - 2 q^{58} - 12 q^{59} - 9 q^{60} - 21 q^{61} + 12 q^{62} - 15 q^{63} + 8 q^{64} + 24 q^{65} - 15 q^{66} + 3 q^{67} - 5 q^{68} - 6 q^{69} - 8 q^{70} + 22 q^{71} + q^{72} + 16 q^{73} + 8 q^{74} - 18 q^{75} + 22 q^{76} - 19 q^{77} + 6 q^{78} + 21 q^{79} - 7 q^{80} + 8 q^{81} - 9 q^{82} + 8 q^{83} + q^{84} + 20 q^{85} - 4 q^{86} + 7 q^{87} - 2 q^{88} - 27 q^{89} + 6 q^{90} - 54 q^{91} - 8 q^{92} + 27 q^{93} - 11 q^{94} - 5 q^{95} - 3 q^{96} + 12 q^{97} + 14 q^{98} + 26 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 - 3 * q^3 - 4 * q^4 - 7 * q^5 + 6 * q^6 - q^7 + 8 * q^8 + q^9 - 7 * q^10 - 2 * q^11 - 3 * q^12 + 2 * q^13 - q^14 + 18 * q^15 - 4 * q^16 - 5 * q^17 + q^18 - 11 * q^19 + 14 * q^20 + q^21 + 4 * q^22 + 4 * q^23 - 3 * q^24 - 3 * q^25 - q^26 + 6 * q^27 + 2 * q^28 + 4 * q^29 - 9 * q^30 - 6 * q^31 - 4 * q^32 - 15 * q^33 + 10 * q^34 - 8 * q^35 - 2 * q^36 + 8 * q^37 - 11 * q^38 - 3 * q^39 - 7 * q^40 + 18 * q^41 - 2 * q^42 + 8 * q^43 - 2 * q^44 - 3 * q^45 + 4 * q^46 - 11 * q^47 + 6 * q^48 - 19 * q^49 + 6 * q^50 + 18 * q^51 - q^52 - q^53 - 3 * q^54 + 20 * q^55 - q^56 + 6 * q^57 - 2 * q^58 - 12 * q^59 - 9 * q^60 - 21 * q^61 + 12 * q^62 - 15 * q^63 + 8 * q^64 + 24 * q^65 - 15 * q^66 + 3 * q^67 - 5 * q^68 - 6 * q^69 - 8 * q^70 + 22 * q^71 + q^72 + 16 * q^73 + 8 * q^74 - 18 * q^75 + 22 * q^76 - 19 * q^77 + 6 * q^78 + 21 * q^79 - 7 * q^80 + 8 * q^81 - 9 * q^82 + 8 * q^83 + q^84 + 20 * q^85 - 4 * q^86 + 7 * q^87 - 2 * q^88 - 27 * q^89 + 6 * q^90 - 54 * q^91 - 8 * q^92 + 27 * q^93 - 11 * q^94 - 5 * q^95 - 3 * q^96 + 12 * q^97 + 14 * q^98 + 26 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$185$	$281$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	−0.873734	+	1.51335i	−0.504451	+	0.873734i	0.495536	+	0.868587i	$0.334972\pi$
$3$	−0.873734	+	1.51335i	−0.504451	+	0.873734i	−0.999987	+	0.00514686i	$0.998362\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−2.13304	−	3.69453i	−0.953924	−	1.65225i	−0.736811	−	0.676099i	$-0.763669\pi$
$5$	−2.13304	−	3.69453i	−0.953924	−	1.65225i	−0.217113	−	0.976146i	$-0.569664\pi$
$6$	1.74747			0.713401
$7$	1.89234	+	1.84906i	0.715239	+	0.698880i
$7$	1.89234	+	1.84906i	0.715239	+	0.698880i
$8$	1.00000			0.353553
$9$	−0.0268230	−	0.0464588i	−0.00894100	−	0.0154863i
$10$	−2.13304	+	3.69453i	−0.674526	+	1.16831i
$11$	−1.59438	+	2.76155i	−0.480724	+	0.832638i	−0.999755	−	0.0221173i	$-0.992959\pi$
$11$	−1.59438	+	2.76155i	−0.480724	+	0.832638i	0.519032	+	0.854755i	$0.326293\pi$
$12$	−0.873734	−	1.51335i	−0.252225	−	0.436867i
$13$	−4.60948			−1.27844			−0.639219	−	0.769024i	$-0.720742\pi$
$13$	−4.60948			−1.27844			−0.639219	+	0.769024i	$0.720742\pi$
$14$	0.655163	−	2.56335i	0.175100	−	0.685084i
$15$	7.45484			1.92483
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.57939	+	2.73559i	−0.383059	+	0.663478i	−0.991498	−	0.130123i	$-0.958463\pi$
$17$	−1.57939	+	2.73559i	−0.383059	+	0.663478i	0.608439	+	0.793601i	$0.291796\pi$
$18$	−0.0268230	+	0.0464588i	−0.00632224	+	0.0109504i
$19$	2.26815	+	3.92856i	0.520350	+	0.901273i	0.999720	+	0.0236597i	$0.00753182\pi$
$19$	2.26815	+	3.92856i	0.520350	+	0.901273i	−0.479370	+	0.877613i	$0.659135\pi$
$20$	4.26608			0.953924
$21$	−4.45169	+	1.24819i	−0.971438	+	0.272378i
$22$	3.18876			0.679846
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i
$24$	−0.873734	+	1.51335i	−0.178350	+	0.308912i
$25$	−6.59971	+	11.4310i	−1.31994	+	2.28621i
$26$	2.30474	+	3.99192i	0.451996	+	0.782881i
$27$	−5.14866			−0.990860
$28$	−2.54751	+	0.714287i	−0.481434	+	0.134988i
$29$	−3.70737			−0.688441			−0.344221	−	0.938889i	$-0.611857\pi$
$29$	−3.70737			−0.688441			−0.344221	+	0.938889i	$0.611857\pi$
$30$	−3.72742	−	6.45608i	−0.680531	−	1.17871i
$31$	−1.61805	+	2.80255i	−0.290611	+	0.503353i	−0.973954	−	0.226744i	$-0.927192\pi$
$31$	−1.61805	+	2.80255i	−0.290611	+	0.503353i	0.683343	+	0.730097i	$0.260525\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−2.78613	−	4.82572i	−0.485003	−	0.840049i
$34$	3.15879			0.541727
$35$	2.79498	−	10.9355i	0.472437	−	1.84843i
$36$	0.0536460			0.00894100
$37$	3.62328	+	6.27570i	0.595663	+	1.03172i	0.993453	+	0.114242i	$0.0364439\pi$
$37$	3.62328	+	6.27570i	0.595663	+	1.03172i	−0.397790	+	0.917477i	$0.630223\pi$
$38$	2.26815	−	3.92856i	0.367943	−	0.637296i
$39$	4.02746	−	6.97576i	0.644909	−	1.11702i
$40$	−2.13304	−	3.69453i	−0.337263	−	0.584157i
$41$	5.11454			0.798757			0.399378	−	0.916786i	$-0.369226\pi$
$41$	5.11454			0.798757			0.399378	+	0.916786i	$0.369226\pi$
$42$	3.30681	+	3.23118i	0.510252	+	0.498582i
$43$	−2.29605			−0.350145			−0.175072	−	0.984556i	$-0.556016\pi$
$43$	−2.29605			−0.350145			−0.175072	+	0.984556i	$0.556016\pi$
$44$	−1.59438	−	2.76155i	−0.240362	−	0.416319i
$45$	−0.114429	+	0.198197i	−0.0170581	+	0.0295454i
$46$	0.500000	−	0.866025i	0.0737210	−	0.127688i
$47$	−2.84899	−	4.93459i	−0.415567	−	0.719783i	0.579921	−	0.814673i	$-0.303084\pi$
$47$	−2.84899	−	4.93459i	−0.415567	−	0.719783i	−0.995488	+	0.0948895i	$0.969750\pi$
$48$	1.74747			0.252225
$49$	0.161936	+	6.99813i	0.0231338	+	0.999732i
$50$	13.1994			1.86668
$51$	−2.75994	−	4.78036i	−0.386469	−	0.669384i
$52$	2.30474	−	3.99192i	0.319610	−	0.553580i
$53$	6.09971	−	10.5650i	0.837860	−	1.45122i	−0.0538200	−	0.998551i	$-0.517140\pi$
$53$	6.09971	−	10.5650i	0.837860	−	1.45122i	0.891680	−	0.452666i	$-0.149527\pi$
$54$	2.57433	+	4.45887i	0.350322	+	0.606775i
$55$	13.6035			1.83430
$56$	1.89234	+	1.84906i	0.252875	+	0.247091i
$57$	−7.92705			−1.04996
$58$	1.85368	+	3.21068i	0.243401	+	0.421582i
$59$	−0.459266	+	0.795473i	−0.0597914	+	0.103562i	−0.894372	−	0.447325i	$-0.852377\pi$
$59$	−0.459266	+	0.795473i	−0.0597914	+	0.103562i	0.834580	+	0.550886i	$0.185710\pi$
$60$	−3.72742	+	6.45608i	−0.481208	+	0.833476i
$61$	−6.74448	−	11.6818i	−0.863542	−	1.49570i	−0.868488	−	0.495711i	$-0.834908\pi$
$61$	−6.74448	−	11.6818i	−0.863542	−	1.49570i	0.00494545	−	0.999988i	$-0.498426\pi$
$62$	3.23611			0.410986
$63$	0.0351469	−	0.137513i	0.00442809	−	0.0173251i
$64$	1.00000			0.125000
$65$	9.83220	+	17.0299i	1.21953	+	2.11229i
$66$	−2.78613	+	4.82572i	−0.342949	+	0.594005i
$67$	−2.37788	+	4.11861i	−0.290505	+	0.503169i	−0.973929	−	0.226852i	$-0.927156\pi$
$67$	−2.37788	+	4.11861i	−0.290505	+	0.503169i	0.683425	+	0.730021i	$0.260490\pi$
$68$	−1.57939	−	2.73559i	−0.191530	−	0.331739i
$69$	−1.74747			−0.210370
$70$	−10.8679	+	3.04721i	−1.29896	+	0.364211i
$71$	3.61960			0.429568			0.214784	−	0.976662i	$-0.431095\pi$
$71$	3.61960			0.429568			0.214784	+	0.976662i	$0.431095\pi$
$72$	−0.0268230	−	0.0464588i	−0.00316112	−	0.00547522i
$73$	6.68525	−	11.5792i	0.782449	−	1.35524i	−0.148062	−	0.988978i	$-0.547304\pi$
$73$	6.68525	−	11.5792i	0.782449	−	1.35524i	0.930511	−	0.366263i	$-0.119363\pi$
$74$	3.62328	−	6.27570i	0.421197	−	0.729535i
$75$	−11.5328	−	19.9754i	−1.33169	−	2.30656i
$76$	−4.53631			−0.520350
$77$	−8.12339	+	2.27769i	−0.925746	+	0.259567i
$78$	−8.05492			−0.912040
$79$	3.71036	+	6.42653i	0.417448	+	0.723041i	0.995682	−	0.0928298i	$-0.0295913\pi$
$79$	3.71036	+	6.42653i	0.417448	+	0.723041i	−0.578234	+	0.815871i	$0.696258\pi$
$80$	−2.13304	+	3.69453i	−0.238481	+	0.413061i
$81$	4.57903	−	7.93111i	0.508781	−	0.881235i
$82$	−2.55727	−	4.42932i	−0.282403	−	0.489137i
$83$	−9.36524			−1.02797			−0.513984	−	0.857800i	$-0.671831\pi$
$83$	−9.36524			−1.02797			−0.513984	+	0.857800i	$0.671831\pi$
$84$	1.14488	−	4.47937i	0.124916	−	0.488740i
$85$	13.4756			1.46164
$86$	1.14803	+	1.98844i	0.123795	+	0.214419i
$87$	3.23926	−	5.61056i	0.347285	−	0.601515i
$88$	−1.59438	+	2.76155i	−0.169961	+	0.294382i
$89$	2.61155	+	4.52334i	0.276824	+	0.479473i	0.970594	−	0.240724i	$-0.0773848\pi$
$89$	2.61155	+	4.52334i	0.276824	+	0.479473i	−0.693770	+	0.720197i	$0.744051\pi$
$90$	0.228858			0.0241238
$91$	−8.72272	−	8.52321i	−0.914389	−	0.893475i
$92$	−1.00000			−0.104257
$93$	−2.82750	−	4.89737i	−0.293198	−	0.507833i
$94$	−2.84899	+	4.93459i	−0.293850	+	0.508964i
$95$	9.67612	−	16.7595i	0.992749	−	1.71949i
$96$	−0.873734	−	1.51335i	−0.0891751	−	0.154456i
$97$	−5.74459			−0.583275			−0.291637	−	0.956529i	$-0.594200\pi$
$97$	−5.74459			−0.583275			−0.291637	+	0.956529i	$0.594200\pi$
$98$	5.97959	−	3.63930i	0.604030	−	0.367625i
$99$	0.171064			0.0171926
$100$	−6.59971	−	11.4310i	−0.659971	−	1.14310i
$101$	−6.45954	+	11.1882i	−0.642748	+	1.11327i	0.342069	+	0.939675i	$0.388872\pi$
$101$	−6.45954	+	11.1882i	−0.642748	+	1.11327i	−0.984817	+	0.173597i	$0.944461\pi$
$102$	−2.75994	+	4.78036i	−0.273275	+	0.473326i
