LMFDB - Embedded newform 882.2.h.n.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(67,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 4]))

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

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

chi := DirichletCharacter("882.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.h (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.1
Root			$-1.18614 + 1.26217i$ of defining polynomial
Character	$\chi$	$=$	882.79
Dual form			882.2.h.n.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-1.18614 - 1.26217i) q^{3} +(-0.500000 + 0.866025i) q^{4} -4.37228 q^{5} +(0.500000 - 1.65831i) q^{6} -1.00000 q^{8} +(-0.186141 + 2.99422i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-1.18614 - 1.26217i) q^{3} +(-0.500000 + 0.866025i) q^{4} -4.37228 q^{5} +(0.500000 - 1.65831i) q^{6} -1.00000 q^{8} +(-0.186141 + 2.99422i) q^{9} +(-2.18614 - 3.78651i) q^{10} -1.37228 q^{11} +(1.68614 - 0.396143i) q^{12} +(1.00000 + 1.73205i) q^{13} +(5.18614 + 5.51856i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.686141 + 1.18843i) q^{17} +(-2.68614 + 1.33591i) q^{18} +(2.50000 - 4.33013i) q^{19} +(2.18614 - 3.78651i) q^{20} +(-0.686141 - 1.18843i) q^{22} -1.62772 q^{23} +(1.18614 + 1.26217i) q^{24} +14.1168 q^{25} +(-1.00000 + 1.73205i) q^{26} +(4.00000 - 3.31662i) q^{27} +(4.37228 - 7.57301i) q^{29} +(-2.18614 + 7.25061i) q^{30} +(1.00000 - 1.73205i) q^{31} +(0.500000 - 0.866025i) q^{32} +(1.62772 + 1.73205i) q^{33} +(-0.686141 + 1.18843i) q^{34} +(-2.50000 - 1.65831i) q^{36} +(-1.00000 + 1.73205i) q^{37} +5.00000 q^{38} +(1.00000 - 3.31662i) q^{39} +4.37228 q^{40} +(2.31386 + 4.00772i) q^{41} +(4.05842 - 7.02939i) q^{43} +(0.686141 - 1.18843i) q^{44} +(0.813859 - 13.0916i) q^{45} +(-0.813859 - 1.40965i) q^{46} +(-0.500000 + 1.65831i) q^{48} +(7.05842 + 12.2255i) q^{50} +(0.686141 - 2.27567i) q^{51} -2.00000 q^{52} +(4.37228 + 7.57301i) q^{53} +(4.87228 + 1.80579i) q^{54} +6.00000 q^{55} +(-8.43070 + 1.98072i) q^{57} +8.74456 q^{58} +(-5.05842 + 8.76144i) q^{59} +(-7.37228 + 1.73205i) q^{60} +(1.55842 + 2.69927i) q^{61} +2.00000 q^{62} +1.00000 q^{64} +(-4.37228 - 7.57301i) q^{65} +(-0.686141 + 2.27567i) q^{66} +(1.05842 - 1.83324i) q^{67} -1.37228 q^{68} +(1.93070 + 2.05446i) q^{69} -7.11684 q^{71} +(0.186141 - 2.99422i) q^{72} +(6.05842 + 10.4935i) q^{73} -2.00000 q^{74} +(-16.7446 - 17.8178i) q^{75} +(2.50000 + 4.33013i) q^{76} +(3.37228 - 0.792287i) q^{78} +(2.55842 + 4.43132i) q^{79} +(2.18614 + 3.78651i) q^{80} +(-8.93070 - 1.11469i) q^{81} +(-2.31386 + 4.00772i) q^{82} +(8.74456 - 15.1460i) q^{83} +(-3.00000 - 5.19615i) q^{85} +8.11684 q^{86} +(-14.7446 + 3.46410i) q^{87} +1.37228 q^{88} +(7.37228 - 12.7692i) q^{89} +(11.7446 - 5.84096i) q^{90} +(0.813859 - 1.40965i) q^{92} +(-3.37228 + 0.792287i) q^{93} +(-10.9307 + 18.9325i) q^{95} +(-1.68614 + 0.396143i) q^{96} +(-4.05842 + 7.02939i) q^{97} +(0.255437 - 4.10891i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} - 4 q^{8} + 5 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 + q^3 - 2 * q^4 - 6 * q^5 + 2 * q^6 - 4 * q^8 + 5 * q^9	$ 4 q + 2 q^{2} + q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} - 4 q^{8} + 5 q^{9} - 3 q^{10} + 6 q^{11} + q^{12} + 4 q^{13} + 15 q^{15} - 2 q^{16} - 3 q^{17} - 5 q^{18} + 10 q^{19} + 3 q^{20} + 3 q^{22} - 18 q^{23} - q^{24} + 22 q^{25} - 4 q^{26} + 16 q^{27} + 6 q^{29} - 3 q^{30} + 4 q^{31} + 2 q^{32} + 18 q^{33} + 3 q^{34} - 10 q^{36} - 4 q^{37} + 20 q^{38} + 4 q^{39} + 6 q^{40} + 15 q^{41} - q^{43} - 3 q^{44} + 9 q^{45} - 9 q^{46} - 2 q^{48} + 11 q^{50} - 3 q^{51} - 8 q^{52} + 6 q^{53} + 8 q^{54} + 24 q^{55} - 5 q^{57} + 12 q^{58} - 3 q^{59} - 18 q^{60} - 11 q^{61} + 8 q^{62} + 4 q^{64} - 6 q^{65} + 3 q^{66} - 13 q^{67} + 6 q^{68} - 21 q^{69} + 6 q^{71} - 5 q^{72} + 7 q^{73} - 8 q^{74} - 44 q^{75} + 10 q^{76} + 2 q^{78} - 7 q^{79} + 3 q^{80} - 7 q^{81} - 15 q^{82} + 12 q^{83} - 12 q^{85} - 2 q^{86} - 36 q^{87} - 6 q^{88} + 18 q^{89} + 24 q^{90} + 9 q^{92} - 2 q^{93} - 15 q^{95} - q^{96} + q^{97} + 24 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 + q^3 - 2 * q^4 - 6 * q^5 + 2 * q^6 - 4 * q^8 + 5 * q^9 - 3 * q^10 + 6 * q^11 + q^12 + 4 * q^13 + 15 * q^15 - 2 * q^16 - 3 * q^17 - 5 * q^18 + 10 * q^19 + 3 * q^20 + 3 * q^22 - 18 * q^23 - q^24 + 22 * q^25 - 4 * q^26 + 16 * q^27 + 6 * q^29 - 3 * q^30 + 4 * q^31 + 2 * q^32 + 18 * q^33 + 3 * q^34 - 10 * q^36 - 4 * q^37 + 20 * q^38 + 4 * q^39 + 6 * q^40 + 15 * q^41 - q^43 - 3 * q^44 + 9 * q^45 - 9 * q^46 - 2 * q^48 + 11 * q^50 - 3 * q^51 - 8 * q^52 + 6 * q^53 + 8 * q^54 + 24 * q^55 - 5 * q^57 + 12 * q^58 - 3 * q^59 - 18 * q^60 - 11 * q^61 + 8 * q^62 + 4 * q^64 - 6 * q^65 + 3 * q^66 - 13 * q^67 + 6 * q^68 - 21 * q^69 + 6 * q^71 - 5 * q^72 + 7 * q^73 - 8 * q^74 - 44 * q^75 + 10 * q^76 + 2 * q^78 - 7 * q^79 + 3 * q^80 - 7 * q^81 - 15 * q^82 + 12 * q^83 - 12 * q^85 - 2 * q^86 - 36 * q^87 - 6 * q^88 + 18 * q^89 + 24 * q^90 + 9 * q^92 - 2 * q^93 - 15 * q^95 - q^96 + q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−1.18614	−	1.26217i	−0.684819	−	0.728714i
$3$	−1.18614	−	1.26217i	−0.684819	−	0.728714i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−4.37228			−1.95534			−0.977672	−	0.210138i	$-0.932609\pi$
$5$	−4.37228			−1.95534			−0.977672	+	0.210138i	$0.932609\pi$
$6$	0.500000	−	1.65831i	0.204124	−	0.677003i
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	−0.186141	+	2.99422i	−0.0620469	+	0.998073i
$10$	−2.18614	−	3.78651i	−0.691318	−	1.19740i
$11$	−1.37228			−0.413758			−0.206879	−	0.978366i	$-0.566331\pi$
$11$	−1.37228			−0.413758			−0.206879	+	0.978366i	$0.566331\pi$
$12$	1.68614	−	0.396143i	0.486747	−	0.114357i
$13$	1.00000	+	1.73205i	0.277350	+	0.480384i	0.970725	−	0.240192i	$-0.0772105\pi$
$13$	1.00000	+	1.73205i	0.277350	+	0.480384i	−0.693375	+	0.720577i	$0.743877\pi$
$14$		0			0
$15$	5.18614	+	5.51856i	1.33906	+	1.42489i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.686141	+	1.18843i	0.166414	+	0.288237i	0.937156	−	0.348910i	$-0.113448\pi$
$17$	0.686141	+	1.18843i	0.166414	+	0.288237i	−0.770743	+	0.637146i	$0.780115\pi$
$18$	−2.68614	+	1.33591i	−0.633129	+	0.314876i
$19$	2.50000	−	4.33013i	0.573539	−	0.993399i	−0.422659	−	0.906289i	$-0.638903\pi$
$19$	2.50000	−	4.33013i	0.573539	−	0.993399i	0.996199	−	0.0871106i	$-0.0277634\pi$
$20$	2.18614	−	3.78651i	0.488836	−	0.846689i
$21$		0			0
$22$	−0.686141	−	1.18843i	−0.146286	−	0.253374i
$23$	−1.62772			−0.339403			−0.169701	−	0.985496i	$-0.554280\pi$
$23$	−1.62772			−0.339403			−0.169701	+	0.985496i	$0.554280\pi$
$24$	1.18614	+	1.26217i	0.242120	+	0.257639i
$25$	14.1168			2.82337
$26$	−1.00000	+	1.73205i	−0.196116	+	0.339683i
$27$	4.00000	−	3.31662i	0.769800	−	0.638285i
$28$		0			0
$29$	4.37228	−	7.57301i	0.811912	−	1.40627i	−0.0996117	−	0.995026i	$-0.531760\pi$
$29$	4.37228	−	7.57301i	0.811912	−	1.40627i	0.911524	−	0.411247i	$-0.134907\pi$
$30$	−2.18614	+	7.25061i	−0.399133	+	1.32377i
$31$	1.00000	−	1.73205i	0.179605	−	0.311086i	−0.762140	−	0.647412i	$-0.775851\pi$
$31$	1.00000	−	1.73205i	0.179605	−	0.311086i	0.941745	+	0.336327i	$0.109185\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	1.62772	+	1.73205i	0.283349	+	0.301511i
$34$	−0.686141	+	1.18843i	−0.117672	+	0.203814i
$35$		0			0
$36$	−2.50000	−	1.65831i	−0.416667	−	0.276385i
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	−0.936442	−	0.350823i	$-0.885902\pi$
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	0.772043	+	0.635571i	$0.219235\pi$
$38$	5.00000			0.811107
$39$	1.00000	−	3.31662i	0.160128	−	0.531085i
$40$	4.37228			0.691318
$41$	2.31386	+	4.00772i	0.361364	+	0.625901i	0.988186	−	0.153262i	$-0.0489778\pi$
$41$	2.31386	+	4.00772i	0.361364	+	0.625901i	−0.626821	+	0.779163i	$0.715644\pi$
$42$		0			0
$43$	4.05842	−	7.02939i	0.618904	−	1.07197i	−0.370783	−	0.928720i	$-0.620910\pi$
$43$	4.05842	−	7.02939i	0.618904	−	1.07197i	0.989686	−	0.143253i	$-0.0457562\pi$
$44$	0.686141	−	1.18843i	0.103440	−	0.179163i
$45$	0.813859	−	13.0916i	0.121323	−	1.95158i
$46$	−0.813859	−	1.40965i	−0.119997	−	0.207841i
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$	−0.500000	+	1.65831i	−0.0721688	+	0.239357i
$49$		0			0
$50$	7.05842	+	12.2255i	0.998212	+	1.72895i
$51$	0.686141	−	2.27567i	0.0960789	−	0.318658i
$52$	−2.00000			−0.277350
$53$	4.37228	+	7.57301i	0.600579	+	1.04023i	0.992733	+	0.120334i	$0.0383965\pi$
$53$	4.37228	+	7.57301i	0.600579	+	1.04023i	−0.392154	+	0.919899i	$0.628270\pi$
$54$	4.87228	+	1.80579i	0.663034	+	0.245737i
$55$	6.00000			0.809040
$56$		0			0
$57$	−8.43070	+	1.98072i	−1.11667	+	0.262352i
$58$	8.74456			1.14822
$59$	−5.05842	+	8.76144i	−0.658550	+	1.14064i	0.322441	+	0.946590i	$0.395497\pi$
$59$	−5.05842	+	8.76144i	−0.658550	+	1.14064i	−0.980991	+	0.194053i	$0.937837\pi$
$60$	−7.37228	+	1.73205i	−0.951757	+	0.223607i
$61$	1.55842	+	2.69927i	0.199535	+	0.345606i	0.948378	−	0.317142i	$-0.102723\pi$
$61$	1.55842	+	2.69927i	0.199535	+	0.345606i	−0.748842	+	0.662748i	$0.769390\pi$
$62$	2.00000			0.254000
$63$		0			0
$64$	1.00000			0.125000
$65$	−4.37228	−	7.57301i	−0.542315	−	0.939317i
$66$	−0.686141	+	2.27567i	−0.0844581	+	0.280116i
$67$	1.05842	−	1.83324i	0.129307	−	0.223966i	−0.794101	−	0.607785i	$-0.792058\pi$
$67$	1.05842	−	1.83324i	0.129307	−	0.223966i	0.923408	+	0.383819i	$0.125391\pi$
$68$	−1.37228			−0.166414
$69$	1.93070	+	2.05446i	0.232429	+	0.247327i
$70$		0			0
$71$	−7.11684			−0.844614			−0.422307	−	0.906453i	$-0.638780\pi$
$71$	−7.11684			−0.844614			−0.422307	+	0.906453i	$0.638780\pi$
$72$	0.186141	−	2.99422i	0.0219369	−	0.352872i
$73$	6.05842	+	10.4935i	0.709085	+	1.22817i	0.965197	+	0.261524i	$0.0842249\pi$
$73$	6.05842	+	10.4935i	0.709085	+	1.22817i	−0.256112	+	0.966647i	$0.582442\pi$
$74$	−2.00000			−0.232495
$75$	−16.7446	−	17.8178i	−1.93350	−	2.05743i
$76$	2.50000	+	4.33013i	0.286770	+	0.496700i
$77$		0			0
$78$	3.37228	−	0.792287i	0.381836	−	0.0897088i
$79$	2.55842	+	4.43132i	0.287845	+	0.498562i	0.973295	−	0.229557i	$-0.0737279\pi$
$79$	2.55842	+	4.43132i	0.287845	+	0.498562i	−0.685450	+	0.728120i	$0.740395\pi$
$80$	2.18614	+	3.78651i	0.244418	+	0.423344i
$81$	−8.93070	−	1.11469i	−0.992300	−	0.123855i
$82$	−2.31386	+	4.00772i	−0.255523	+	0.442579i
$83$	8.74456	−	15.1460i	0.959840	−	1.66249i	0.236960	−	0.971519i	$-0.423849\pi$
$83$	8.74456	−	15.1460i	0.959840	−	1.66249i	0.722881	−	0.690973i	$-0.242818\pi$
$84$		0			0
$85$	−3.00000	−	5.19615i	−0.325396	−	0.563602i
$86$	8.11684			0.875262
$87$	−14.7446	+	3.46410i	−1.58078	+	0.371391i
$88$	1.37228			0.146286
$89$	7.37228	−	12.7692i	0.781460	−	1.35353i	−0.149631	−	0.988742i	$-0.547808\pi$
$89$	7.37228	−	12.7692i	0.781460	−	1.35353i	0.931091	−	0.364787i	$-0.118858\pi$
$90$	11.7446	−	5.84096i	1.23799	−	0.615692i
$91$		0			0
$92$	0.813859	−	1.40965i	0.0848507	−	0.146966i
$93$	−3.37228	+	0.792287i	−0.349689	+	0.0821563i
$94$		0			0
$95$	−10.9307	+	18.9325i	−1.12147	+	1.94244i
$96$	−1.68614	+	0.396143i	−0.172091	+	0.0404312i
$97$	−4.05842	+	7.02939i	−0.412070	+	0.713727i	−0.995116	−	0.0987127i	$-0.968528\pi$
$97$	−4.05842	+	7.02939i	−0.412070	+	0.713727i	0.583046	+	0.812439i	$0.301861\pi$
$98$		0			0
$99$	0.255437	−	4.10891i	0.0256724	−	0.412961i
$100$	−7.05842	+	12.2255i	−0.705842	+	1.22255i
$101$	−1.62772			−0.161964			−0.0809820	−	0.996716i	$-0.525806\pi$
$101$	−1.62772			−0.161964			−0.0809820	+	0.996716i	$0.525806\pi$
$102$	2.31386	−	0.543620i	0.229106	−	0.0538264i
$103$	10.0000			0.985329			0.492665	−	0.870219i	$-0.336023\pi$
$103$	10.0000			0.985329			0.492665	+	0.870219i	$0.336023\pi$
$104$	−1.00000	−	1.73205i	−0.0980581	−	0.169842i
$105$		0			0
$106$	−4.37228	+	7.57301i	−0.424674	+	0.735556i
$107$	3.68614	−	6.38458i	0.356353	−	0.617221i	−0.630996	−	0.775786i	$-0.717354\pi$