$103$	−2.73041	−	4.72921i	−0.269035	−	0.465982i	0.699578	−	0.714556i	$-0.253371\pi$
$103$	−2.73041	−	4.72921i	−0.269035	−	0.465982i	−0.968613	+	0.248574i	$0.920038\pi$
$104$	−4.60948			−0.451996
$105$	14.1071	+	13.7845i	1.37671	+	1.34523i
$106$	−12.1994			−1.18491
$107$	5.11562	+	8.86051i	0.494545	+	0.856578i	0.999980	−	0.00628719i	$-0.00200129\pi$
$107$	5.11562	+	8.86051i	0.494545	+	0.856578i	−0.505435	+	0.862865i	$0.668668\pi$
$108$	2.57433	−	4.45887i	0.247715	−	0.429055i
$109$	−4.41565	+	7.64814i	−0.422943	+	0.732559i	−0.996226	−	0.0867987i	$-0.972336\pi$
$109$	−4.41565	+	7.64814i	−0.422943	+	0.732559i	0.573283	+	0.819358i	$0.305670\pi$
$110$	−6.80175	−	11.7810i	−0.648521	−	1.12327i
$111$	−12.6631			−1.20193
$112$	0.655163	−	2.56335i	0.0619071	−	0.242214i
$113$	−18.6201			−1.75164			−0.875818	−	0.482641i	$-0.839677\pi$
$113$	−18.6201			−1.75164			−0.875818	+	0.482641i	$0.839677\pi$
$114$	3.96353	+	6.86503i	0.371218	+	0.642969i
$115$	2.13304	−	3.69453i	0.198907	−	0.344517i
$116$	1.85368	−	3.21068i	0.172110	−	0.298104i
$117$	0.123640	+	0.214151i	0.0114305	+	0.0197982i
$118$	0.918533			0.0845578
$119$	−8.04703	+	2.25628i	−0.737670	+	0.206833i
$120$	7.45484			0.680531
$121$	0.415907	+	0.720372i	0.0378097	+	0.0654883i
$122$	−6.74448	+	11.6818i	−0.610616	+	1.05762i
$123$	−4.46875	+	7.74010i	−0.402934	+	0.697901i
$124$	−1.61805	−	2.80255i	−0.145305	−	0.251676i
$125$	34.9794			3.12865
$126$	−0.136664	+	0.0383187i	−0.0121750	+	0.00341370i
$127$	1.03070			0.0914598			0.0457299	−	0.998954i	$-0.485439\pi$
$127$	1.03070			0.0914598			0.0457299	+	0.998954i	$0.485439\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	2.00614	−	3.47473i	0.176631	−	0.305933i
$130$	9.83220	−	17.0299i	0.862341	−	1.49362i
$131$	3.78939	+	6.56341i	0.331080	+	0.573448i	0.982724	−	0.185077i	$-0.0592535\pi$
$131$	3.78939	+	6.56341i	0.331080	+	0.573448i	−0.651644	+	0.758525i	$0.725920\pi$
$132$	5.57226			0.485003
$133$	−2.97202	+	11.6281i	−0.257707	+	1.00829i
$134$	4.75576			0.410835
$135$	10.9823	+	19.0219i	0.945206	+	1.63714i
$136$	−1.57939	+	2.73559i	−0.135432	+	0.234575i
$137$	−6.22913	+	10.7892i	−0.532190	+	0.921781i	0.467103	+	0.884203i	$0.345298\pi$
$137$	−6.22913	+	10.7892i	−0.532190	+	0.921781i	−0.999294	+	0.0375781i	$0.988036\pi$
$138$	0.873734	+	1.51335i	0.0743772	+	0.128825i
$139$	16.3739			1.38882			0.694409	−	0.719581i	$-0.255666\pi$
$139$	16.3739			1.38882			0.694409	+	0.719581i	$0.255666\pi$
$140$	8.07289	+	7.88825i	0.682284	+	0.666678i
$141$	9.95702			0.838533
$142$	−1.80980	−	3.13467i	−0.151875	−	0.263056i
$143$	7.34926	−	12.7293i	0.614576	−	1.06448i
$144$	−0.0268230	+	0.0464588i	−0.00223525	+	0.00387157i
$145$	7.90797	+	13.6970i	0.656721	+	1.13747i
$146$	−13.3705			−1.10655
$147$	−10.7321	−	5.86944i	−0.885170	−	0.484103i
$148$	−7.24655			−0.595663
$149$	4.85261	+	8.40497i	0.397541	+	0.688562i	0.993422	−	0.114511i	$-0.0365302\pi$
$149$	4.85261	+	8.40497i	0.397541	+	0.688562i	−0.595881	+	0.803073i	$0.703197\pi$
$150$	−11.5328	+	19.9754i	−0.941649	+	1.63098i
$151$	6.03918	−	10.4602i	0.491462	−	0.851237i	−0.508490	−	0.861068i	$-0.669796\pi$
$151$	6.03918	−	10.4602i	0.491462	−	0.851237i	0.999952	+	0.00983118i	$0.00312941\pi$
$152$	2.26815	+	3.92856i	0.183971	+	0.318648i
$153$	0.169456			0.0136997
$154$	6.03423	+	5.89622i	0.486252	+	0.475131i
$155$	13.8055			1.10888
$156$	4.02746	+	6.97576i	0.322455	+	0.558508i
$157$	0.589045	−	1.02026i	0.0470109	−	0.0814253i	−0.841562	−	0.540160i	$-0.818364\pi$
$157$	0.589045	−	1.02026i	0.0470109	−	0.0814253i	0.888573	+	0.458735i	$0.151697\pi$
$158$	3.71036	−	6.42653i	0.295180	−	0.511267i
$159$	10.6591	+	18.4620i	0.845318	+	1.46413i
$160$	4.26608			0.337263
$161$	−0.655163	+	2.56335i	−0.0516341	+	0.202020i
$162$	−9.15806			−0.719525
$163$	−7.23223	−	12.5266i	−0.566472	−	0.981158i	−0.996911	−	0.0785386i	$-0.974975\pi$
$163$	−7.23223	−	12.5266i	−0.566472	−	0.981158i	0.430439	−	0.902620i	$-0.358359\pi$
$164$	−2.55727	+	4.42932i	−0.199689	+	0.345872i
$165$	−11.8858	+	20.5869i	−0.925312	+	1.60269i
$166$	4.68262	+	8.11054i	0.363442	+	0.629500i
$167$	−6.95702			−0.538351			−0.269175	−	0.963091i	$-0.586751\pi$
$167$	−6.95702			−0.538351			−0.269175	+	0.963091i	$0.586751\pi$
$168$	−4.45169	+	1.24819i	−0.343455	+	0.0963003i
$169$	8.24728			0.634406
$170$	−6.73782	−	11.6702i	−0.516767	−	0.895067i
$171$	0.121677	−	0.210751i	0.00930490	−	0.0161166i
$172$	1.14803	−	1.98844i	0.0875361	−	0.151617i
$173$	1.67836	+	2.90701i	0.127603	+	0.221016i	0.922748	−	0.385405i	$-0.125938\pi$
$173$	1.67836	+	2.90701i	0.127603	+	0.221016i	−0.795144	+	0.606420i	$0.792605\pi$
$174$	−6.47851			−0.491135
$175$	−33.6256	+	9.42818i	−2.54186	+	0.712704i
$176$	3.18876			0.240362
$177$	−0.802553	−	1.39006i	−0.0603236	−	0.104484i
$178$	2.61155	−	4.52334i	0.195744	−	0.339039i
$179$	9.52084	−	16.4906i	0.711621	−	1.23256i	−0.252627	−	0.967564i	$-0.581295\pi$
$179$	9.52084	−	16.4906i	0.711621	−	1.23256i	0.964248	−	0.265001i	$-0.0853721\pi$
$180$	−0.114429	−	0.198197i	−0.00852904	−	0.0147727i
$181$	9.25380			0.687830			0.343915	−	0.939001i	$-0.388247\pi$
$181$	9.25380			0.687830			0.343915	+	0.939001i	$0.388247\pi$
$182$	−3.01996	+	11.8157i	−0.223854	+	0.875838i
$183$	23.5715			1.74246
$184$	0.500000	+	0.866025i	0.0368605	+	0.0638442i
$185$	15.4572	−	26.7726i	1.13643	−	1.96836i
$186$	−2.82750	+	4.89737i	−0.207322	+	0.359092i
$187$	−5.03631	−	8.72314i	−0.368291	−	0.637899i
$188$	5.69797			0.415567
$189$	−9.74304	−	9.52019i	−0.708702	−	0.692492i
$190$	−19.3522			−1.40396
$191$	−7.68525	−	13.3112i	−0.556085	−	0.963167i	−0.997818	−	0.0660209i	$-0.978970\pi$
$191$	−7.68525	−	13.3112i	−0.556085	−	0.963167i	0.441733	−	0.897146i	$-0.354364\pi$
$192$	−0.873734	+	1.51335i	−0.0630563	+	0.109217i
$193$	−0.282979	+	0.490133i	−0.0203693	+	0.0352806i	−0.876030	−	0.482256i	$-0.839818\pi$
$193$	−0.282979	+	0.490133i	−0.0203693	+	0.0352806i	0.855661	+	0.517537i	$0.173151\pi$
$194$	2.87230	+	4.97496i	0.206219	+	0.357181i
$195$	−34.3629			−2.46078
$196$	−6.14152	−	3.35882i	−0.438680	−	0.239916i
$197$	−8.71335			−0.620800			−0.310400	−	0.950606i	$-0.600463\pi$
$197$	−8.71335			−0.620800			−0.310400	+	0.950606i	$0.600463\pi$
$198$	−0.0855321	−	0.148146i	−0.00607850	−	0.0105283i
$199$	−6.54977	+	11.3445i	−0.464301	+	0.804193i	−0.999170	−	0.0407424i	$-0.987028\pi$
$199$	−6.54977	+	11.3445i	−0.464301	+	0.804193i	0.534869	+	0.844935i	$0.320361\pi$
$200$	−6.59971	+	11.4310i	−0.466670	+	0.808297i
$201$	−4.15527	−	7.19715i	−0.293090	−	0.507648i
$202$	12.9191			0.908983
$203$	−7.01562	−	6.85516i	−0.492400	−	0.481138i
$204$	5.51988			0.386469
$205$	−10.9095	−	18.8958i	−0.761954	−	1.31974i
$206$	−2.73041	+	4.72921i	−0.190237	+	0.329499i
$207$	0.0268230	−	0.0464588i	0.00186433	−	0.00322911i
$208$	2.30474	+	3.99192i	0.159805	+	0.276790i
$209$	−14.4652			−1.00058
$210$	4.88413	−	19.1094i	0.337037	−	1.31867i
$211$	6.67125			0.459268			0.229634	−	0.973277i	$-0.426247\pi$
$211$	6.67125			0.459268			0.229634	+	0.973277i	$0.426247\pi$
$212$	6.09971	+	10.5650i	0.418930	+	0.725608i
$213$	−3.16257	+	5.47773i	−0.216696	+	0.375328i
$214$	5.11562	−	8.86051i	0.349696	−	0.605692i
$215$	4.89757	+	8.48284i	0.334011	+	0.578525i
$216$	−5.14866			−0.350322
$217$	−8.24400	+	2.31151i	−0.559640	+	0.156916i
$218$	8.83131			0.598132
$219$	11.6823	+	20.2343i	0.789414	+	1.36730i
$220$	−6.80175	+	11.7810i	−0.458574	+	0.794273i
$221$	7.28018	−	12.6096i	0.489718	−	0.848216i
$222$	6.33156	+	10.9666i	0.424947	+	0.736029i
$223$	16.9305			1.13375			0.566874	−	0.823804i	$-0.308153\pi$
$223$	16.9305			1.13375			0.566874	+	0.823804i	$0.308153\pi$
$224$	−2.54751	+	0.714287i	−0.170212	+	0.0477253i
$225$	0.708097			0.0472064
$226$	9.31007	+	16.1255i	0.619297	+	1.07265i
$227$	−9.13766	+	15.8269i	−0.606488	+	1.05047i	0.385327	+	0.922780i	$0.374089\pi$
$227$	−9.13766	+	15.8269i	−0.606488	+	1.05047i	−0.991814	+	0.127688i	$0.959245\pi$
$228$	3.96353	−	6.86503i	0.262491	−	0.454648i
$229$	−1.59538	−	2.76328i	−0.105426	−	0.182602i	0.808486	−	0.588515i	$-0.200287\pi$
$229$	−1.59538	−	2.76328i	−0.105426	−	0.182602i	−0.913912	+	0.405912i	$0.866954\pi$
$230$	−4.26608			−0.281297
$231$	3.65073	−	14.2836i	0.240201	−	0.939795i
$232$	−3.70737			−0.243401
$233$	−1.99945	−	3.46315i	−0.130988	−	0.226878i	0.793070	−	0.609131i	$-0.208482\pi$
$233$	−1.99945	−	3.46315i	−0.130988	−	0.226878i	−0.924058	+	0.382253i	$0.875148\pi$
$234$	0.123640	−	0.214151i	0.00808260	−	0.0139995i
$235$	−12.1540	+	21.0513i	−0.792839	+	1.37324i
$236$	−0.459266	−	0.795473i	−0.0298957	−	0.0517809i
$237$	−12.9675			−0.842328
$238$	5.97751	+	5.84079i	0.387465	+	0.378602i
$239$	19.5912			1.26725			0.633625	−	0.773640i	$-0.281566\pi$
$239$	19.5912			1.26725			0.633625	+	0.773640i	$0.281566\pi$
$240$	−3.72742	−	6.45608i	−0.240604	−	0.416738i
$241$	−4.15217	+	7.19178i	−0.267465	+	0.463263i	−0.968207	−	0.250152i	$-0.919519\pi$
$241$	−4.15217	+	7.19178i	−0.267465	+	0.463263i	0.700741	+	0.713415i	$0.252853\pi$
$242$	0.415907	−	0.720372i	0.0267355	−	0.0463073i
$243$	0.278720	+	0.482756i	0.0178799	+	0.0309688i
$244$	13.4890			0.863542
$245$	25.5094	−	15.5256i	1.62974	−	0.991892i
$246$	8.93750			0.569834
$247$	−10.4550	−	18.1086i	−0.665236	−	1.15222i
$248$	−1.61805	+	2.80255i	−0.102746	+	0.177962i
$249$	8.18273	−	14.1729i	0.518560	−	0.898172i
$250$	−17.4897	−	30.2931i	−1.10615	−	1.91590i
$251$	22.1789			1.39992			0.699958	−	0.714184i	$-0.253202\pi$
$251$	22.1789			1.39992			0.699958	+	0.714184i	$0.253202\pi$
$252$	0.101517	+	0.0991948i	0.00639495	+	0.00624868i
$253$	−3.18876			−0.200476
$254$	−0.515350	−	0.892612i	−0.0323359	−	0.0560074i
$255$	−11.7741	+	20.3934i	−0.737324	+	1.27708i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	4.48853	+	7.77436i	0.279987	+	0.484951i	0.971381	−	0.237526i	$-0.0763366\pi$
$257$	4.48853	+	7.77436i	0.279987	+	0.484951i	−0.691394	+	0.722477i	$0.743003\pi$
$258$	−4.01228			−0.249793
$259$	−4.74767	+	18.5755i	−0.295006	+	1.15422i
$260$	−19.6644			−1.21953
$261$	0.0994428	+	0.172240i	0.00615535	+	0.0106614i
$262$	3.78939	−	6.56341i	0.234109	−	0.405489i
$263$	7.89143	−	13.6684i	0.486606	−	0.842827i	−0.513275	−	0.858224i	$-0.671568\pi$
$263$	7.89143	−	13.6684i	0.486606	−	0.842827i	0.999881	+	0.0153972i	$0.00490127\pi$
$264$	−2.78613	−	4.82572i	−0.171474	−	0.297002i
$265$	−52.0437			−3.19702
$266$	11.5563	−	3.24023i	0.708560	−	0.198671i
$267$	−9.12721			−0.558576
$268$	−2.37788	−	4.11861i	−0.145252	−	0.251584i
$269$	3.12220	−	5.40781i	0.190364	−	0.329720i	−0.755007	−	0.655717i	$-0.772367\pi$
$269$	3.12220	−	5.40781i	0.190364	−	0.329720i	0.945371	+	0.325997i	$0.105700\pi$
$270$	10.9823	−	19.0219i	0.668361	−	1.15764i
$271$	14.3243	+	24.8103i	0.870137	+	1.50712i	0.861855	+	0.507155i	$0.169303\pi$
$271$	14.3243	+	24.8103i	0.870137	+	1.50712i	0.00828171	+	0.999966i	$0.497364\pi$
$272$	3.15879			0.191530
$273$	20.5200	−	5.75352i	1.24192	−	0.348219i
$274$	12.4583			0.752631
$275$	−21.0449	−	36.4508i	−1.26906	−	2.19807i
$276$	0.873734	−	1.51335i	0.0525926	−	0.0910931i
$277$	7.42813	−	12.8659i	0.446313	−	0.773037i	−0.551830	−	0.833957i	$-0.686070\pi$
$277$	7.42813	−	12.8659i	0.446313	−	0.773037i	0.998143	+	0.0609202i	$0.0194035\pi$
$278$	−8.18696	−	14.1802i	−0.491021	−	0.850473i
$279$	0.173604			0.0103934
$280$	2.79498	−	10.9355i	0.167032	−	0.653518i
$281$	−1.93983			−0.115721			−0.0578604	−	0.998325i	$-0.518428\pi$
$281$	−1.93983			−0.115721			−0.0578604	+	0.998325i	$0.518428\pi$
$282$	−4.97851	−	8.62304i	−0.296466	−	0.513494i
$283$	−12.7097	+	22.0139i	−0.755514	+	1.30859i	0.189604	+	0.981861i	$0.439280\pi$
$283$	−12.7097	+	22.0139i	−0.755514	+	1.30859i	−0.945118	+	0.326728i	$0.894054\pi$
$284$	−1.80980	+	3.13467i	−0.107392	+	0.186008i
$285$	16.9087	+	29.2867i	1.00159	+	1.73480i
$286$	−14.6985			−0.869141
$287$	9.67847	+	9.45710i	0.571302	+	0.558235i
$288$	0.0536460			0.00316112
$289$	3.51103	+	6.08129i	0.206531	+	0.357723i
$290$	7.90797	−	13.6970i	0.464372	−	0.804315i
$291$	5.01925	−	8.69359i	0.294233	−	0.509627i
$292$	6.68525	+	11.5792i	0.391224	+	0.677621i
$293$	−19.8987			−1.16249			−0.581246	−	0.813728i	$-0.697435\pi$
$293$	−19.8987			−1.16249			−0.581246	+	0.813728i	$0.697435\pi$
$294$	0.282979	+	12.2290i	0.0165037	+	0.713210i
$295$	3.91853			0.228146
$296$	3.62328	+	6.27570i	0.210599	+	0.364768i
$297$	8.20892	−	14.2183i	0.476330	−	0.825027i
$298$	4.85261	−	8.40497i	0.281104	−	0.486887i
$299$	−2.30474	−	3.99192i	−0.133286	−	0.230859i
$300$	23.0656			1.33169
$301$	−4.34492	−	4.24554i	−0.250437	−	0.244709i
$302$	−12.0784			−0.695032
$303$	−11.2878	−	19.5511i	−0.648469	−	1.12318i
$304$	2.26815	−	3.92856i	0.130087	−	0.225318i
$305$	−28.7725	+	49.8354i	−1.64751	+	2.85357i
$306$	−0.0847281	−	0.146753i	−0.00484359	−	0.00838934i
$307$	7.30872			0.417131			0.208565	−	0.978008i	$-0.433121\pi$
$307$	7.30872			0.417131			0.208565	+	0.978008i	$0.433121\pi$
$308$	2.08916	−	8.17391i	0.119041	−	0.465751i
$309$	9.54260			0.542860
$310$	−6.90274	−	11.9559i	−0.392049	−	0.679050i
$311$	−14.0863	+	24.3982i	−0.798762	+	1.38350i	0.121660	+	0.992572i	$0.461178\pi$
$311$	−14.0863	+	24.3982i	−0.798762	+	1.38350i	−0.920422	+	0.390925i	$0.872155\pi$
$312$	4.02746	−	6.97576i	0.228010	−	0.394925i
$313$	−5.18696	−	8.98407i	−0.293184	−	0.507810i	0.681377	−	0.731933i	$-0.261382\pi$
$313$	−5.18696	−	8.98407i	−0.293184	−	0.507810i	−0.974561	+	0.224123i	$0.928048\pi$
$314$	−1.17809			−0.0664835
$315$	−0.583018	+	0.163470i	−0.0328493	+	0.00921051i
$316$	−7.42072			−0.417448
$317$	−7.57325	−	13.1173i	−0.425356	−	0.736739i	0.571097	−	0.820882i	$-0.306518\pi$
$317$	−7.57325	−	13.1173i	−0.425356	−	0.736739i	−0.996454	+	0.0841436i	$0.973185\pi$
$318$	10.6591	−	18.4620i	0.597730	−	1.03530i
$319$	5.91096	−	10.2381i	0.330950	−	0.573222i
$320$	−2.13304	−	3.69453i	−0.119241	−	0.206531i
$321$	−17.8788			−0.997895
$322$	2.54751	−	0.714287i	0.141967	−	0.0398057i
$323$	−14.3292			−0.797299
$324$	4.57903	+	7.93111i	0.254391	+	0.440617i
$325$	30.4212	−	52.6911i	1.68747	−	2.92278i
$326$	−7.23223	+	12.5266i	−0.400556	+	0.693784i
$327$	−7.71622	−	13.3649i	−0.426708	−	0.739080i
$328$	5.11454			0.282403
$329$	3.73310	−	14.6059i	0.205812	−	0.805249i
$330$	23.7717			1.30859
$331$	9.01717	+	15.6182i	0.495629	+	0.858454i	0.999987	−	0.00504036i	$-0.00160440\pi$
$331$	9.01717	+	15.6182i	0.495629	+	0.858454i	−0.504359	+	0.863494i	$0.668271\pi$
$332$	4.68262	−	8.11054i	0.256992	−	0.445124i
$333$	0.194374	−	0.336666i	0.0106516	−	0.0184492i
$334$	3.47851	+	6.02496i	0.190336	+	0.329671i
$335$	20.2885			1.10848
$336$	3.30681	+	3.23118i	0.180401	+	0.176275i
$337$	24.1008			1.31285			0.656427	−	0.754389i	$-0.272067\pi$
$337$	24.1008			1.31285			0.656427	+	0.754389i	$0.272067\pi$
$338$	−4.12364	−	7.14235i	−0.224296	−	0.388493i
$339$	16.2691	−	28.1788i	0.883614	−	1.53046i
$340$	−6.73782	+	11.6702i	−0.365409	+	0.632908i
$341$	−5.15958	−	8.93666i	−0.279407	−	0.483947i
$342$	−0.243355			−0.0131591
$343$	−12.6335	+	13.5423i	−0.682147	+	0.731215i
$344$	−2.29605			−0.123795
$345$	3.72742	+	6.45608i	0.200677	+	0.347584i
$346$	1.67836	−	2.90701i	0.0902293	−	0.156282i
$347$	11.3487	−	19.6566i	0.609232	−	1.05522i	−0.382135	−	0.924106i	$-0.624811\pi$
$347$	11.3487	−	19.6566i	0.609232	−	1.05522i	0.991367	−	0.131114i	$-0.0418555\pi$
$348$	3.23926	+	5.61056i	0.173642	+	0.300757i
$349$	22.9733			1.22973			0.614865	−	0.788632i	$-0.289210\pi$
$349$	22.9733			1.22973			0.614865	+	0.788632i	$0.289210\pi$
$350$	24.9779	+	24.4066i	1.33512	+	1.30459i
$351$	23.7326			1.26675
$352$	−1.59438	−	2.76155i	−0.0849807	−	0.147191i
$353$	−8.79262	+	15.2293i	−0.467984	+	0.810572i	−0.999331	−	0.0365824i	$-0.988353\pi$
$353$	−8.79262	+	15.2293i	−0.467984	+	0.810572i	0.531347	+	0.847155i	$0.321686\pi$
$354$	−0.802553	+	1.39006i	−0.0426552	+	0.0738810i
$355$	−7.72076	−	13.3727i	−0.409775	−	0.709751i
$356$	−5.22310			−0.276824
$357$	3.61642	−	14.1494i	0.191401	−	0.748865i
$358$	−19.0417			−1.00638
$359$	1.73237	+	3.00055i	0.0914310	+	0.158363i	0.908113	−	0.418724i	$-0.137523\pi$
$359$	1.73237	+	3.00055i	0.0914310	+	0.158363i	−0.816682	+	0.577087i	$0.804189\pi$
$360$	−0.114429	+	0.198197i	−0.00603094	+	0.0104459i
$361$	−0.789034	+	1.36665i	−0.0415281	+	0.0719288i
$362$	−4.62690	−	8.01403i	−0.243185	−	0.421208i
$363$	−1.45357			−0.0762925
$364$	11.7427	−	3.29249i	0.615484	−	0.172573i
$365$	−57.0396			−2.98559
$366$	−11.7858	−	20.4135i	−0.616052	−	1.06703i
$367$	−0.550385	+	0.953295i	−0.0287299	+	0.0497616i	−0.880033	−	0.474913i	$-0.842480\pi$
$367$	−0.550385	+	0.953295i	−0.0287299	+	0.0497616i	0.851303	+	0.524674i	$0.175813\pi$
$368$	0.500000	−	0.866025i	0.0260643	−	0.0451447i
$369$	−0.137187	−	0.237615i	−0.00714169	−	0.0123698i
$370$	−30.9144			−1.60716
$371$	31.0781	−	8.71390i	1.61350	−	0.452403i
$372$	5.65499			0.293198
$373$	11.8710	+	20.5612i	0.614658	+	1.06462i	0.990444	+	0.137913i	$0.0440393\pi$
$373$	11.8710	+	20.5612i	0.614658	+	1.06462i	−0.375786	+	0.926706i	$0.622627\pi$
$374$	−5.03631	+	8.72314i	−0.260421	+	0.451063i
$375$	−30.5627	+	52.9362i	−1.57825	+	2.73361i
$376$	−2.84899	−	4.93459i	−0.146925	−	0.254482i
$377$	17.0890			0.880130