$107$	3.68614	−	6.38458i	0.356353	−	0.617221i	0.987348	+	0.158565i	$0.0506868\pi$
$108$	0.872281	+	5.12241i	0.0839353	+	0.492905i
$109$	−7.00000	−	12.1244i	−0.670478	−	1.16130i	−0.977769	−	0.209687i	$-0.932756\pi$
$109$	−7.00000	−	12.1244i	−0.670478	−	1.16130i	0.307290	−	0.951616i	$-0.400578\pi$
$110$	3.00000	+	5.19615i	0.286039	+	0.495434i
$111$	3.37228	−	0.792287i	0.320083	−	0.0752006i
$112$		0			0
$113$	2.18614	+	3.78651i	0.205655	+	0.356205i	0.950341	−	0.311210i	$-0.100734\pi$
$113$	2.18614	+	3.78651i	0.205655	+	0.356205i	−0.744686	+	0.667415i	$0.767401\pi$
$114$	−5.93070	−	6.31084i	−0.555461	−	0.591065i
$115$	7.11684			0.663649
$116$	4.37228	+	7.57301i	0.405956	+	0.703137i
$117$	−5.37228	+	2.67181i	−0.496668	+	0.247009i
$118$	−10.1168			−0.931331
$119$		0			0
$120$	−5.18614	−	5.51856i	−0.473428	−	0.503773i
$121$	−9.11684			−0.828804
$122$	−1.55842	+	2.69927i	−0.141093	+	0.244380i
$123$	2.31386	−	7.67420i	0.208634	−	0.691960i
$124$	1.00000	+	1.73205i	0.0898027	+	0.155543i
$125$	−39.8614			−3.56531
$126$		0			0
$127$	3.11684			0.276575			0.138288	−	0.990392i	$-0.455840\pi$
$127$	3.11684			0.276575			0.138288	+	0.990392i	$0.455840\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−13.6861	+	3.21543i	−1.20500	+	0.283103i
$130$	4.37228	−	7.57301i	0.383474	−	0.664197i
$131$	1.62772			0.142214			0.0711072	−	0.997469i	$-0.477347\pi$
$131$	1.62772			0.142214			0.0711072	+	0.997469i	$0.477347\pi$
$132$	−2.31386	+	0.543620i	−0.201396	+	0.0473161i
$133$		0			0
$134$	2.11684			0.182867
$135$	−17.4891	+	14.5012i	−1.50522	+	1.24807i
$136$	−0.686141	−	1.18843i	−0.0588361	−	0.101907i
$137$	10.6277			0.907987			0.453994	−	0.891005i	$-0.349999\pi$
$137$	10.6277			0.907987			0.453994	+	0.891005i	$0.349999\pi$
$138$	−0.813859	+	2.69927i	−0.0692803	+	0.229777i
$139$	6.61684	+	11.4607i	0.561233	+	0.972085i	0.997389	+	0.0722136i	$0.0230063\pi$
$139$	6.61684	+	11.4607i	0.561233	+	0.972085i	−0.436156	+	0.899871i	$0.643660\pi$
$140$		0			0
$141$		0			0
$142$	−3.55842	−	6.16337i	−0.298616	−	0.517218i
$143$	−1.37228	−	2.37686i	−0.114756	−	0.198763i
$144$	2.68614	−	1.33591i	0.223845	−	0.111326i
$145$	−19.1168	+	33.1113i	−1.58757	+	2.74975i
$146$	−6.05842	+	10.4935i	−0.501399	+	0.868448i
$147$		0			0
$148$	−1.00000	−	1.73205i	−0.0821995	−	0.142374i
$149$	3.25544			0.266696			0.133348	−	0.991069i	$-0.457427\pi$
$149$	3.25544			0.266696			0.133348	+	0.991069i	$0.457427\pi$
$150$	7.05842	−	23.4101i	0.576318	−	1.91143i
$151$	9.11684			0.741918			0.370959	−	0.928649i	$-0.379029\pi$
$151$	9.11684			0.741918			0.370959	+	0.928649i	$0.379029\pi$
$152$	−2.50000	+	4.33013i	−0.202777	+	0.351220i
$153$	−3.68614	+	1.83324i	−0.298007	+	0.148209i
$154$		0			0
$155$	−4.37228	+	7.57301i	−0.351190	+	0.608279i
$156$	2.37228	+	2.52434i	0.189935	+	0.202109i
$157$	4.55842	−	7.89542i	0.363802	−	0.630123i	−0.624781	−	0.780800i	$-0.714812\pi$
$157$	4.55842	−	7.89542i	0.363802	−	0.630123i	0.988583	+	0.150677i	$0.0481453\pi$
$158$	−2.55842	+	4.43132i	−0.203537	+	0.352537i
$159$	4.37228	−	14.5012i	0.346744	−	1.15002i
$160$	−2.18614	+	3.78651i	−0.172830	+	0.299350i
$161$		0			0
$162$	−3.50000	−	8.29156i	−0.274986	−	0.651447i
$163$	9.11684	−	15.7908i	0.714086	−	1.23683i	−0.249225	−	0.968446i	$-0.580176\pi$
$163$	9.11684	−	15.7908i	0.714086	−	1.23683i	0.963311	−	0.268388i	$-0.0864909\pi$
$164$	−4.62772			−0.361364
$165$	−7.11684	−	7.57301i	−0.554046	−	0.589558i
$166$	17.4891			1.35742
$167$	−2.74456	−	4.75372i	−0.212381	−	0.367854i	0.740078	−	0.672521i	$-0.234788\pi$
$167$	−2.74456	−	4.75372i	−0.212381	−	0.367854i	−0.952459	+	0.304666i	$0.901455\pi$
$168$		0			0
$169$	4.50000	−	7.79423i	0.346154	−	0.599556i
$170$	3.00000	−	5.19615i	0.230089	−	0.398527i
$171$	12.5000	+	8.29156i	0.955899	+	0.634072i
$172$	4.05842	+	7.02939i	0.309452	+	0.535986i
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	0.729155	−	0.684349i	$-0.239913\pi$
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	−0.957241	+	0.289292i	$0.906580\pi$
$174$	−10.3723	−	11.0371i	−0.786321	−	0.836722i
$175$		0			0
$176$	0.686141	+	1.18843i	0.0517198	+	0.0895813i
$177$	17.0584	−	4.00772i	1.28219	−	0.301239i
$178$	14.7446			1.10515
$179$	−1.62772	−	2.81929i	−0.121661	−	0.210724i	0.798762	−	0.601648i	$-0.205489\pi$
$179$	−1.62772	−	2.81929i	−0.121661	−	0.210724i	−0.920423	+	0.390924i	$0.872156\pi$
$180$	10.9307	+	7.25061i	0.814727	+	0.540428i
$181$	−0.883156			−0.0656445			−0.0328222	−	0.999461i	$-0.510450\pi$
$181$	−0.883156			−0.0656445			−0.0328222	+	0.999461i	$0.510450\pi$
$182$		0			0
$183$	1.55842	−	5.16870i	0.115202	−	0.382081i
$184$	1.62772			0.119997
$185$	4.37228	−	7.57301i	0.321457	−	0.556779i
$186$	−2.37228	−	2.52434i	−0.173944	−	0.185093i
$187$	−0.941578	−	1.63086i	−0.0688550	−	0.119260i
$188$		0			0
$189$		0			0
$190$	−21.8614			−1.58599
$191$	9.55842	+	16.5557i	0.691623	+	1.19793i	0.971306	+	0.237834i	$0.0764374\pi$
$191$	9.55842	+	16.5557i	0.691623	+	1.19793i	−0.279683	+	0.960092i	$0.590229\pi$
$192$	−1.18614	−	1.26217i	−0.0856023	−	0.0910892i
$193$	3.50000	−	6.06218i	0.251936	−	0.436365i	−0.712123	−	0.702055i	$-0.752266\pi$
$193$	3.50000	−	6.06218i	0.251936	−	0.436365i	0.964059	+	0.265689i	$0.0855996\pi$
$194$	−8.11684			−0.582755
$195$	−4.37228	+	14.5012i	−0.313106	+	1.03845i
$196$		0			0
$197$	−6.00000			−0.427482			−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000			−0.427482			−0.213741	+	0.976890i	$0.568565\pi$
$198$	3.68614	−	1.83324i	0.261963	−	0.130283i
$199$	−5.00000	−	8.66025i	−0.354441	−	0.613909i	0.632581	−	0.774494i	$-0.281995\pi$
$199$	−5.00000	−	8.66025i	−0.354441	−	0.613909i	−0.987022	+	0.160585i	$0.948662\pi$
$200$	−14.1168			−0.998212
$201$	−3.56930	+	0.838574i	−0.251759	+	0.0591484i
$202$	−0.813859	−	1.40965i	−0.0572629	−	0.0991823i
$203$		0			0
$204$	1.62772	+	1.73205i	0.113963	+	0.121268i
$205$	−10.1168	−	17.5229i	−0.706591	−	1.22385i
$206$	5.00000	+	8.66025i	0.348367	+	0.603388i
$207$	0.302985	−	4.87375i	0.0210589	−	0.338749i
$208$	1.00000	−	1.73205i	0.0693375	−	0.120096i
$209$	−3.43070	+	5.94215i	−0.237307	+	0.411027i
$210$		0			0
$211$	8.00000	+	13.8564i	0.550743	+	0.953914i	0.998221	+	0.0596196i	$0.0189888\pi$
$211$	8.00000	+	13.8564i	0.550743	+	0.953914i	−0.447478	+	0.894295i	$0.647678\pi$
$212$	−8.74456			−0.600579
$213$	8.44158	+	8.98266i	0.578407	+	0.615482i
$214$	7.37228			0.503959
$215$	−17.7446	+	30.7345i	−1.21017	+	2.09607i
$216$	−4.00000	+	3.31662i	−0.272166	+	0.225668i
$217$		0			0
$218$	7.00000	−	12.1244i	0.474100	−	0.821165i
$219$	6.05842	−	20.0935i	0.409390	−	1.35779i
$220$	−3.00000	+	5.19615i	−0.202260	+	0.350325i
$221$	−1.37228	+	2.37686i	−0.0923096	+	0.159885i
$222$	2.37228	+	2.52434i	0.159217	+	0.169422i
$223$	−2.00000	+	3.46410i	−0.133930	+	0.231973i	−0.925188	−	0.379509i	$-0.876093\pi$
$223$	−2.00000	+	3.46410i	−0.133930	+	0.231973i	0.791258	+	0.611482i	$0.209426\pi$
$224$		0			0
$225$	−2.62772	+	42.2689i	−0.175181	+	2.81793i
$226$	−2.18614	+	3.78651i	−0.145420	+	0.251875i
$227$	12.2554			0.813422			0.406711	−	0.913557i	$-0.366676\pi$
$227$	12.2554			0.813422			0.406711	+	0.913557i	$0.366676\pi$
$228$	2.50000	−	8.29156i	0.165567	−	0.549122i
$229$	2.88316			0.190524			0.0952622	−	0.995452i	$-0.469631\pi$
$229$	2.88316			0.190524			0.0952622	+	0.995452i	$0.469631\pi$
$230$	3.55842	+	6.16337i	0.234635	+	0.406400i
$231$		0			0
$232$	−4.37228	+	7.57301i	−0.287054	+	0.497193i
$233$	0.127719	−	0.221215i	0.00836713	−	0.0144923i	−0.861812	−	0.507229i	$-0.830670\pi$
$233$	0.127719	−	0.221215i	0.00836713	−	0.0144923i	0.870179	+	0.492736i	$0.164003\pi$
$234$	−5.00000	−	3.31662i	−0.326860	−	0.216815i
$235$		0			0
$236$	−5.05842	−	8.76144i	−0.329275	−	0.570321i
$237$	2.55842	−	8.48533i	0.166187	−	0.551181i
$238$		0			0
$239$	−4.93070	−	8.54023i	−0.318941	−	0.552421i	0.661327	−	0.750098i	$-0.269994\pi$
$239$	−4.93070	−	8.54023i	−0.318941	−	0.552421i	−0.980267	+	0.197677i	$0.936660\pi$
$240$	2.18614	−	7.25061i	0.141115	−	0.468025i
$241$	−18.1168			−1.16701			−0.583504	−	0.812110i	$-0.698319\pi$
$241$	−18.1168			−1.16701			−0.583504	+	0.812110i	$0.698319\pi$
$242$	−4.55842	−	7.89542i	−0.293026	−	0.507537i
$243$	9.18614	+	12.5942i	0.589291	+	0.807921i
$244$	−3.11684			−0.199535
$245$		0			0
$246$	7.80298	−	1.83324i	0.497500	−	0.116883i
$247$	10.0000			0.636285
$248$	−1.00000	+	1.73205i	−0.0635001	+	0.109985i
$249$	−29.4891	+	6.92820i	−1.86880	+	0.439057i
$250$	−19.9307	−	34.5210i	−1.26053	−	2.18330i
$251$	9.00000			0.568075			0.284037	−	0.958813i	$-0.408326\pi$
$251$	9.00000			0.568075			0.284037	+	0.958813i	$0.408326\pi$
$252$		0			0
$253$	2.23369			0.140431
$254$	1.55842	+	2.69927i	0.0977841	+	0.169367i
$255$	−3.00000	+	9.94987i	−0.187867	+	0.623085i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	6.86141			0.428003			0.214001	−	0.976833i	$-0.431350\pi$
$257$	6.86141			0.428003			0.214001	+	0.976833i	$0.431350\pi$
$258$	−9.62772	−	10.2448i	−0.599396	−	0.637815i
$259$		0			0
$260$	8.74456			0.542315
$261$	21.8614	+	14.5012i	1.35319	+	0.897603i
$262$	0.813859	+	1.40965i	0.0502804	+	0.0870882i
$263$	7.62772			0.470345			0.235173	−	0.971954i	$-0.424434\pi$
$263$	7.62772			0.470345			0.235173	+	0.971954i	$0.424434\pi$
$264$	−1.62772	−	1.73205i	−0.100179	−	0.106600i
$265$	−19.1168	−	33.1113i	−1.17434	−	2.03401i
$266$		0			0
$267$	−24.8614	+	5.84096i	−1.52149	+	0.357461i
$268$	1.05842	+	1.83324i	0.0646534	+	0.111983i
$269$	−0.813859	−	1.40965i	−0.0496219	−	0.0859476i	0.840148	−	0.542358i	$-0.182468\pi$
$269$	−0.813859	−	1.40965i	−0.0496219	−	0.0859476i	−0.889769	+	0.456410i	$0.849135\pi$
$270$	−21.3030	−	7.89542i	−1.29646	−	0.480500i
$271$	8.11684	−	14.0588i	0.493063	−	0.854010i	−0.506905	−	0.862002i	$-0.669210\pi$
$271$	8.11684	−	14.0588i	0.493063	−	0.854010i	0.999968	+	0.00799154i	$0.00254381\pi$
$272$	0.686141	−	1.18843i	0.0416034	−	0.0720592i
$273$		0			0
$274$	5.31386	+	9.20387i	0.321022	+	0.556026i
$275$	−19.3723			−1.16819
$276$	−2.74456	+	0.644810i	−0.165203	+	0.0388130i
$277$	−12.2337			−0.735051			−0.367526	−	0.930013i	$-0.619795\pi$
$277$	−12.2337			−0.735051			−0.367526	+	0.930013i	$0.619795\pi$
$278$	−6.61684	+	11.4607i	−0.396852	+	0.687368i
$279$	5.00000	+	3.31662i	0.299342	+	0.198561i
$280$		0			0
$281$	−8.18614	+	14.1788i	−0.488344	+	0.845837i	−0.999910	−	0.0134071i	$-0.995732\pi$
$281$	−8.18614	+	14.1788i	−0.488344	+	0.845837i	0.511566	+	0.859244i	$0.329066\pi$
$282$		0			0
$283$	13.5584	−	23.4839i	0.805965	−	1.39597i	−0.109673	−	0.993968i	$-0.534981\pi$
$283$	13.5584	−	23.4839i	0.805965	−	1.39597i	0.915638	−	0.402004i	$-0.131686\pi$
$284$	3.55842	−	6.16337i	0.211153	−	0.365729i
$285$	36.8614	−	8.66025i	2.18348	−	0.512989i
$286$	1.37228	−	2.37686i	0.0811447	−	0.140547i
$287$		0			0
$288$	2.50000	+	1.65831i	0.147314	+	0.0977170i
$289$	7.55842	−	13.0916i	0.444613	−	0.770092i
$290$	−38.2337			−2.24516
$291$	13.6861	−	3.21543i	0.802296	−	0.188492i
$292$	−12.1168			−0.709085
$293$	−5.18614	−	8.98266i	−0.302978	−	0.524773i	0.673831	−	0.738885i	$-0.264647\pi$
$293$	−5.18614	−	8.98266i	−0.302978	−	0.524773i	−0.976809	+	0.214113i	$0.931314\pi$
$294$		0			0
$295$	22.1168	−	38.3075i	1.28769	−	2.23035i
$296$	1.00000	−	1.73205i	0.0581238	−	0.100673i
$297$	−5.48913	+	4.55134i	−0.318511	+	0.264096i
$298$	1.62772	+	2.81929i	0.0942912	+	0.163317i
$299$	−1.62772	−	2.81929i	−0.0941334	−	0.163044i
$300$	23.8030	−	5.59230i	1.37427	−	0.322871i
$301$		0			0
$302$	4.55842	+	7.89542i	0.262308	+	0.454330i
$303$	1.93070	+	2.05446i	0.110916	+	0.118025i
$304$	−5.00000			−0.286770
$305$	−6.81386	−	11.8020i	−0.390160	−	0.675778i
$306$	−3.43070	−	2.27567i	−0.196120	−	0.130091i
$307$	13.0000			0.741949			0.370975	−	0.928643i	$-0.379024\pi$
$307$	13.0000			0.741949			0.370975	+	0.928643i	$0.379024\pi$
$308$		0			0
$309$	−11.8614	−	12.6217i	−0.674772	−	0.718023i