$378$	−3.37321	+	13.1978i	−0.173499	+	0.678823i
$379$	−3.03959			−0.156133			−0.0780667	−	0.996948i	$-0.524875\pi$
$379$	−3.03959			−0.156133			−0.0780667	+	0.996948i	$0.524875\pi$
$380$	9.67612	+	16.7595i	0.496374	+	0.859746i
$381$	−0.900557	+	1.55981i	−0.0461369	+	0.0799115i
$382$	−7.68525	+	13.3112i	−0.393211	+	0.681062i
$383$	7.27034	+	12.5926i	0.371497	+	0.643452i	0.989796	−	0.142491i	$-0.0455113\pi$
$383$	7.27034	+	12.5926i	0.371497	+	0.643452i	−0.618299	+	0.785943i	$0.712178\pi$
$384$	1.74747			0.0891751
$385$	25.7425	+	25.1537i	1.31196	+	1.28195i
$386$	0.565957			0.0288065
$387$	0.0615870	+	0.106672i	0.00313064	+	0.00542243i
$388$	2.87230	−	4.97496i	0.145819	−	0.252565i
$389$	−15.6587	+	27.1217i	−0.793927	+	1.37512i	0.129591	+	0.991568i	$0.458634\pi$
$389$	−15.6587	+	27.1217i	−0.793927	+	1.37512i	−0.923518	+	0.383555i	$0.874700\pi$
$390$	17.1815	+	29.7592i	0.870017	+	1.50691i
$391$	−3.15879			−0.159747
$392$	0.161936	+	6.99813i	0.00817902	+	0.353459i
$393$	−13.2437			−0.668055
$394$	4.35667	+	7.54598i	0.219486	+	0.380161i
$395$	15.8287	−	27.4161i	0.796428	−	1.37945i
$396$	−0.0855321	+	0.148146i	−0.00429815	+	0.00744461i
$397$	8.80952	+	15.2585i	0.442137	+	0.765804i	0.997848	−	0.0655717i	$-0.0208871\pi$
$397$	8.80952	+	15.2585i	0.442137	+	0.765804i	−0.555711	+	0.831376i	$0.687554\pi$
$398$	13.0995			0.656621
$399$	−15.0007	−	14.6576i	−0.750975	−	0.733798i
$400$	13.1994			0.659971
$401$	0.483100	+	0.836754i	0.0241249	+	0.0417855i	0.877836	−	0.478962i	$-0.158987\pi$
$401$	0.483100	+	0.836754i	0.0241249	+	0.0417855i	−0.853711	+	0.520747i	$0.825653\pi$
$402$	−4.15527	+	7.19715i	−0.207246	+	0.358961i
$403$	7.45838	−	12.9183i	0.371528	−	0.643506i
$404$	−6.45954	−	11.1882i	−0.321374	−	0.556636i
$405$	−39.0690			−1.94135
$406$	−2.42893	+	9.50329i	−0.120546	+	0.471640i
$407$	−23.1075			−1.14540
$408$	−2.75994	−	4.78036i	−0.136637	−	0.236663i
$409$	16.5328	−	28.6357i	0.817496	−	1.41595i	−0.0900250	−	0.995940i	$-0.528695\pi$
$409$	16.5328	−	28.6357i	0.817496	−	1.41595i	0.907521	−	0.420006i	$-0.137972\pi$
$410$	−10.9095	+	18.8958i	−0.538783	+	0.933199i
$411$	−10.8852	−	18.8537i	−0.536928	−	0.929986i
$412$	5.46082			0.269035
$413$	−2.33997	+	0.656096i	−0.115142	+	0.0322844i
$414$	−0.0536460			−0.00263656
$415$	19.9764	+	34.6002i	0.980604	+	1.69846i
$416$	2.30474	−	3.99192i	0.112999	−	0.195720i
$417$	−14.3064	+	24.7795i	−0.700590	+	1.21346i
$418$	7.23259	+	12.5272i	0.353758	+	0.612726i
$419$	30.6704			1.49835			0.749173	−	0.662375i	$-0.230451\pi$
$419$	30.6704			1.49835			0.749173	+	0.662375i	$0.230451\pi$
$420$	−18.9913	+	5.32490i	−0.926678	+	0.259828i
$421$	3.14483			0.153270			0.0766349	−	0.997059i	$-0.475582\pi$
$421$	3.14483			0.153270			0.0766349	+	0.997059i	$0.475582\pi$
$422$	−3.33563	−	5.77747i	−0.162376	−	0.281243i
$423$	−0.152837	+	0.264721i	−0.00743117	+	0.0128712i
$424$	6.09971	−	10.5650i	0.296228	−	0.513082i
$425$	−20.8471	−	36.1082i	−1.01123	−	1.75151i
$426$	6.32514			0.306454
$427$	8.83746	−	34.5769i	0.427675	−	1.67329i
$428$	−10.2312			−0.494545
$429$	12.8426	+	22.2440i	0.620046	+	1.07395i
$430$	4.89757	−	8.48284i	0.236182	−	0.409079i
$431$	3.34132	−	5.78734i	0.160946	−	0.278767i	−0.774262	−	0.632865i	$-0.781879\pi$
$431$	3.34132	−	5.78734i	0.160946	−	0.278767i	0.935208	+	0.354098i	$0.115212\pi$
$432$	2.57433	+	4.45887i	0.123858	+	0.214528i
$433$	−14.1421			−0.679628			−0.339814	−	0.940493i	$-0.610364\pi$
$433$	−14.1421			−0.679628			−0.339814	+	0.940493i	$0.610364\pi$
$434$	6.12383	+	5.98376i	0.293953	+	0.287230i
$435$	−27.6378			−1.32513
$436$	−4.41565	−	7.64814i	−0.211472	−	0.366279i
$437$	−2.26815	+	3.92856i	−0.108500	+	0.187928i
$438$	11.6823	−	20.2343i	0.558200	−	0.966830i
$439$	0.742769	+	1.28651i	0.0354504	+	0.0614019i	0.883206	−	0.468985i	$-0.155380\pi$
$439$	0.742769	+	1.28651i	0.0354504	+	0.0614019i	−0.847756	+	0.530387i	$0.822047\pi$
$440$	13.6035			0.648521
$441$	0.320781	−	0.195234i	0.0152753	−	0.00929686i
$442$	−14.5604			−0.692566
$443$	6.54536	+	11.3369i	0.310979	+	0.538632i	0.978575	−	0.205892i	$-0.0660097\pi$
$443$	6.54536	+	11.3369i	0.310979	+	0.538632i	−0.667595	+	0.744524i	$0.732676\pi$
$444$	6.33156	−	10.9666i	0.300483	−	0.520451i
$445$	11.1411	−	19.2969i	0.528138	−	0.914762i
$446$	−8.46524	−	14.6622i	−0.400841	−	0.694276i
$447$	−16.9596			−0.802160
$448$	1.89234	+	1.84906i	0.0894049	+	0.0873600i
$449$	−28.0004			−1.32142			−0.660710	−	0.750641i	$-0.729745\pi$
$449$	−28.0004			−1.32142			−0.660710	+	0.750641i	$0.729745\pi$
$450$	−0.354048	−	0.613230i	−0.0166900	−	0.0289079i
$451$	−8.15452	+	14.1240i	−0.383981	+	0.665075i
$452$	9.31007	−	16.1255i	0.437909	−	0.758481i
$453$	10.5533	+	18.2788i	0.495836	+	0.858814i
$454$	18.2753			0.857703
$455$	−12.8834	+	50.4067i	−0.603982	+	2.36310i
$456$	−7.92705			−0.371218
$457$	1.94239	+	3.36433i	0.0908614	+	0.157377i	0.907874	−	0.419244i	$-0.137705\pi$
$457$	1.94239	+	3.36433i	0.0908614	+	0.157377i	−0.817012	+	0.576620i	$0.804371\pi$
$458$	−1.59538	+	2.76328i	−0.0745471	+	0.129119i
$459$	8.13176	−	14.0846i	0.379558	−	0.657414i
$460$	2.13304	+	3.69453i	0.0994535	+	0.172258i
$461$	−21.7186			−1.01154			−0.505768	−	0.862670i	$-0.668791\pi$
$461$	−21.7186			−1.01154			−0.505768	+	0.862670i	$0.668791\pi$
$462$	−14.1954	+	3.98019i	−0.660428	+	0.185175i
$463$	4.97234			0.231084			0.115542	−	0.993303i	$-0.463139\pi$
$463$	4.97234			0.231084			0.115542	+	0.993303i	$0.463139\pi$
$464$	1.85368	+	3.21068i	0.0860552	+	0.149052i
$465$	−12.0623	+	20.8926i	−0.559377	+	0.968869i
$466$	−1.99945	+	3.46315i	−0.0926226	+	0.160427i
$467$	3.42464	+	5.93166i	0.158474	+	0.274484i	0.934318	−	0.356439i	$-0.116009\pi$
$467$	3.42464	+	5.93166i	0.158474	+	0.274484i	−0.775845	+	0.630924i	$0.782676\pi$
$468$	−0.247280			−0.0114305
$469$	−12.1153	+	3.39698i	−0.559435	+	0.156858i
$470$	24.3080			1.12124
$471$	1.02934	+	1.78286i	0.0474294	+	0.0821501i
$472$	−0.459266	+	0.795473i	−0.0211394	+	0.0366146i
$473$	3.66078	−	6.34065i	0.168323	−	0.291544i
$474$	6.48374	+	11.2302i	0.297808	+	0.515818i
$475$	−59.8766			−2.74733
$476$	2.06952	−	8.09708i	0.0948563	−	0.371129i
$477$	−0.654451			−0.0299652
$478$	−9.79561	−	16.9665i	−0.448041	−	0.776029i
$479$	−5.00235	+	8.66432i	−0.228563	+	0.395883i	−0.957382	−	0.288823i	$-0.906736\pi$
$479$	−5.00235	+	8.66432i	−0.228563	+	0.395883i	0.728819	+	0.684706i	$0.240069\pi$
$480$	−3.72742	+	6.45608i	−0.170133	+	0.294678i
$481$	−16.7014	−	28.9277i	−0.761519	−	1.31899i
$482$	8.30435			0.378253
$483$	−3.30681	−	3.23118i	−0.150465	−	0.147024i
$484$	−0.831814			−0.0378097
$485$	12.2534	+	21.2236i	0.556400	+	0.963713i
$486$	0.278720	−	0.482756i	0.0126430	−	0.0218983i
$487$	−13.4580	+	23.3099i	−0.609840	+	1.05627i	0.381427	+	0.924399i	$0.375433\pi$
$487$	−13.4580	+	23.3099i	−0.609840	+	1.05627i	−0.991266	+	0.131874i	$0.957901\pi$
$488$	−6.74448	−	11.6818i	−0.305308	−	0.528809i
$489$	25.2762			1.14303
$490$	−26.2002	−	14.3290i	−1.18361	−	0.647318i
$491$	−17.6787			−0.797827			−0.398914	−	0.916989i	$-0.630613\pi$
$491$	−17.6787			−0.797827			−0.398914	+	0.916989i	$0.630613\pi$
$492$	−4.46875	−	7.74010i	−0.201467	−	0.348951i
$493$	5.85540	−	10.1418i	0.263714	−	0.456766i
$494$	−10.4550	+	18.1086i	−0.470393	+	0.814744i
$495$	−0.364887	−	0.632002i	−0.0164004	−	0.0284064i
$496$	3.23611			0.145305
$497$	6.84954	+	6.69287i	0.307244	+	0.300216i
$498$	−16.3655			−0.733354
$499$	−10.7720	−	18.6577i	−0.482223	−	0.835235i	0.517569	−	0.855642i	$-0.326837\pi$
$499$	−10.7720	−	18.6577i	−0.482223	−	0.835235i	−0.999792	+	0.0204067i	$0.993504\pi$
$500$	−17.4897	+	30.2931i	−0.782163	+	1.35475i
$501$	6.07859	−	10.5284i	0.271571	−	0.470375i
$502$	−11.0894	−	19.2075i	−0.494945	−	0.857271i
$503$	−30.0934			−1.34180			−0.670900	−	0.741548i	$-0.734092\pi$
$503$	−30.0934			−1.34180			−0.670900	+	0.741548i	$0.734092\pi$
$504$	0.0351469	−	0.137513i	0.00156557	−	0.00612534i
$505$	55.1138			2.45253
$506$	1.59438	+	2.76155i	0.0708788	+	0.122766i
$507$	−7.20593	+	12.4810i	−0.320027	+	0.554302i
$508$	−0.515350	+	0.892612i	−0.0228649	+	0.0396032i
$509$	8.83400	+	15.3009i	0.391560	+	0.678202i	0.992656	−	0.120975i	$-0.0386022\pi$
$509$	8.83400	+	15.3009i	0.391560	+	0.678202i	−0.601095	+	0.799177i	$0.705269\pi$
$510$	23.5482			1.04273
$511$	34.0614	−	9.55037i	1.50679	−	0.422484i
$512$	1.00000			0.0441942
$513$	−11.6779	−	20.2268i	−0.515594	−	0.893035i
$514$	4.48853	−	7.77436i	0.197980	−	0.342912i
$515$	−11.6481	+	20.1752i	−0.513278	+	0.889024i
$516$	2.00614	+	3.47473i	0.0883153	+	0.152967i
$517$	18.1695			0.799092
$518$	18.4606	−	5.17612i	0.811114	−	0.227426i