$310$	−8.74456			−0.496658
$311$	4.11684	−	7.13058i	0.233445	−	0.404338i	−0.725375	−	0.688354i	$-0.758334\pi$
$311$	4.11684	−	7.13058i	0.233445	−	0.404338i	0.958820	+	0.284016i	$0.0916668\pi$
$312$	−1.00000	+	3.31662i	−0.0566139	+	0.187767i
$313$	−10.0584	−	17.4217i	−0.568536	−	0.984733i	−0.996711	−	0.0810370i	$-0.974177\pi$
$313$	−10.0584	−	17.4217i	−0.568536	−	0.984733i	0.428175	−	0.903696i	$-0.359157\pi$
$314$	9.11684			0.514493
$315$		0			0
$316$	−5.11684			−0.287845
$317$	3.00000	+	5.19615i	0.168497	+	0.291845i	0.937892	−	0.346929i	$-0.112775\pi$
$317$	3.00000	+	5.19615i	0.168497	+	0.291845i	−0.769395	+	0.638774i	$0.779442\pi$
$318$	14.7446	−	3.46410i	0.826834	−	0.194257i
$319$	−6.00000	+	10.3923i	−0.335936	+	0.581857i
$320$	−4.37228			−0.244418
$321$	−12.4307	+	2.92048i	−0.693814	+	0.163005i
$322$		0			0
$323$	6.86141			0.381779
$324$	5.43070	−	7.17687i	0.301706	−	0.398715i
$325$	14.1168	+	24.4511i	0.783062	+	1.35630i
$326$	18.2337			1.00987
$327$	−7.00000	+	23.2164i	−0.387101	+	1.28387i
$328$	−2.31386	−	4.00772i	−0.127762	−	0.221289i
$329$		0			0
$330$	3.00000	−	9.94987i	0.165145	−	0.547723i
$331$	−11.1168	−	19.2549i	−0.611037	−	1.05835i	−0.991066	−	0.133373i	$-0.957419\pi$
$331$	−11.1168	−	19.2549i	−0.611037	−	1.05835i	0.380029	−	0.924975i	$-0.375914\pi$
$332$	8.74456	+	15.1460i	0.479920	+	0.831246i
$333$	−5.00000	−	3.31662i	−0.273998	−	0.181750i
$334$	2.74456	−	4.75372i	0.150176	−	0.260112i
$335$	−4.62772	+	8.01544i	−0.252839	+	0.437930i
$336$		0			0
$337$	4.05842	+	7.02939i	0.221076	+	0.382915i	0.955135	−	0.296171i	$-0.0957097\pi$
$337$	4.05842	+	7.02939i	0.221076	+	0.382915i	−0.734059	+	0.679086i	$0.762376\pi$
$338$	9.00000			0.489535
$339$	2.18614	−	7.25061i	0.118735	−	0.393799i
$340$	6.00000			0.325396
$341$	−1.37228	+	2.37686i	−0.0743132	+	0.128714i
$342$	−0.930703	+	14.9711i	−0.0503267	+	0.809544i
$343$		0			0
$344$	−4.05842	+	7.02939i	−0.218815	+	0.378999i
$345$	−8.44158	−	8.98266i	−0.454479	−	0.483610i
$346$	3.00000	−	5.19615i	0.161281	−	0.279347i
$347$	5.05842	−	8.76144i	0.271550	−	0.470339i	−0.697709	−	0.716382i	$-0.745797\pi$
$347$	5.05842	−	8.76144i	0.271550	−	0.470339i	0.969259	+	0.246043i	$0.0791303\pi$
$348$	4.37228	−	14.5012i	0.234379	−	0.777347i
$349$	−11.0000	+	19.0526i	−0.588817	+	1.01986i	0.405571	+	0.914063i	$0.367073\pi$
$349$	−11.0000	+	19.0526i	−0.588817	+	1.01986i	−0.994388	+	0.105797i	$0.966261\pi$
$350$		0			0
$351$	9.74456	+	3.61158i	0.520126	+	0.192772i
$352$	−0.686141	+	1.18843i	−0.0365714	+	0.0633436i
$353$	13.3723			0.711735			0.355867	−	0.934536i	$-0.384185\pi$
$353$	13.3723			0.711735			0.355867	+	0.934536i	$0.384185\pi$
$354$	12.0000	+	12.7692i	0.637793	+	0.678674i
$355$	31.1168			1.65151
$356$	7.37228	+	12.7692i	0.390730	+	0.676764i
$357$		0			0
$358$	1.62772	−	2.81929i	0.0860276	−	0.149004i
$359$	−10.9307	+	18.9325i	−0.576900	+	0.999221i	0.418932	+	0.908018i	$0.362405\pi$
$359$	−10.9307	+	18.9325i	−0.576900	+	0.999221i	−0.995832	+	0.0912032i	$0.970929\pi$
$360$	−0.813859	+	13.0916i	−0.0428942	+	0.689986i
$361$	−3.00000	−	5.19615i	−0.157895	−	0.273482i
$362$	−0.441578	−	0.764836i	−0.0232088	−	0.0401989i
$363$	10.8139	+	11.5070i	0.567580	+	0.603961i
$364$		0			0
$365$	−26.4891	−	45.8805i	−1.38650	−	2.40150i
$366$	5.25544	−	1.23472i	0.274706	−	0.0645397i
$367$	12.2337			0.638593			0.319297	−	0.947655i	$-0.396553\pi$
$367$	12.2337			0.638593			0.319297	+	0.947655i	$0.396553\pi$
$368$	0.813859	+	1.40965i	0.0424254	+	0.0734829i
$369$	−12.4307	+	6.18220i	−0.647117	+	0.321833i
$370$	8.74456			0.454608
$371$		0			0
$372$	1.00000	−	3.31662i	0.0518476	−	0.171959i
$373$	−10.0000			−0.517780			−0.258890	−	0.965907i	$-0.583357\pi$
$373$	−10.0000			−0.517780			−0.258890	+	0.965907i	$0.583357\pi$
$374$	0.941578	−	1.63086i	0.0486878	−	0.0843298i
$375$	47.2812	+	50.3118i	2.44159	+	2.59809i
$376$		0			0
$377$	17.4891			0.900736
$378$		0			0
$379$	−8.11684			−0.416934			−0.208467	−	0.978029i	$-0.566847\pi$
$379$	−8.11684			−0.416934			−0.208467	+	0.978029i	$0.566847\pi$
$380$	−10.9307	−	18.9325i	−0.560733	−	0.971218i
$381$	−3.69702	−	3.93398i	−0.189404	−	0.201544i
$382$	−9.55842	+	16.5557i	−0.489051	+	0.847062i
$383$	32.7446			1.67317			0.836584	−	0.547838i	$-0.184549\pi$
$383$	32.7446			1.67317			0.836584	+	0.547838i	$0.184549\pi$
$384$	0.500000	−	1.65831i	0.0255155	−	0.0846254i
$385$		0			0
$386$	7.00000			0.356291
$387$	20.2921	+	13.4603i	1.03151	+	0.684224i
$388$	−4.05842	−	7.02939i	−0.206035	−	0.356863i
$389$	10.9783			0.556619			0.278310	−	0.960491i	$-0.410226\pi$
$389$	10.9783			0.556619			0.278310	+	0.960491i	$0.410226\pi$
$390$	−14.7446	+	3.46410i	−0.746620	+	0.175412i
$391$	−1.11684	−	1.93443i	−0.0564812	−	0.0978284i
$392$		0			0
$393$	−1.93070	−	2.05446i	−0.0973911	−	0.103634i
$394$	−3.00000	−	5.19615i	−0.151138	−	0.261778i
$395$	−11.1861	−	19.3750i	−0.562836	−	0.974860i
$396$	3.43070	+	2.27567i	0.172399	+	0.114357i
$397$	−11.0000	+	19.0526i	−0.552074	+	0.956221i	0.446051	+	0.895008i	$0.352830\pi$
$397$	−11.0000	+	19.0526i	−0.552074	+	0.956221i	−0.998125	+	0.0612128i	$0.980503\pi$
$398$	5.00000	−	8.66025i	0.250627	−	0.434099i
$399$		0			0
$400$	−7.05842	−	12.2255i	−0.352921	−	0.611277i
$401$	−11.7446			−0.586495			−0.293248	−	0.956036i	$-0.594736\pi$
$401$	−11.7446			−0.586495			−0.293248	+	0.956036i	$0.594736\pi$
$402$	−2.51087	−	2.67181i	−0.125231	−	0.133258i
$403$	4.00000			0.199254
$404$	0.813859	−	1.40965i	0.0404910	−	0.0701325i
$405$	39.0475	+	4.87375i	1.94029	+	0.242178i
$406$		0			0
$407$	1.37228	−	2.37686i	0.0680215	−	0.117817i
$408$	−0.686141	+	2.27567i	−0.0339690	+	0.112663i
$409$	−11.1753	+	19.3561i	−0.552581	+	0.957099i	0.445506	+	0.895279i	$0.353024\pi$
$409$	−11.1753	+	19.3561i	−0.552581	+	0.957099i	−0.998087	+	0.0618200i	$0.980310\pi$
$410$	10.1168	−	17.5229i	0.499635	−	0.865394i
$411$	−12.6060	−	13.4140i	−0.621807	−	0.661663i
$412$	−5.00000	+	8.66025i	−0.246332	+	0.426660i
$413$		0			0
$414$	4.37228	−	2.17448i	0.214886	−	0.106870i
$415$	−38.2337	+	66.2227i	−1.87682	+	3.25074i
$416$	2.00000			0.0980581
$417$	6.61684	−	21.9456i	0.324028	−	1.07468i
$418$	−6.86141			−0.335602
$419$	−6.30298	−	10.9171i	−0.307921	−	0.533335i	0.669986	−	0.742373i	$-0.266300\pi$
$419$	−6.30298	−	10.9171i	−0.307921	−	0.533335i	−0.977907	+	0.209039i	$0.932967\pi$
$420$		0			0
$421$	−17.1168	+	29.6472i	−0.834224	+	1.44492i	0.0604368	+	0.998172i	$0.480751\pi$
$421$	−17.1168	+	29.6472i	−0.834224	+	1.44492i	−0.894661	+	0.446746i	$0.852583\pi$
$422$	−8.00000	+	13.8564i	−0.389434	+	0.674519i
$423$		0			0
$424$	−4.37228	−	7.57301i	−0.212337	−	0.367778i
$425$	9.68614	+	16.7769i	0.469847	+	0.813799i
$426$	−3.55842	+	11.8020i	−0.172406	+	0.571806i
$427$		0			0
$428$	3.68614	+	6.38458i	0.178176	+	0.308610i
$429$	−1.37228	+	4.55134i	−0.0662544	+	0.219741i
$430$	−35.4891			−1.71144
$431$	3.25544	+	5.63858i	0.156809	+	0.271601i	0.933716	−	0.358014i	$-0.116546\pi$
$431$	3.25544	+	5.63858i	0.156809	+	0.271601i	−0.776907	+	0.629615i	$0.783213\pi$
$432$	−4.87228	−	1.80579i	−0.234418	−	0.0868811i
$433$	20.1168			0.966754			0.483377	−	0.875412i	$-0.339410\pi$
$433$	20.1168			0.966754			0.483377	+	0.875412i	$0.339410\pi$
$434$		0			0
$435$	64.4674	−	15.1460i	3.09097	−	0.726196i
$436$	14.0000			0.670478
$437$	−4.06930	+	7.04823i	−0.194661	+	0.337162i
$438$	20.4307	−	4.80001i	0.976217	−	0.229353i
$439$	4.00000	+	6.92820i	0.190910	+	0.330665i	0.945552	−	0.325471i	$-0.105523\pi$
$439$	4.00000	+	6.92820i	0.190910	+	0.330665i	−0.754642	+	0.656136i	$0.772190\pi$
$440$	−6.00000			−0.286039
$441$		0			0
$442$	−2.74456			−0.130546
$443$	20.0584	+	34.7422i	0.953004	+	1.65065i	0.738870	+	0.673848i	$0.235360\pi$
$443$	20.0584	+	34.7422i	0.953004	+	1.65065i	0.214134	+	0.976804i	$0.431307\pi$
$444$	−1.00000	+	3.31662i	−0.0474579	+	0.157400i
$445$	−32.2337	+	55.8304i	−1.52802	+	2.64661i
$446$	−4.00000			−0.189405
$447$	−3.86141	−	4.10891i	−0.182638	−	0.194345i
$448$		0			0
$449$	33.0000			1.55737			0.778683	−	0.627417i	$-0.215888\pi$
$449$	33.0000			1.55737			0.778683	+	0.627417i	$0.215888\pi$
$450$	−37.9198	+	18.8588i	−1.78756	+	0.889012i
$451$	−3.17527	−	5.49972i	−0.149517	−	0.258972i
$452$	−4.37228			−0.205655
$453$	−10.8139	−	11.5070i	−0.508079	−	0.540646i
$454$	6.12772	+	10.6135i	0.287588	+	0.498117i
$455$		0			0
$456$	8.43070	−	1.98072i	0.394804	−	0.0927556i
$457$	17.7337	+	30.7156i	0.829547	+	1.43682i	0.898394	+	0.439190i	$0.144735\pi$
$457$	17.7337	+	30.7156i	0.829547	+	1.43682i	−0.0688472	+	0.997627i	$0.521932\pi$
$458$	1.44158	+	2.49689i	0.0673605	+	0.116672i
$459$	6.68614	+	2.47805i	0.312082	+	0.115666i
$460$	−3.55842	+	6.16337i	−0.165912	+	0.287368i
$461$	1.06930	−	1.85208i	0.0498021	−	0.0862598i	−0.840050	−	0.542509i	$-0.817474\pi$
$461$	1.06930	−	1.85208i	0.0498021	−	0.0862598i	0.889852	+	0.456250i	$0.150808\pi$
$462$		0			0
$463$	11.5584	+	20.0198i	0.537165	+	0.930398i	0.999055	+	0.0434604i	$0.0138382\pi$
$463$	11.5584	+	20.0198i	0.537165	+	0.930398i	−0.461890	+	0.886937i	$0.652828\pi$
$464$	−8.74456			−0.405956
$465$	14.7446	−	3.46410i	0.683763	−	0.160644i
$466$	0.255437			0.0118329
$467$	16.5475	−	28.6612i	0.765729	−	1.32628i	−0.174131	−	0.984722i	$-0.555712\pi$
$467$	16.5475	−	28.6612i	0.765729	−	1.32628i	0.939860	−	0.341559i	$-0.110955\pi$
$468$	0.372281	−	5.98844i	0.0172087	−	0.276816i
$469$		0			0
$470$		0			0
$471$	−15.3723	+	3.61158i	−0.708317	+	0.166413i
$472$	5.05842	−	8.76144i	0.232833	−	0.403278i
$473$	−5.56930	+	9.64630i	−0.256077	+	0.443538i
$474$	8.62772	−	2.02700i	0.396284	−	0.0931034i
$475$	35.2921	−	61.1277i	1.61931	−	2.80473i
$476$		0			0
$477$	−23.4891	+	11.6819i	−1.07549	+	0.534879i
$478$	4.93070	−	8.54023i	0.225525	−	0.390621i
$479$	−32.7446			−1.49614			−0.748069	−	0.663621i	$-0.769019\pi$
$479$	−32.7446			−1.49614			−0.748069	+	0.663621i	$0.769019\pi$
$480$	7.37228	−	1.73205i	0.336497	−	0.0790569i
$481$	−4.00000			−0.182384
$482$	−9.05842	−	15.6896i	−0.412600	−	0.714644i
$483$		0			0
$484$	4.55842	−	7.89542i	0.207201	−	0.358883i
$485$	17.7446	−	30.7345i	0.805739	−	1.39558i
$486$	−6.31386	+	14.2525i	−0.286402	+	0.646509i
$487$	−17.6753	−	30.6145i	−0.800943	−	1.38727i	−0.918996	−	0.394266i	$-0.870999\pi$
$487$	−17.6753	−	30.6145i	−0.800943	−	1.38727i	0.118053	−	0.993007i	$-0.462335\pi$
$488$	−1.55842	−	2.69927i	−0.0705464	−	0.122190i
$489$	−30.7446	+	7.22316i	−1.39032	+	0.326642i
$490$		0			0
$491$	12.6861	+	21.9730i	0.572518	+	0.991629i	0.996306	+	0.0858685i	$0.0273665\pi$
$491$	12.6861	+	21.9730i	0.572518	+	0.991629i	−0.423789	+	0.905761i	$0.639300\pi$
$492$	5.48913	+	5.84096i	0.247469	+	0.263331i
$493$	12.0000			0.540453
$494$	5.00000	+	8.66025i	0.224961	+	0.389643i
$495$	−1.11684	+	17.9653i	−0.0501984	+	0.807481i
$496$	−2.00000			−0.0898027
$497$		0			0
$498$	−20.7446	−	22.0742i	−0.929586	−	0.989170i
$499$	18.1168			0.811021			0.405511	−	0.914090i	$-0.367094\pi$
$499$	18.1168			0.811021			0.405511	+	0.914090i	$0.367094\pi$
$500$	19.9307	−	34.5210i	0.891328	−	1.54383i
$501$	−2.74456	+	9.10268i	−0.122618	+	0.406678i
$502$	4.50000	+	7.79423i	0.200845	+	0.347873i
$503$	32.2337			1.43723			0.718615	−	0.695409i	$-0.244777\pi$
$503$	32.2337			1.43723			0.718615	+	0.695409i	$0.244777\pi$
$504$		0			0
$505$	7.11684			0.316695
$506$	1.11684	+	1.93443i	0.0496498	+	0.0859959i
$507$	−15.1753	+	3.56529i	−0.673957	+	0.158340i
$508$	−1.55842	+	2.69927i	−0.0691438	+	0.119761i
$509$	28.9783			1.28444			0.642219	−	0.766521i	$-0.278014\pi$
$509$	28.9783			1.28444			0.642219	+	0.766521i	$0.278014\pi$
$510$	−10.1168	+	2.37686i	−0.447981	+	0.105249i
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	−4.36141	−	25.6121i	−0.192561	−	1.13080i
$514$	3.43070	+	5.94215i	0.151322	+	0.262097i
$515$	−43.7228			−1.92666
$516$	4.05842	−	13.4603i	0.178662	−	0.592555i
$517$		0			0
$518$		0			0