$519$	−5.86577			−0.257479
$520$	9.83220	+	17.0299i	0.431170	+	0.746809i
$521$	7.07497	−	12.2542i	0.309960	−	0.536866i	−0.668393	−	0.743808i	$-0.733018\pi$
$521$	7.07497	−	12.2542i	0.309960	−	0.536866i	0.978353	+	0.206942i	$0.0663510\pi$
$522$	0.0994428	−	0.172240i	0.00435249	−	0.00753874i
$523$	15.1714	+	26.2777i	0.663401	+	1.14904i	0.979716	+	0.200390i	$0.0642208\pi$
$523$	15.1714	+	26.2777i	0.663401	+	1.14904i	−0.316316	+	0.948654i	$0.602446\pi$
$524$	−7.57878			−0.331080
$525$	15.1117	−	59.1252i	0.659529	−	2.58043i
$526$	−15.7829			−0.688165
$527$	−5.11109	−	8.85266i	−0.222642	−	0.385628i
$528$	−2.78613	+	4.82572i	−0.121251	+	0.210012i
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$	26.0219	+	45.0712i	1.13032	+	1.95777i
$531$	0.0492756			0.00213838
$532$	−8.58425	−	8.38791i	−0.372175	−	0.363662i
$533$	−23.5754			−1.02116
$534$	4.56360	+	7.90439i	0.197486	+	0.342057i
$535$	21.8236	−	37.7996i	0.943517	−	1.63422i
$536$	−2.37788	+	4.11861i	−0.102709	+	0.177897i
$537$	16.6374	+	28.8168i	0.717956	+	1.24354i
$538$	−6.24440			−0.269215
$539$	−19.5838	−	10.7105i	−0.843536	−	0.461333i
$540$	−21.9646			−0.945206
$541$	−12.2064	−	21.1420i	−0.524793	−	0.908967i	−0.999583	−	0.0288686i	$-0.990810\pi$
$541$	−12.2064	−	21.1420i	−0.524793	−	0.908967i	0.474791	−	0.880099i	$-0.342524\pi$
$542$	14.3243	−	24.8103i	0.615279	−	1.06570i
$543$	−8.08536	+	14.0043i	−0.346976	+	0.600980i
$544$	−1.57939	−	2.73559i	−0.0677159	−	0.117287i
$545$	37.6751			1.61382
$546$	−15.2427	−	14.8940i	−0.652326	−	0.637406i
$547$	19.8203			0.847455			0.423727	−	0.905790i	$-0.360721\pi$
$547$	19.8203			0.847455			0.423727	+	0.905790i	$0.360721\pi$
$548$	−6.22913	−	10.7892i	−0.266095	−	0.460890i
$549$	−0.361814	+	0.626681i	−0.0154419	+	0.0267461i
$550$	−21.0449	+	36.4508i	−0.897358	+	1.55427i
$551$	−8.40888	−	14.5646i	−0.358230	−	0.620473i
$552$	−1.74747			−0.0743772
$553$	−4.86178	+	19.0219i	−0.206744	+	0.808893i
$554$	−14.8563			−0.631182
$555$	27.0109	+	46.7843i	1.14655	+	1.98588i
$556$	−8.18696	+	14.1802i	−0.347204	+	0.601376i
$557$	−0.890251	+	1.54196i	−0.0377212	+	0.0653350i	−0.884270	−	0.466977i	$-0.845343\pi$
$557$	−0.890251	+	1.54196i	−0.0377212	+	0.0653350i	0.846548	+	0.532312i	$0.178677\pi$
$558$	−0.0868021	−	0.150346i	−0.00367462	−	0.00636464i
$559$	10.5836			0.447638
$560$	−10.8679	+	3.04721i	−0.459251	+	0.128768i
$561$	17.6016			0.743139
$562$	0.969916	+	1.67994i	0.0409134	+	0.0708642i
$563$	−17.2114	+	29.8109i	−0.725372	+	1.25638i	0.233448	+	0.972369i	$0.424999\pi$
$563$	−17.2114	+	29.8109i	−0.725372	+	1.25638i	−0.958821	+	0.284012i	$0.908334\pi$
$564$	−4.97851	+	8.62304i	−0.209633	+	0.363095i
$565$	39.7175	+	68.7927i	1.67093	+	2.89413i
$566$	25.4194			1.06846
$567$	23.3302	−	6.54149i	0.979777	−	0.274717i
$568$	3.61960			0.151875
$569$	−6.52737	−	11.3057i	−0.273642	−	0.473961i	0.696150	−	0.717897i	$-0.254895\pi$
$569$	−6.52737	−	11.3057i	−0.273642	−	0.473961i	−0.969792	+	0.243935i	$0.921562\pi$
$570$	16.9087	−	29.2867i	0.708228	−	1.22669i
$571$	12.7005	−	21.9979i	0.531500	−	0.920584i	−0.467824	−	0.883821i	$-0.654962\pi$
$571$	12.7005	−	21.9979i	0.531500	−	0.920584i	0.999324	−	0.0367628i	$-0.0117046\pi$
$572$	7.34926	+	12.7293i	0.307288	+	0.532238i
$573$	26.8595			1.12207
$574$	3.35086	−	13.1104i	0.139862	−	0.547216i
$575$	−13.1994			−0.550454
$576$	−0.0268230	−	0.0464588i	−0.00111762	−	0.00193578i
$577$	20.9638	−	36.3104i	0.872736	−	1.51162i	0.0135816	−	0.999908i	$-0.495677\pi$
$577$	20.9638	−	36.3104i	0.872736	−	1.51162i	0.859155	−	0.511716i	$-0.170990\pi$
$578$	3.51103	−	6.08129i	0.146040	−	0.252948i
$579$	−0.494496	−	0.856493i	−0.0205506	−	0.0355946i
$580$	−15.8159			−0.656721
$581$	−17.7223	−	17.3169i	−0.735243	−	0.718427i
$582$	−10.0385			−0.416109
$583$	19.4505	+	33.6893i	0.805558	+	1.39527i
$584$	6.68525	−	11.5792i	0.276637	−	0.479150i
$585$	0.527458	−	0.913584i	0.0218077	−	0.0377721i
$586$	9.94933	+	17.2328i	0.411003	+	0.711878i
$587$	27.1223			1.11946			0.559729	−	0.828676i	$-0.310905\pi$
$587$	27.1223			1.11946			0.559729	+	0.828676i	$0.310905\pi$
$588$	10.4491	−	6.35957i	0.430915	−	0.262264i
$589$	−14.6800			−0.604878
$590$	−1.95927	−	3.39355i	−0.0806617	−	0.139710i
$591$	7.61315	−	13.1864i	0.313163	−	0.542415i
$592$	3.62328	−	6.27570i	0.148916	−	0.257930i
$593$	0.784054	+	1.35802i	0.0321972	+	0.0557673i	0.881675	−	0.471857i	$-0.156416\pi$
$593$	0.784054	+	1.35802i	0.0321972	+	0.0557673i	−0.849478	+	0.527624i	$0.823083\pi$
$594$	−16.4178			−0.673632
$595$	25.5005	+	24.9173i	1.04542	+	1.02151i
$596$	−9.70522			−0.397541
$597$	−11.4455	−	19.8242i	−0.468434	−	0.811351i
$598$	−2.30474	+	3.99192i	−0.0942478	+	0.163242i
$599$	−21.1389	+	36.6136i	−0.863711	+	1.49599i	0.00461091	+	0.999989i	$0.498532\pi$
$599$	−21.1389	+	36.6136i	−0.863711	+	1.49599i	−0.868322	+	0.496002i	$0.834801\pi$
$600$	−11.5328	−	19.9754i	−0.470824	−	0.815492i
$601$	−29.1651			−1.18967			−0.594834	−	0.803848i	$-0.702782\pi$
$601$	−29.1651			−1.18967			−0.594834	+	0.803848i	$0.702782\pi$
$602$	−1.50429	+	5.88558i	−0.0613102	+	0.239878i
$603$	0.255128			0.0103896
$604$	6.03918	+	10.4602i	0.245731	+	0.425618i
$605$	1.77429	−	3.07316i	0.0721352	−	0.124942i
$606$	−11.2878	+	19.5511i	−0.458537	+	0.794210i
$607$	−5.29634	−	9.17353i	−0.214972	−	0.372342i	0.738292	−	0.674481i	$-0.235633\pi$
$607$	−5.29634	−	9.17353i	−0.214972	−	0.372342i	−0.953264	+	0.302139i	$0.902299\pi$
$608$	−4.53631			−0.183971
$609$	16.5041	−	4.62752i	0.668778	−	0.187517i
$610$	57.5450			2.32993
$611$	13.1323	+	22.7459i	0.531277	+	0.920199i
$612$	−0.0847281	+	0.146753i	−0.00342493	+	0.00593216i
$613$	5.40730	−	9.36572i	0.218399	−	0.378278i	−0.735920	−	0.677069i	$-0.763250\pi$
$613$	5.40730	−	9.36572i	0.218399	−	0.378278i	0.954319	+	0.298791i	$0.0965833\pi$
$614$	−3.65436	−	6.32954i	−0.147478	−	0.255439i
$615$	38.1281			1.53747
$616$	−8.12339	+	2.27769i	−0.327301	+	0.0917708i
$617$	−18.2246			−0.733693			−0.366846	−	0.930281i	$-0.619563\pi$
$617$	−18.2246			−0.733693			−0.366846	+	0.930281i	$0.619563\pi$
$618$	−4.77130	−	8.26414i	−0.191930	−	0.332432i
$619$	−16.3438	+	28.3083i	−0.656914	+	1.13781i	0.324496	+	0.945887i	$0.394805\pi$
$619$	−16.3438	+	28.3083i	−0.656914	+	1.13781i	−0.981410	+	0.191921i	$0.938528\pi$
$620$	−6.90274	+	11.9559i	−0.277221	+	0.480161i
$621$	−2.57433	−	4.45887i	−0.103304	−	0.178928i
$622$	28.1727			1.12962
$623$	−3.42198	+	13.3886i	−0.137099	+	0.536404i
$624$	−8.05492			−0.322455
$625$	−41.6139	−	72.0774i	−1.66456	−	2.88309i
$626$	−5.18696	+	8.98407i	−0.207312	+	0.359076i
$627$	12.6387	−	21.8909i	0.504742	−	0.874239i
$628$	0.589045	+	1.02026i	0.0235055	+	0.0407126i
$629$	−22.8903			−0.912697
$630$	0.433078	+	0.423173i	0.0172543	+	0.0168596i
$631$	−16.7672			−0.667492			−0.333746	−	0.942663i	$-0.608313\pi$
$631$	−16.7672			−0.667492			−0.333746	+	0.942663i	$0.608313\pi$
$632$	3.71036	+	6.42653i	0.147590	+	0.255634i
$633$	−5.82890	+	10.0960i	−0.231678	+	0.401278i
$634$	−7.57325	+	13.1173i	−0.300772	+	0.520953i
$635$	−2.19852	−	3.80795i	−0.0872457	−	0.151114i
$636$	−21.3181			−0.845318
$637$	−0.746442	−	32.2577i	−0.0295751	−	1.27810i
$638$	−11.8219			−0.468034
$639$	−0.0970886	−	0.168162i	−0.00384077	−	0.00665240i
$640$	−2.13304	+	3.69453i	−0.0843158	+	0.146039i
$641$	16.2952	−	28.2242i	0.643624	−	1.11479i	−0.340994	−	0.940065i	$-0.610764\pi$
$641$	16.2952	−	28.2242i	0.643624	−	1.11479i	0.984618	−	0.174723i	$-0.0559031\pi$
$642$	8.93938	+	15.4835i	0.352809	+	0.611083i
$643$	−6.41984			−0.253174			−0.126587	−	0.991956i	$-0.540402\pi$
$643$	−6.41984			−0.253174			−0.126587	+	0.991956i	$0.540402\pi$
$644$	−1.89234	−	1.84906i	−0.0745688	−	0.0728633i
$645$	−17.1167			−0.673969
$646$	7.16461	+	12.4095i	0.281888	+	0.488244i
$647$	8.13548	−	14.0911i	0.319839	−	0.553977i	−0.660616	−	0.750724i	$-0.729705\pi$
$647$	8.13548	−	14.0911i	0.319839	−	0.553977i	0.980454	+	0.196748i	$0.0630380\pi$
$648$	4.57903	−	7.93111i	0.179881	−	0.311564i
$649$	−1.46449	−	2.53657i	−0.0574863	−	0.0995691i
$650$	−60.8425			−2.38644
$651$	3.70494	−	14.4957i	0.145208	−	0.568132i
$652$	14.4645			0.566472
$653$	−11.8989	−	20.6094i	−0.465639	−	0.806510i	0.533591	−	0.845742i	$-0.320842\pi$
$653$	−11.8989	−	20.6094i	−0.465639	−	0.806510i	−0.999230	+	0.0392326i	$0.987509\pi$
$654$	−7.71622	+	13.3649i	−0.301728	+	0.522608i
$655$	16.1658	−	28.0000i	0.631651	−	1.09405i
$656$	−2.55727	−	4.42932i	−0.0998446	−	0.172936i
$657$	−0.717273			−0.0279835
$658$	−14.5156	+	4.06999i	−0.565878	+	0.158665i
$659$	42.1039			1.64013			0.820067	−	0.572268i	$-0.193936\pi$