$519$	−3.00000	+	9.94987i	−0.131685	+	0.436751i
$520$	4.37228	+	7.57301i	0.191737	+	0.332099i
$521$	−12.4307	−	21.5306i	−0.544599	−	0.943273i	−0.998632	−	0.0522883i	$-0.983349\pi$
$521$	−12.4307	−	21.5306i	−0.544599	−	0.943273i	0.454033	−	0.890985i	$-0.349985\pi$
$522$	−1.62772	+	26.1831i	−0.0712433	+	1.14600i
$523$	−17.5584	+	30.4121i	−0.767776	+	1.32983i	0.170990	+	0.985273i	$0.445303\pi$
$523$	−17.5584	+	30.4121i	−0.767776	+	1.32983i	−0.938766	+	0.344555i	$0.888030\pi$
$524$	−0.813859	+	1.40965i	−0.0355536	+	0.0615807i
$525$		0			0
$526$	3.81386	+	6.60580i	0.166292	+	0.288026i
$527$	2.74456			0.119555
$528$	0.686141	−	2.27567i	0.0298604	−	0.0990359i
$529$	−20.3505			−0.884806
$530$	19.1168	−	33.1113i	0.830383	−	1.43826i
$531$	−25.2921	−	16.7769i	−1.09758	−	0.728055i
$532$		0			0
$533$	−4.62772	+	8.01544i	−0.200449	+	0.347187i
$534$	−17.4891	−	18.6101i	−0.756828	−	0.805339i
$535$	−16.1168	+	27.9152i	−0.696792	+	1.20688i
$536$	−1.05842	+	1.83324i	−0.0457169	+	0.0791839i
$537$	−1.62772	+	5.39853i	−0.0702412	+	0.232964i
$538$	0.813859	−	1.40965i	0.0350880	−	0.0607741i
$539$		0			0
$540$	−3.81386	−	22.3966i	−0.164122	−	0.963798i
$541$	3.11684	−	5.39853i	0.134004	−	0.232101i	−0.791213	−	0.611541i	$-0.790550\pi$
$541$	3.11684	−	5.39853i	0.134004	−	0.232101i	0.925216	+	0.379440i	$0.123883\pi$
$542$	16.2337			0.697297
$543$	1.04755	+	1.11469i	0.0449546	+	0.0478360i
$544$	1.37228			0.0588361
$545$	30.6060	+	53.0111i	1.31102	+	2.27075i
$546$		0			0
$547$	−9.05842	+	15.6896i	−0.387310	+	0.670841i	−0.992087	−	0.125554i	$-0.959929\pi$
$547$	−9.05842	+	15.6896i	−0.387310	+	0.670841i	0.604777	+	0.796395i	$0.293262\pi$
$548$	−5.31386	+	9.20387i	−0.226997	+	0.393170i
$549$	−8.37228	+	4.16381i	−0.357320	+	0.177707i
$550$	−9.68614	−	16.7769i	−0.413018	−	0.715369i
$551$	−21.8614	−	37.8651i	−0.931327	−	1.61311i
$552$	−1.93070	−	2.05446i	−0.0821762	−	0.0874434i
$553$		0			0
$554$	−6.11684	−	10.5947i	−0.259880	−	0.450125i
$555$	−14.7446	+	3.46410i	−0.625872	+	0.147043i
$556$	−13.2337			−0.561233
$557$	−14.7446	−	25.5383i	−0.624747	−	1.08209i	−0.988590	−	0.150633i	$-0.951869\pi$
$557$	−14.7446	−	25.5383i	−0.624747	−	1.08209i	0.363843	−	0.931460i	$-0.381465\pi$
$558$	−0.372281	+	5.98844i	−0.0157599	+	0.253511i
$559$	16.2337			0.686612
$560$		0			0
$561$	−0.941578	+	3.12286i	−0.0397535	+	0.131847i
$562$	−16.3723			−0.690623
$563$	1.50000	−	2.59808i	0.0632175	−	0.109496i	−0.832684	−	0.553748i	$-0.813197\pi$
$563$	1.50000	−	2.59808i	0.0632175	−	0.109496i	0.895902	+	0.444252i	$0.146530\pi$
$564$		0			0
$565$	−9.55842	−	16.5557i	−0.402126	−	0.696502i
$566$	27.1168			1.13981
$567$		0			0
$568$	7.11684			0.298616
$569$	−8.05842	−	13.9576i	−0.337827	−	0.585133i	0.646197	−	0.763171i	$-0.276358\pi$
$569$	−8.05842	−	13.9576i	−0.337827	−	0.585133i	−0.984024	+	0.178038i	$0.943025\pi$
$570$	25.9307	+	27.5928i	1.08612	+	1.15573i
$571$	11.1753	−	19.3561i	0.467670	−	0.810029i	−0.531647	−	0.846966i	$-0.678427\pi$
$571$	11.1753	−	19.3561i	0.467670	−	0.810029i	0.999318	+	0.0369371i	$0.0117601\pi$
$572$	2.74456			0.114756
$573$	9.55842	−	31.7017i	0.399309	−	1.32436i
$574$		0			0
$575$	−22.9783			−0.958259
$576$	−0.186141	+	2.99422i	−0.00775586	+	0.124759i
$577$	4.94158	+	8.55906i	0.205721	+	0.356319i	0.950362	−	0.311146i	$-0.100713\pi$
$577$	4.94158	+	8.55906i	0.205721	+	0.356319i	−0.744641	+	0.667465i	$0.767380\pi$
$578$	15.1168			0.628778
$579$	−11.8030	+	2.77300i	−0.490515	+	0.115242i
$580$	−19.1168	−	33.1113i	−0.793784	−	1.37487i
$581$		0			0
$582$	9.62772	+	10.2448i	0.399082	+	0.424662i
$583$	−6.00000	−	10.3923i	−0.248495	−	0.430405i
$584$	−6.05842	−	10.4935i	−0.250699	−	0.434224i
$585$	23.4891	−	11.6819i	0.971156	−	0.482988i
$586$	5.18614	−	8.98266i	0.214237	−	0.371070i
$587$	7.24456	−	12.5480i	0.299015	−	0.517909i	−0.676896	−	0.736079i	$-0.736675\pi$
$587$	7.24456	−	12.5480i	0.299015	−	0.517909i	0.975911	+	0.218170i	$0.0700086\pi$
$588$		0			0
$589$	−5.00000	−	8.66025i	−0.206021	−	0.356840i
$590$	44.2337			1.82107
$591$	7.11684	+	7.57301i	0.292748	+	0.311512i
$592$	2.00000			0.0821995
$593$	7.37228	−	12.7692i	0.302743	−	0.524367i	−0.674013	−	0.738719i	$-0.735431\pi$
$593$	7.37228	−	12.7692i	0.302743	−	0.524367i	0.976756	+	0.214353i	$0.0687642\pi$
$594$	−6.68614	−	2.47805i	−0.274336	−	0.101676i
$595$		0			0
$596$	−1.62772	+	2.81929i	−0.0666740	+	0.115483i
$597$	−5.00000	+	16.5831i	−0.204636	+	0.678702i
$598$	1.62772	−	2.81929i	0.0665624	−	0.115289i
$599$	−12.0000	+	20.7846i	−0.490307	+	0.849236i	−0.999938	−	0.0111569i	$-0.996449\pi$
$599$	−12.0000	+	20.7846i	−0.490307	+	0.849236i	0.509631	+	0.860393i	$0.329782\pi$
$600$	16.7446	+	17.8178i	0.683594	+	0.727410i
$601$	12.0584	−	20.8858i	0.491873	−	0.851950i	−0.508083	−	0.861308i	$-0.669646\pi$
$601$	12.0584	−	20.8858i	0.491873	−	0.851950i	0.999956	+	0.00935863i	$0.00297899\pi$
$602$		0			0
$603$	5.29211	+	3.51039i	0.215511	+	0.142954i
$604$	−4.55842	+	7.89542i	−0.185480	+	0.321260i
$605$	39.8614			1.62060
$606$	−0.813859	+	2.69927i	−0.0330608	+	0.109650i
$607$	−22.2337			−0.902438			−0.451219	−	0.892413i	$-0.649011\pi$
$607$	−22.2337			−0.902438			−0.451219	+	0.892413i	$0.649011\pi$
$608$	−2.50000	−	4.33013i	−0.101388	−	0.175610i
$609$		0			0
$610$	6.81386	−	11.8020i	0.275885	−	0.477847i
$611$		0			0
$612$	0.255437	−	4.10891i	0.0103254	−	0.166093i
$613$	18.1168	+	31.3793i	0.731732	+	1.26740i	0.956142	+	0.292903i	$0.0946213\pi$
$613$	18.1168	+	31.3793i	0.731732	+	1.26740i	−0.224410	+	0.974495i	$0.572045\pi$
$614$	6.50000	+	11.2583i	0.262319	+	0.454349i
$615$	−10.1168	+	33.5538i	−0.407951	+	1.35302i
$616$		0			0
$617$	−9.43070	−	16.3345i	−0.379666	−	0.657600i	0.611348	−	0.791362i	$-0.290628\pi$
$617$	−9.43070	−	16.3345i	−0.379666	−	0.657600i	−0.991014	+	0.133762i	$0.957294\pi$
$618$	5.00000	−	16.5831i	0.201129	−	0.667071i
$619$	−45.4674			−1.82749			−0.913744	−	0.406290i	$-0.866822\pi$