$659$	42.1039			1.64013			0.820067	+	0.572268i	$0.193936\pi$
$660$	−11.8858	−	20.5869i	−0.462656	−	0.801343i
$661$	−25.4182	+	44.0255i	−0.988652	+	1.71240i	−0.364227	+	0.931310i	$0.618667\pi$
$661$	−25.4182	+	44.0255i	−0.988652	+	1.71240i	−0.624424	+	0.781085i	$0.714666\pi$
$662$	9.01717	−	15.6182i	0.350462	−	0.607019i
$663$	12.7219	+	22.0349i	0.494077	+	0.855766i
$664$	−9.36524			−0.363442
$665$	49.3000	−	13.8231i	1.91177	−	0.536035i
$666$	−0.388749			−0.0150637
$667$	−1.85368	−	3.21068i	−0.0717750	−	0.124318i
$668$	3.47851	−	6.02496i	0.134588	−	0.233113i
$669$	−14.7927	+	25.6218i	−0.571920	+	0.990595i
$670$	−10.1442	−	17.5703i	−0.391906	−	0.678801i
$671$	43.0130			1.66050
$672$	1.14488	−	4.47937i	0.0441646	−	0.172796i
$673$	20.5556			0.792360			0.396180	−	0.918173i	$-0.370336\pi$
$673$	20.5556			0.792360			0.396180	+	0.918173i	$0.370336\pi$
$674$	−12.0504	−	20.8719i	−0.464164	−	0.803956i
$675$	33.9797	−	58.8545i	1.30788	−	2.26531i
$676$	−4.12364	+	7.14235i	−0.158602	+	0.274706i
$677$	19.0863	+	33.0584i	0.733546	+	1.27054i	0.955358	+	0.295450i	$0.0954694\pi$
$677$	19.0863	+	33.0584i	0.733546	+	1.27054i	−0.221812	+	0.975089i	$0.571197\pi$
$678$	−32.5381			−1.24962
$679$	−10.8707	−	10.6221i	−0.417181	−	0.407639i
$680$	13.4756			0.516767
$681$	−15.9678	−	27.6570i	−0.611887	−	1.05982i
$682$	−5.15958	+	8.93666i	−0.197571	+	0.342202i
$683$	−1.32368	+	2.29269i	−0.0506494	+	0.0877273i	−0.890239	−	0.455495i	$-0.849462\pi$
$683$	−1.32368	+	2.29269i	−0.0506494	+	0.0877273i	0.839589	+	0.543222i	$0.182796\pi$
$684$	0.121677	+	0.210751i	0.00465245	+	0.00805828i
$685$	53.1479			2.03068
$686$	18.0447	+	4.16981i	0.688951	+	0.159204i
$687$	5.57575			0.212728
$688$	1.14803	+	1.98844i	0.0437681	+	0.0758085i
$689$	−28.1165	+	48.6992i	−1.07115	+	1.85529i
$690$	3.72742	−	6.45608i	0.141900	−	0.245779i
$691$	−22.4274	−	38.8454i	−0.853178	−	1.47775i	−0.878325	−	0.478065i	$-0.841338\pi$
$691$	−22.4274	−	38.8454i	−0.853178	−	1.47775i	0.0251461	−	0.999684i	$-0.491995\pi$
$692$	−3.35672			−0.127603
$693$	0.323712	+	0.316308i	0.0122968	+	0.0120156i
$694$	−22.6975			−0.861584
$695$	−34.9262	−	60.4940i	−1.32483	−	2.29467i
$696$	3.23926	−	5.61056i	0.122784	−	0.212668i
$697$	−8.07787	+	13.9913i	−0.305971	+	0.529958i
$698$	−11.4866	−	19.8954i	−0.434775	−	0.753053i
$699$	6.98795			0.264308
$700$	8.64777	−	33.8348i	0.326855	−	1.27883i
$701$	−3.67590			−0.138837			−0.0694185	−	0.997588i	$-0.522114\pi$
$701$	−3.67590			−0.138837			−0.0694185	+	0.997588i	$0.522114\pi$
$702$	−11.8663	−	20.5531i	−0.447865	−	0.775725i
$703$	−16.4363	+	28.4685i	−0.619906	+	1.07371i
$704$	−1.59438	+	2.76155i	−0.0600904	+	0.104080i
$705$	−21.2387	−	36.7865i	−0.799897	−	1.38546i
$706$	17.5852			0.661829
$707$	−32.9114	+	9.22793i	−1.23776	+	0.347052i
$708$	1.60511			0.0603236
$709$	3.54427	+	6.13886i	0.133108	+	0.230550i	0.924873	−	0.380276i	$-0.124171\pi$
$709$	3.54427	+	6.13886i	0.133108	+	0.230550i	−0.791765	+	0.610826i	$0.790838\pi$
$710$	−7.72076	+	13.3727i	−0.289755	+	0.501870i
$711$	0.199046	−	0.344758i	0.00746480	−	0.0129294i
$712$	2.61155	+	4.52334i	0.0978720	+	0.169519i
$713$	−3.23611			−0.121193
$714$	−14.0619	+	3.94278i	−0.526255	+	0.147555i
$715$	−62.7050			−2.34503
$716$	9.52084	+	16.4906i	0.355811	+	0.616282i
$717$	−17.1175	+	29.6484i	−0.639266	+	1.10724i
$718$	1.73237	−	3.00055i	0.0646515	−	0.111980i
$719$	7.43661	+	12.8806i	0.277339	+	0.480365i	0.970723	−	0.240204i	$-0.0772142\pi$
$719$	7.43661	+	12.8806i	0.277339	+	0.480365i	−0.693384	+	0.720569i	$0.743881\pi$
$720$	0.228858			0.00852904
$721$	3.57772	−	13.9980i	0.133241	−	0.521312i
$722$	1.57807			0.0587296
$723$	−7.25579	−	12.5674i	−0.269846	−	0.467387i
$724$	−4.62690	+	8.01403i	−0.171957	+	0.297839i
$725$	24.4676	−	42.3791i	0.908703	−	1.57392i
$726$	0.726784	+	1.25883i	0.0269735	+	0.0467195i
$727$	14.9667			0.555086			0.277543	−	0.960713i	$-0.410480\pi$
$727$	14.9667			0.555086			0.277543	+	0.960713i	$0.410480\pi$
$728$	−8.72272	−	8.52321i	−0.323285	−	0.315891i
$729$	26.5001			0.981484
$730$	28.5198	+	49.3977i	1.05556	+	1.82829i
$731$	3.62637	−	6.28105i	0.134126	−	0.232313i
$732$	−11.7858	+	20.4135i	−0.435614	+	0.754506i
$733$	−23.2343	−	40.2430i	−0.858178	−	1.48641i	−0.873665	−	0.486528i	$-0.838263\pi$
$733$	−23.2343	−	40.2430i	−0.858178	−	1.48641i	0.0154865	−	0.999880i	$-0.495070\pi$
$734$	1.10077			0.0406302
$735$	1.20721	+	52.1699i	0.0445286	+	1.92432i
$736$	−1.00000			−0.0368605
$737$	−7.58249	−	13.1333i	−0.279305	−	0.483770i
$738$	−0.137187	+	0.237615i	−0.00504993	+	0.00874674i
$739$	−17.4393	+	30.2058i	−0.641516	+	1.11114i	0.343579	+	0.939124i	$0.388361\pi$
$739$	−17.4393	+	30.2058i	−0.641516	+	1.11114i	−0.985095	+	0.172014i	$0.944973\pi$
$740$	15.4572	+	26.7726i	0.568217	+	0.984181i
$741$	36.5396			1.34231
$742$	−23.0855	−	22.5575i	−0.847496	−	0.828112i
$743$	5.81935			0.213491			0.106746	−	0.994286i	$-0.465957\pi$
$743$	5.81935			0.213491			0.106746	+	0.994286i	$0.465957\pi$
$744$	−2.82750	−	4.89737i	−0.103661	−	0.179546i
$745$	20.7016	−	35.8562i	0.758448	−	1.31367i
$746$	11.8710	−	20.5612i	0.434629	−	0.752799i
$747$	0.251204	+	0.435098i	0.00919107	+	0.0159194i
$748$	10.0726			0.368291
$749$	−6.70312	+	26.2262i	−0.244927	+	0.958285i
$750$	61.1254			2.23198
$751$	25.1195	+	43.5082i	0.916623	+	1.58764i	0.804508	+	0.593942i	$0.202429\pi$
$751$	25.1195	+	43.5082i	0.916623	+	1.58764i	0.112115	+	0.993695i	$0.464237\pi$
$752$	−2.84899	+	4.93459i	−0.103892	+	0.179946i
$753$	−19.3784	+	33.5644i	−0.706189	+	1.22316i
$754$	−8.54452	−	14.7995i	−0.311173	−	0.538967i
$755$	−51.5273			−1.87527
$756$	13.1163	−	3.67762i	0.477033	−	0.133754i
$757$	45.5514			1.65559			0.827797	−	0.561028i	$-0.189594\pi$
$757$	45.5514			1.65559			0.827797	+	0.561028i	$0.189594\pi$
$758$	1.51980	+	2.63237i	0.0552015	+	0.0956118i
$759$	2.78613	−	4.82572i	0.101130	−	0.175162i
$760$	9.67612	−	16.7595i	0.350990	−	0.607932i
$761$	9.64315	+	16.7024i	0.349564	+	0.605463i	0.986172	−	0.165725i	$-0.0529964\pi$
$761$	9.64315	+	16.7024i	0.349564	+	0.605463i	−0.636608	+	0.771188i	$0.719663\pi$
$762$	1.80111			0.0652475
$763$	−22.4978	+	6.30809i	−0.814476	+	0.228368i
$764$	15.3705			0.556085
$765$	−0.361457	−	0.626062i	−0.0130685	−	0.0226353i
$766$	7.27034	−	12.5926i	0.262688	−	0.454989i
$767$	2.11698	−	3.66671i	0.0764396	−	0.132397i
$768$	−0.873734	−	1.51335i	−0.0315282	−	0.0546084i
$769$	−37.7235			−1.36034			−0.680171	−	0.733053i	$-0.738095\pi$
$769$	−37.7235			−1.36034			−0.680171	+	0.733053i	$0.738095\pi$
$770$	8.91251	−	34.8705i	0.321184	−	1.25665i
$771$	−15.6871			−0.564958
$772$	−0.282979	−	0.490133i	−0.0101846	−	0.0176403i
$773$	8.72968	−	15.1203i	0.313985	−	0.543838i	−0.665236	−	0.746633i	$-0.731669\pi$
$773$	8.72968	−	15.1203i	0.313985	−	0.543838i	0.979221	+	0.202795i	$0.0650026\pi$
$774$	0.0615870	−	0.106672i	0.00221370	−	0.00383424i
$775$	−21.3574	−	36.9921i	−0.767180	−	1.32879i
$776$	−5.74459			−0.206219
$777$	−23.9630	−	23.4149i	−0.859668	−	0.840005i
$778$	31.3174			1.12278
$779$	11.6006	+	20.0928i	0.415633	+	0.719898i
$780$	17.1815	−	29.7592i	0.615195	−	1.06555i
$781$	−5.77102	+	9.99570i	−0.206503	+	0.357674i
$782$	1.57939	+	2.73559i	0.0564790	+	0.0978245i
$783$	19.0880			0.682149
$784$	5.97959	−	3.63930i	0.213557	−	0.129975i
$785$	−5.02582			−0.179379
$786$	6.62184	+	11.4694i	0.236193	+	0.409098i
$787$	6.71442	−	11.6297i	0.239343	−	0.414554i	−0.721183	−	0.692745i	$-0.756401\pi$
$787$	6.71442	−	11.6297i	0.239343	−	0.414554i	0.960526	+	0.278190i	$0.0897346\pi$
$788$	4.35667	−	7.54598i	0.155200	−	0.268814i
$789$	13.7900	+	23.8850i	0.490938	+	0.850329i
$790$	−31.6574			−1.12632
$791$	−35.2357	−	34.4298i	−1.25284	−	1.22418i
$792$	0.171064			0.00607850
$793$	31.0885	+	53.8469i	1.10399	+	1.91216i
$794$	8.80952	−	15.2585i	0.312638	−	0.541505i
$795$	45.4724	−	78.7605i	1.61274	−	2.79335i
$796$	−6.54977	−	11.3445i	−0.232150	−	0.402096i
$797$	21.3322			0.755624			0.377812	−	0.925882i	$-0.376677\pi$
$797$	21.3322			0.755624			0.377812	+	0.925882i	$0.376677\pi$
$798$	−5.19351	+	20.3198i	−0.183848	+	0.719313i
$799$	17.9987			0.636747
$800$	−6.59971	−	11.4310i	−0.233335	−	0.404148i
$801$	0.140099	−	0.242659i	0.00495016	−	0.00857394i
$802$	0.483100	−	0.836754i	0.0170589	−	0.0295468i
$803$	21.3176	+	36.9232i	0.752283	+	1.30299i
$804$	8.31055			0.293090
$805$	10.8679	−	3.04721i	0.383042	−	0.107400i
$806$	−14.9168			−0.525420
$807$	5.45595	+	9.44998i	0.192058	+	0.332655i
$808$	−6.45954	+	11.1882i	−0.227246	+	0.393601i
$809$	21.1488	−	36.6308i	0.743552	−	1.28787i	−0.207316	−	0.978274i	$-0.566473\pi$
$809$	21.1488	−	36.6308i	0.743552	−	1.28787i	0.950868	−	0.309596i	$-0.100194\pi$
$810$	19.5345	+	33.8348i	0.686372	+	1.18883i
$811$	−23.5400			−0.826603			−0.413301	−	0.910594i	$-0.635624\pi$
$811$	−23.5400			−0.826603			−0.413301	+	0.910594i	$0.635624\pi$
$812$	9.44455	−	2.64813i	0.331439	−	0.0929310i
$813$	−50.0624			−1.75576
$814$	11.5538	+	20.0117i	0.404959	+	0.701410i
$815$	−30.8533	+	53.4394i	−1.08074	+	1.87190i
$816$	−2.75994	+	4.78036i	−0.0966172	+	0.167346i
$817$	−5.20780	−	9.02017i	−0.182198	−	0.315576i
$818$	−33.0657			−1.15611
$819$	−0.162009	+	0.633865i	−0.00566104	+	0.0221490i
$820$	21.8190			0.761954
$821$	−11.1547	−	19.3205i	−0.389302	−	0.674292i	0.603053	−	0.797701i	$-0.293951\pi$
$821$	−11.1547	−	19.3205i	−0.389302	−	0.674292i	−0.992356	+	0.123409i	$0.960617\pi$
$822$	−10.8852	+	18.8537i	−0.379665	+	0.657599i
$823$	−6.80437	+	11.7855i	−0.237185	+	0.410817i	−0.959906	−	0.280324i	$-0.909558\pi$
$823$	−6.80437	+	11.7855i	−0.237185	+	0.410817i	0.722720	+	0.691141i	$0.242892\pi$
$824$	−2.73041	−	4.72921i	−0.0951183	−	0.164750i
$825$	73.5506			2.56070
$826$	1.73818	+	1.69842i	0.0604790	+	0.0590957i
$827$	−15.3089			−0.532344			−0.266172	−	0.963926i	$-0.585759\pi$
$827$	−15.3089			−0.532344			−0.266172	+	0.963926i	$0.585759\pi$
$828$	0.0268230	+	0.0464588i	0.000932164	+	0.00161455i
$829$	−12.4505	+	21.5649i	−0.432424	+	0.748979i	−0.997081	−	0.0763456i	$-0.975675\pi$
$829$	−12.4505	+	21.5649i	−0.432424	+	0.748979i	0.564658	+	0.825325i	$0.309008\pi$
$830$	19.9764	−	34.6002i	0.693392	−	1.20099i
$831$	12.9804	+	22.4827i	0.450286	+	0.779918i
$832$	−4.60948			−0.159805
$833$	−19.3998	−	10.6098i	−0.672162	−	0.367608i
$834$	28.6129			0.990784
$835$	14.8396	+	25.7030i	0.513546	+	0.889487i
$836$	7.23259	−	12.5272i	0.250144	−	0.433263i
$837$	8.33081	−	14.4294i	0.287955	−	0.498752i
$838$	−15.3352	−	26.5613i	−0.529745	−	0.917546i
$839$	45.3719			1.56641			0.783205	−	0.621763i	$-0.213583\pi$
$839$	45.3719			1.56641			0.783205	+	0.621763i	$0.213583\pi$
$840$	14.1071	+	13.7845i	0.486742	+	0.475609i
$841$	−15.2554			−0.526049
$842$	−1.57242	−	2.72351i	−0.0541891	−	0.0938582i
$843$	1.69490	−	2.93565i	0.0583754	−	0.101109i
$844$	−3.33563	+	5.77747i	−0.114817	+	0.198869i
$845$	−17.5918	−	30.4698i	−0.605175	−	1.04819i
$846$	0.305673			0.0105093
$847$	−0.544973	+	2.13223i	−0.0187255	+	0.0732643i
$848$	−12.1994			−0.418930
$849$	−22.2098	−	38.4685i	−0.762239	−	1.32024i
$850$	−20.8471	+	36.1082i	−0.715049	+	1.23850i
$851$	−3.62328	+	6.27570i	−0.124204	+	0.215128i
$852$	−3.16257	−	5.47773i	−0.108348	−	0.187664i
$853$	1.29412			0.0443099			0.0221550	−	0.999755i	$-0.492947\pi$
$853$	1.29412			0.0443099			0.0221550	+	0.999755i	$0.492947\pi$
$854$	−34.3632	+	9.63499i	−1.17589	+	0.329703i
$855$	−1.03817			−0.0355047
$856$	5.11562	+	8.86051i	0.174848	+	0.302846i
$857$	9.51667	−	16.4834i	0.325083	−	0.563061i	−0.656446	−	0.754373i	$-0.727941\pi$
$857$	9.51667	−	16.4834i	0.325083	−	0.563061i	0.981529	+	0.191312i	$0.0612744\pi$
$858$	12.8426	−	22.2440i	0.438439	−	0.759399i
$859$	14.6601	+	25.3920i	0.500195	+	0.866363i	1.00000		0.000224817i	$7.15615e-5\pi$
$859$	14.6601	+	25.3920i	0.500195	+	0.866363i	−0.499805	+	0.866138i	$0.666595\pi$
$860$	−9.79514			−0.334011
$861$	−22.7683	+	6.38394i	−0.775943	+	0.217564i
$862$	−6.68265			−0.227612
$863$	−11.9702	−	20.7331i	−0.407472	−	0.705762i	0.587134	−	0.809490i	$-0.300256\pi$
$863$	−11.9702	−	20.7331i	−0.407472	−	0.705762i	−0.994606	+	0.103728i	$0.966923\pi$
$864$	2.57433	−	4.45887i	0.0875805	−	0.151694i
$865$	7.16002	−	12.4015i	0.243448	−	0.421664i
$866$	7.07107	+	12.2475i	0.240285	+	0.416185i
$867$	−12.2708			−0.416740
$868$	2.12018	−	8.29527i	0.0719635	−	0.281560i
$869$	−23.6629			−0.802708
$870$	13.8189	+	23.9351i	0.468505	+	0.811475i
$871$	10.9608	−	18.9847i	0.371392	−	0.643270i
$872$	−4.41565	+	7.64814i	−0.149533	+	0.258999i
$873$	0.154087	+	0.266887i	0.00521506	+	0.00903275i
$874$	4.53631			0.153443
$875$	66.1931	+	64.6791i	2.23774	+	2.18655i
$876$	−23.3645			−0.789414
$877$	21.0040	+	36.3800i	0.709256	+	1.22847i	0.965134	+	0.261758i	$0.0843021\pi$
$877$	21.0040	+	36.3800i	0.709256	+	1.22847i	−0.255878	+	0.966709i	$0.582365\pi$
$878$	0.742769	−	1.28651i	0.0250672	−	0.0434177i
$879$	17.3861	−	30.1137i	0.586420	−	1.01571i
$880$	−6.80175	−	11.7810i	−0.229287	−	0.397137i
$881$	−37.3864			−1.25958			−0.629790	−	0.776766i	$-0.716859\pi$
$881$	−37.3864			−1.25958			−0.629790	+	0.776766i	$0.716859\pi$
$882$	−0.329468	−	0.180187i	−0.0110938	−	0.00606722i
$883$	−38.6925			−1.30211			−0.651053	−	0.759032i	$-0.725672\pi$
$883$	−38.6925			−1.30211			−0.651053	+	0.759032i	$0.725672\pi$
$884$	7.28018	+	12.6096i	0.244859	+	0.424108i
$885$	−3.42376	+	5.93012i	−0.115088	+	0.199339i
$886$	6.54536	−	11.3369i	0.219896	−	0.380870i
$887$	−11.8769	−	20.5714i	−0.398786	−	0.690718i	0.594790	−	0.803881i	$-0.297235\pi$
$887$	−11.8769	−	20.5714i	−0.398786	−	0.690718i	−0.993576	+	0.113163i	$0.963902\pi$
$888$	−12.6631			−0.424947
$889$	1.95044	+	1.90583i	0.0654156	+	0.0639194i
$890$	−22.2822			−0.746900
$891$	14.6014	+	25.2904i	0.489166	+	0.847261i
$892$	−8.46524	+	14.6622i	−0.283437	+	0.490927i
$893$	12.9239	−	22.3848i	0.432481	−	0.749079i
$894$	8.47978	+	14.6874i	0.283606	+	0.491221i
$895$	−81.2333			−2.71533
$896$	0.655163	−	2.56335i	0.0218875	−	0.0856355i
$897$	8.05492			0.268946
$898$	14.0002	+	24.2490i	0.467193	+	0.809201i
$899$	5.99872	−	10.3901i	0.200069	−	0.346529i
$900$	−0.354048	+	0.613230i	−0.0118016	+	0.0204410i
$901$	19.2677	+	33.3726i	0.641900	+	1.11180i
$902$	16.3090			0.543032
$903$	10.2213	−	2.86592i	0.340144	−	0.0953718i
$904$	−18.6201			−0.619297
$905$	−19.7387	−	34.1885i	−0.656137	−	1.13646i
$906$	10.5533	−	18.2788i	0.350609	−	0.607273i
$907$	−12.5929	+	21.8116i	−0.418141	+	0.724242i	−0.995753	−	0.0920698i	$-0.970652\pi$
$907$	−12.5929	+	21.8116i	−0.418141	+	0.724242i	0.577611	+	0.816312i	$0.303985\pi$
$908$	−9.13766	−	15.8269i	−0.303244	−	0.525234i
$909$	0.693057			0.0229872
$910$	50.0952	−	14.0460i	1.66064	−	0.465621i
$911$	−33.9550			−1.12498			−0.562490	−	0.826804i	$-0.690156\pi$
$911$	−33.9550			−1.12498			−0.562490	+	0.826804i	$0.690156\pi$
$912$	3.96353	+	6.86503i	0.131245	+	0.227324i
$913$	14.9318	−	25.8626i	0.494169	−	0.855926i
$914$	1.94239	−	3.36433i	0.0642487	−	0.111282i
$915$	−50.2790	−	87.0858i	−1.66217	−	2.87897i
$916$	3.19076			0.105426
$917$	−4.96533	+	19.4271i	−0.163970	+	0.641538i
$918$	−16.2635			−0.536776
$919$	−16.9370	−	29.3357i	−0.558699	−	0.967695i	−0.997605	−	0.0691625i	$-0.977967\pi$
$919$	−16.9370	−	29.3357i	−0.558699	−	0.967695i	0.438906	−	0.898533i	$-0.355366\pi$
$920$	2.13304	−	3.69453i	0.0703242	−	0.121805i
$921$	−6.38588	+	11.0607i	−0.210422	+	0.364461i
$922$	10.8593	+	18.8088i	0.357632	+	0.619436i
$923$	−16.6845			−0.549176
$924$	10.5446	+	10.3034i	0.346893	+	0.338959i
$925$	−95.6504			−3.14496
$926$	−2.48617	−	4.30618i	−0.0817007	−	0.141510i
$927$	−0.146475	+	0.253703i	−0.00481089	+	0.00833270i
$928$	1.85368	−	3.21068i	0.0608502	−	0.105396i
$929$	7.44452	+	12.8943i	0.244247	+	0.423048i	0.961920	−	0.273333i	$-0.0881259\pi$
$929$	7.44452	+	12.8943i	0.244247	+	0.423048i	−0.717673	+	0.696381i	$0.754793\pi$
$930$	24.1246			0.791078
$931$	−27.1252	+	16.5090i	−0.888994	+	0.541061i
$932$	3.99890			0.130988
$933$	−24.6154	−	42.6351i	−0.805872	−	1.39581i
$934$	3.42464	−	5.93166i	0.112058	−	0.194090i
$935$	−21.4853	+	37.2136i	−0.702644	+	1.21701i
$936$	0.123640	+	0.214151i	0.00404130	+	0.00699974i
$937$	10.1786			0.332520			0.166260	−	0.986082i	$-0.446831\pi$
$937$	10.1786			0.332520			0.166260	+	0.986082i	$0.446831\pi$
$938$	8.99954	+	8.79370i	0.293846	+	0.287125i
$939$	18.1281			0.591588
$940$	−12.1540	−	21.0513i	−0.396420	−	0.686619i
$941$	−14.6699	+	25.4090i	−0.478224	+	0.828309i	−0.999688	−	0.0249644i	$-0.992053\pi$
$941$	−14.6699	+	25.4090i	−0.478224	+	0.828309i	0.521464	+	0.853273i	$0.325386\pi$
$942$	1.02934	−	1.78286i	0.0335376	−	0.0580889i
$943$	2.55727	+	4.42932i	0.0832762	+	0.144239i
$944$	0.918533			0.0298957
$945$	−14.3904	+	56.3029i	−0.468119	+	1.83153i
$946$	−7.32156			−0.238044
$947$	−20.0264	−	34.6867i	−0.650770	−	1.12717i	−0.982936	−	0.183945i	$-0.941113\pi$
$947$	−20.0264	−	34.6867i	−0.650770	−	1.12717i	0.332167	−	0.943221i	$-0.392220\pi$
$948$	6.48374	−	11.2302i	0.210582	−	0.364739i
$949$	−30.8155	+	53.3740i	−1.00031	+	1.73259i
$950$	29.9383	+	51.8547i	0.971327	+	1.68239i
$951$	26.4680			0.858285
$952$	−8.04703	+	2.25628i	−0.260806	+	0.0731265i
$953$	53.5369			1.73423			0.867115	−	0.498107i	$-0.165971\pi$
$953$	53.5369			1.73423			0.867115	+	0.498107i	$0.165971\pi$
$954$	0.327225	+	0.566771i	0.0105943	+	0.0183499i
$955$	−32.7859	+	56.7868i	−1.06093	+	1.83758i
$956$	−9.79561	+	16.9665i	−0.316813	+	0.548736i
$957$	10.3292	+	17.8907i	0.333896	+	0.578325i
$958$	10.0047			0.323237
$959$	−31.7375	+	8.89878i	−1.02486	+	0.287356i
$960$	7.45484			0.240604
$961$	10.2638	+	17.7774i	0.331091	+	0.573466i
$962$	−16.7014	+	28.9277i	−0.538475	+	0.932666i
$963$	0.274432	−	0.475331i	0.00884346	−	0.0153173i
$964$	−4.15217	−	7.19178i	−0.133733	−	0.231631i
$965$	2.41442			0.0777229
$966$	−1.14488	+	4.47937i	−0.0368358	+	0.144121i
$967$	−10.1189			−0.325400			−0.162700	−	0.986676i	$-0.552020\pi$
$967$	−10.1189			−0.325400			−0.162700	+	0.986676i	$0.552020\pi$
$968$	0.415907	+	0.720372i	0.0133678	+	0.0231536i
$969$	12.5199	−	21.6852i	0.402198	−	0.696628i
$970$	12.2534	−	21.2236i	0.393434	−	0.681448i
$971$	−14.5231	−	25.1548i	−0.466069	−	0.807255i	0.533180	−	0.846002i	$-0.320997\pi$
$971$	−14.5231	−	25.1548i	−0.466069	−	0.807255i	−0.999249	+	0.0387464i	$0.987664\pi$
$972$	−0.557439			−0.0178799
$973$	30.9851	+	30.2764i	0.993336	+	0.970616i
$974$	26.9160			0.862443
$975$	53.1601	+	92.0761i	1.70249	+	2.94879i
$976$	−6.74448	+	11.6818i	−0.215886	+	0.373925i
$977$	−6.95721	+	12.0502i	−0.222581	+	0.385521i	−0.955591	−	0.294696i	$-0.904781\pi$
$977$	−6.95721	+	12.0502i	−0.222581	+	0.385521i	0.733010	+	0.680218i	$0.238115\pi$
$978$	−12.6381	−	21.8898i	−0.404122	−	0.699959i
$979$	−16.6552			−0.532303
$980$	0.690833	+	29.8546i	0.0220679	+	0.953669i
$981$	0.473764			0.0151261
$982$	8.83933	+	15.3102i	0.282074	+	0.488567i
$983$	−14.9668	+	25.9232i	−0.477366	+	0.826823i	−0.999663	−	0.0259408i	$-0.991742\pi$
$983$	−14.9668	+	25.9232i	−0.477366	+	0.826823i	0.522297	+	0.852764i	$0.325075\pi$
$984$	−4.46875	+	7.74010i	−0.142459	+	0.246745i
$985$	18.5859	+	32.1917i	0.592196	+	1.02571i
$986$	−11.7108			−0.372948
$987$	18.8421	+	18.4112i	0.599751	+	0.586034i
$988$	20.9100			0.665236
$989$	−1.14803	−	1.98844i	−0.0365051	−	0.0632287i
$990$	−0.364887	+	0.632002i	−0.0115969	+	0.0200863i
$991$	21.0305	−	36.4258i	0.668055	−	1.15710i	−0.310393	−	0.950608i	$-0.600461\pi$
$991$	21.0305	−	36.4258i	0.668055	−	1.15710i	0.978447	−	0.206496i	$-0.0662062\pi$
$992$	−1.61805	−	2.80255i	−0.0513732	−	0.0889811i
$993$	−31.5144			−1.00008
$994$	2.37143	−	9.27831i	0.0752172	−	0.294290i
$995$	55.8837			1.77163
$996$	8.18273	+	14.1729i	0.259280	+	0.449086i
$997$	4.92042	−	8.52241i	0.155831	−	0.269908i	−0.777530	−	0.628846i	$-0.783528\pi$
$997$	4.92042	−	8.52241i	0.155831	−	0.269908i	0.933361	+	0.358938i	$0.116861\pi$
$998$	−10.7720	+	18.6577i	−0.340983	+	0.590600i
$999$	−18.6550	−	32.3114i	−0.590219	−	1.02229i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.e.a.277.2	yes	8
7.2	even	3	inner	322.2.e.a.93.2	✓	8
7.3	odd	6		2254.2.a.x.1.2		4
7.4	even	3		2254.2.a.z.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.e.a.93.2	✓	8	7.2	even	3	inner
322.2.e.a.277.2	yes	8	1.1	even	1	trivial
2254.2.a.x.1.2		4	7.3	odd	6
2254.2.a.z.1.3		4	7.4	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)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.873734 + 1.51335i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.13304 - 3.69453i) q^{5} +1.74747 q^{6} +(1.89234 + 1.84906i) q^{7} +1.00000 q^{8} +(-0.0268230 - 0.0464588i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.873734 + 1.51335i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.13304 - 3.69453i) q^{5} +1.74747 q^{6} +(1.89234 + 1.84906i) q^{7} +1.00000 q^{8} +(-0.0268230 - 0.0464588i) q^{9} +(-2.13304 + 3.69453i) q^{10} +(-1.59438 + 2.76155i) q^{11} +(-0.873734 - 1.51335i) q^{12} -4.60948 q^{13} +(0.655163 - 2.56335i) q^{14} +7.45484 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.57939 + 2.73559i) q^{17} +(-0.0268230 + 0.0464588i) q^{18} +(2.26815 + 3.92856i) q^{19} +4.26608 q^{20} +(-4.45169 + 1.24819i) q^{21} +3.18876 q^{22} +(0.500000 + 0.866025i) q^{23} +(-0.873734 + 1.51335i) q^{24} +(-6.59971 + 11.4310i) q^{25} +(2.30474 + 3.99192i) q^{26} -5.14866 q^{27} +(-2.54751 + 0.714287i) q^{28} -3.70737 q^{29} +(-3.72742 - 6.45608i) q^{30} +(-1.61805 + 2.80255i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.78613 - 4.82572i) q^{33} +3.15879 q^{34} +(2.79498 - 10.9355i) q^{35} +0.0536460 q^{36} +(3.62328 + 6.27570i) q^{37} +(2.26815 - 3.92856i) q^{38} +(4.02746 - 6.97576i) q^{39} +(-2.13304 - 3.69453i) q^{40} +5.11454 q^{41} +(3.30681 + 3.23118i) q^{42} -2.29605 q^{43} +(-1.59438 - 2.76155i) q^{44} +(-0.114429 + 0.198197i) q^{45} +(0.500000 - 0.866025i) q^{46} +(-2.84899 - 4.93459i) q^{47} +1.74747 q^{48} +(0.161936 + 6.99813i) q^{49} +13.1994 q^{50} +(-2.75994 - 4.78036i) q^{51} +(2.30474 - 3.99192i) q^{52} +(6.09971 - 10.5650i) q^{53} +(2.57433 + 4.45887i) q^{54} +13.6035 q^{55} +(1.89234 + 1.84906i) q^{56} -7.92705 q^{57} +(1.85368 + 3.21068i) q^{58} +(-0.459266 + 0.795473i) q^{59} +(-3.72742 + 6.45608i) q^{60} +(-6.74448 - 11.6818i) q^{61} +3.23611 q^{62} +(0.0351469 - 0.137513i) q^{63} +1.00000 q^{64} +(9.83220 + 17.0299i) q^{65} +(-2.78613 + 4.82572i) q^{66} +(-2.37788 + 4.11861i) q^{67} +(-1.57939 - 2.73559i) q^{68} -1.74747 q^{69} +(-10.8679 + 3.04721i) q^{70} +3.61960 q^{71} +(-0.0268230 - 0.0464588i) q^{72} +(6.68525 - 11.5792i) q^{73} +(3.62328 - 6.27570i) q^{74} +(-11.5328 - 19.9754i) q^{75} -4.53631 q^{76} +(-8.12339 + 2.27769i) q^{77} -8.05492 q^{78} +(3.71036 + 6.42653i) q^{79} +(-2.13304 + 3.69453i) q^{80} +(4.57903 - 7.93111i) q^{81} +(-2.55727 - 4.42932i) q^{82} -9.36524 q^{83} +(1.14488 - 4.47937i) q^{84} +13.4756 q^{85} +(1.14803 + 1.98844i) q^{86} +(3.23926 - 5.61056i) q^{87} +(-1.59438 + 2.76155i) q^{88} +(2.61155 + 4.52334i) q^{89} +0.228858 q^{90} +(-8.72272 - 8.52321i) q^{91} -1.00000 q^{92} +(-2.82750 - 4.89737i) q^{93} +(-2.84899 + 4.93459i) q^{94} +(9.67612 - 16.7595i) q^{95} +(-0.873734 - 1.51335i) q^{96} -5.74459 q^{97} +(5.97959 - 3.63930i) q^{98} +0.171064 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 3 q^{3} - 4 q^{4} - 7 q^{5} + 6 q^{6} - q^{7} + 8 q^{8} + q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 - 3 * q^3 - 4 * q^4 - 7 * q^5 + 6 * q^6 - q^7 + 8 * q^8 + q^9	\( 8 q - 4 q^{2} - 3 q^{3} - 4 q^{4} - 7 q^{5} + 6 q^{6} - q^{7} + 8 q^{8} + q^{9} - 7 q^{10} - 2 q^{11} - 3 q^{12} + 2 q^{13} - q^{14} + 18 q^{15} - 4 q^{16} - 5 q^{17} + q^{18} - 11 q^{19} + 14 q^{20} + q^{21} + 4 q^{22} + 4 q^{23} - 3 q^{24} - 3 q^{25} - q^{26} + 6 q^{27} + 2 q^{28} + 4 q^{29} - 9 q^{30} - 6 q^{31} - 4 q^{32} - 15 q^{33} + 10 q^{34} - 8 q^{35} - 2 q^{36} + 8 q^{37} - 11 q^{38} - 3 q^{39} - 7 q^{40} + 18 q^{41} - 2 q^{42} + 8 q^{43} - 2 q^{44} - 3 q^{45} + 4 q^{46} - 11 q^{47} + 6 q^{48} - 19 q^{49} + 6 q^{50} + 18 q^{51} - q^{52} - q^{53} - 3 q^{54} + 20 q^{55} - q^{56} + 6 q^{57} - 2 q^{58} - 12 q^{59} - 9 q^{60} - 21 q^{61} + 12 q^{62} - 15 q^{63} + 8 q^{64} + 24 q^{65} - 15 q^{66} + 3 q^{67} - 5 q^{68} - 6 q^{69} - 8 q^{70} + 22 q^{71} + q^{72} + 16 q^{73} + 8 q^{74} - 18 q^{75} + 22 q^{76} - 19 q^{77} + 6 q^{78} + 21 q^{79} - 7 q^{80} + 8 q^{81} - 9 q^{82} + 8 q^{83} + q^{84} + 20 q^{85} - 4 q^{86} + 7 q^{87} - 2 q^{88} - 27 q^{89} + 6 q^{90} - 54 q^{91} - 8 q^{92} + 27 q^{93} - 11 q^{94} - 5 q^{95} - 3 q^{96} + 12 q^{97} + 14 q^{98} + 26 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 - 3 * q^3 - 4 * q^4 - 7 * q^5 + 6 * q^6 - q^7 + 8 * q^8 + q^9 - 7 * q^10 - 2 * q^11 - 3 * q^12 + 2 * q^13 - q^14 + 18 * q^15 - 4 * q^16 - 5 * q^17 + q^18 - 11 * q^19 + 14 * q^20 + q^21 + 4 * q^22 + 4 * q^23 - 3 * q^24 - 3 * q^25 - q^26 + 6 * q^27 + 2 * q^28 + 4 * q^29 - 9 * q^30 - 6 * q^31 - 4 * q^32 - 15 * q^33 + 10 * q^34 - 8 * q^35 - 2 * q^36 + 8 * q^37 - 11 * q^38 - 3 * q^39 - 7 * q^40 + 18 * q^41 - 2 * q^42 + 8 * q^43 - 2 * q^44 - 3 * q^45 + 4 * q^46 - 11 * q^47 + 6 * q^48 - 19 * q^49 + 6 * q^50 + 18 * q^51 - q^52 - q^53 - 3 * q^54 + 20 * q^55 - q^56 + 6 * q^57 - 2 * q^58 - 12 * q^59 - 9 * q^60 - 21 * q^61 + 12 * q^62 - 15 * q^63 + 8 * q^64 + 24 * q^65 - 15 * q^66 + 3 * q^67 - 5 * q^68 - 6 * q^69 - 8 * q^70 + 22 * q^71 + q^72 + 16 * q^73 + 8 * q^74 - 18 * q^75 + 22 * q^76 - 19 * q^77 + 6 * q^78 + 21 * q^79 - 7 * q^80 + 8 * q^81 - 9 * q^82 + 8 * q^83 + q^84 + 20 * q^85 - 4 * q^86 + 7 * q^87 - 2 * q^88 - 27 * q^89 + 6 * q^90 - 54 * q^91 - 8 * q^92 + 27 * q^93 - 11 * q^94 - 5 * q^95 - 3 * q^96 + 12 * q^97 + 14 * q^98 + 26 * q^99

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