$619$	−45.4674			−1.82749			−0.913744	+	0.406290i	$0.866822\pi$
$620$	−4.37228	−	7.57301i	−0.175595	−	0.304140i
$621$	−6.51087	+	5.39853i	−0.261272	+	0.216636i
$622$	8.23369			0.330141
$623$		0			0
$624$	−3.37228	+	0.792287i	−0.134999	+	0.0317169i
$625$	103.701			4.14804
$626$	10.0584	−	17.4217i	0.402015	−	0.696311i
$627$	11.5693	−	2.71810i	0.462033	−	0.108551i
$628$	4.55842	+	7.89542i	0.181901	+	0.315061i
$629$	−2.74456			−0.109433
$630$		0			0
$631$	−37.3505			−1.48690			−0.743451	−	0.668791i	$-0.766812\pi$
$631$	−37.3505			−1.48690			−0.743451	+	0.668791i	$0.766812\pi$
$632$	−2.55842	−	4.43132i	−0.101769	−	0.176268i
$633$	8.00000	−	26.5330i	0.317971	−	1.05459i
$634$	−3.00000	+	5.19615i	−0.119145	+	0.206366i
$635$	−13.6277			−0.540800
$636$	10.3723	+	11.0371i	0.411288	+	0.437650i
$637$		0			0
$638$	−12.0000			−0.475085
$639$	1.32473	−	21.3094i	0.0524057	−	0.842987i
$640$	−2.18614	−	3.78651i	−0.0864148	−	0.149675i
$641$	34.2119			1.35129			0.675645	−	0.737227i	$-0.263865\pi$
$641$	34.2119			1.35129			0.675645	+	0.737227i	$0.263865\pi$
$642$	−8.74456	−	9.30506i	−0.345120	−	0.367242i
$643$	13.1753	+	22.8202i	0.519582	+	0.899942i	0.999741	+	0.0227606i	$0.00724556\pi$
$643$	13.1753	+	22.8202i	0.519582	+	0.899942i	−0.480159	+	0.877181i	$0.659421\pi$
$644$		0			0
$645$	59.8397	−	14.0588i	2.35618	−	0.553564i
$646$	3.43070	+	5.94215i	0.134979	+	0.233791i
$647$	2.74456	+	4.75372i	0.107900	+	0.186888i	0.914919	−	0.403637i	$-0.132254\pi$
$647$	2.74456	+	4.75372i	0.107900	+	0.186888i	−0.807019	+	0.590525i	$0.798921\pi$
$648$	8.93070	+	1.11469i	0.350831	+	0.0437892i
$649$	6.94158	−	12.0232i	0.272481	−	0.471951i
$650$	−14.1168	+	24.4511i	−0.553708	+	0.959051i
$651$		0			0
$652$	9.11684	+	15.7908i	0.357043	+	0.618417i
$653$	−26.7446			−1.04660			−0.523298	−	0.852150i	$-0.675298\pi$
$653$	−26.7446			−1.04660			−0.523298	+	0.852150i	$0.675298\pi$
$654$	−23.6060	+	5.54601i	−0.923066	+	0.216866i
$655$	−7.11684			−0.278078
$656$	2.31386	−	4.00772i	0.0903410	−	0.156475i
$657$	−32.5475	+	16.1870i	−1.26980	+	0.631514i
$658$		0			0
$659$	10.3723	−	17.9653i	0.404047	−	0.699829i	−0.590163	−	0.807284i	$-0.700937\pi$
$659$	10.3723	−	17.9653i	0.404047	−	0.699829i	0.994210	+	0.107454i	$0.0342700\pi$
$660$	10.1168	−	2.37686i	0.393798	−	0.0925192i
$661$	13.5584	−	23.4839i	0.527361	−	0.913417i	−0.472130	−	0.881529i	$-0.656515\pi$
$661$	13.5584	−	23.4839i	0.527361	−	0.913417i	0.999491	−	0.0318879i	$-0.0101520\pi$
$662$	11.1168	−	19.2549i	0.432068	−	0.748364i
$663$	4.62772	−	1.08724i	0.179726	−	0.0422249i
$664$	−8.74456	+	15.1460i	−0.339355	+	0.587780i
$665$		0			0
$666$	0.372281	−	5.98844i	0.0144256	−	0.232047i
$667$	−7.11684	+	12.3267i	−0.275565	+	0.477293i
$668$	5.48913			0.212381
$669$	6.74456	−	1.58457i	0.260760	−	0.0612632i
$670$	−9.25544			−0.357569
$671$	−2.13859	−	3.70415i	−0.0825595	−	0.142997i
$672$		0			0
$673$	1.44158	−	2.49689i	0.0555687	−	0.0962479i	−0.836903	−	0.547351i	$-0.815636\pi$
$673$	1.44158	−	2.49689i	0.0555687	−	0.0962479i	0.892472	+	0.451103i	$0.148969\pi$
$674$	−4.05842	+	7.02939i	−0.156325	+	0.270762i
$675$	56.4674	−	46.8203i	2.17343	−	1.80211i
$676$	4.50000	+	7.79423i	0.173077	+	0.299778i
$677$	17.2337	+	29.8496i	0.662344	+	1.14721i	0.979998	+	0.199007i	$0.0637718\pi$
$677$	17.2337	+	29.8496i	0.662344	+	1.14721i	−0.317654	+	0.948207i	$0.602895\pi$
$678$	7.37228	−	1.73205i	0.283131	−	0.0665190i
$679$		0			0
$680$	3.00000	+	5.19615i	0.115045	+	0.199263i
$681$	−14.5367	−	15.4684i	−0.557047	−	0.592752i
$682$	−2.74456			−0.105095
$683$	−14.9198	−	25.8419i	−0.570891	−	0.988813i	−0.996475	−	0.0838936i	$-0.973264\pi$
$683$	−14.9198	−	25.8419i	−0.570891	−	0.988813i	0.425583	−	0.904919i	$-0.360069\pi$
$684$	−13.4307	+	6.67954i	−0.513536	+	0.255398i
$685$	−46.4674			−1.77543
$686$		0			0
$687$	−3.41983	−	3.63903i	−0.130475	−	0.138838i
$688$	−8.11684			−0.309452
$689$	−8.74456	+	15.1460i	−0.333141	+	0.577018i
$690$	3.55842	−	11.8020i	0.135467	−	0.449293i
$691$	−11.5584	−	20.0198i	−0.439703	−	0.761588i	0.557963	−	0.829866i	$-0.311583\pi$
$691$	−11.5584	−	20.0198i	−0.439703	−	0.761588i	−0.997666	+	0.0682775i	$0.978250\pi$
$692$	6.00000			0.228086
$693$		0			0
$694$	10.1168			0.384030
$695$	−28.9307	−	50.1094i	−1.09740	−	1.90076i
$696$	14.7446	−	3.46410i	0.558891	−	0.131306i
$697$	−3.17527	+	5.49972i	−0.120272	+	0.208317i
$698$	−22.0000			−0.832712
$699$	−0.430703	+	0.101190i	−0.0162907	+	0.00382735i
$700$		0			0
$701$	−38.2337			−1.44407			−0.722033	−	0.691858i	$-0.756792\pi$
$701$	−38.2337			−1.44407			−0.722033	+	0.691858i	$0.756792\pi$
$702$	1.74456	+	10.2448i	0.0658443	+	0.386666i
$703$	5.00000	+	8.66025i	0.188579	+	0.326628i
$704$	−1.37228			−0.0517198
$705$		0			0
$706$	6.68614	+	11.5807i	0.251636	+	0.435847i
$707$		0			0
$708$	−5.05842	+	16.7769i	−0.190107	+	0.630514i
$709$	−22.0000	−	38.1051i	−0.826227	−	1.43107i	−0.900978	−	0.433865i	$-0.857149\pi$
$709$	−22.0000	−	38.1051i	−0.826227	−	1.43107i	0.0747503	−	0.997202i	$-0.476184\pi$
$710$	15.5584	+	26.9480i	0.583897	+	1.01134i
$711$	−13.7446	+	6.83563i	−0.515461	+	0.256356i
$712$	−7.37228	+	12.7692i	−0.276288	+	0.478545i
$713$	−1.62772	+	2.81929i	−0.0609585	+	0.105583i
$714$		0			0
$715$	6.00000	+	10.3923i	0.224387	+	0.388650i
$716$	3.25544			0.121661
$717$	−4.93070	+	16.3533i	−0.184140	+	0.610725i
$718$	−21.8614			−0.815860
$719$	1.37228	−	2.37686i	0.0511775	−	0.0886420i	−0.839302	−	0.543666i	$-0.817036\pi$
$719$	1.37228	−	2.37686i	0.0511775	−	0.0886420i	0.890479	+	0.455024i	$0.150369\pi$
$720$	−11.7446	+	5.84096i	−0.437694	+	0.217680i
$721$		0			0
$722$	3.00000	−	5.19615i	0.111648	−	0.193381i
$723$	21.4891	+	22.8665i	0.799189	+	0.850415i
$724$	0.441578	−	0.764836i	0.0164111	−	0.0284249i
$725$	61.7228	−	106.907i	2.29233	−	3.97043i
$726$	−4.55842	+	15.1186i	−0.169179	+	0.561103i
$727$	−18.1168	+	31.3793i	−0.671917	+	1.16379i	0.305443	+	0.952210i	$0.401195\pi$
$727$	−18.1168	+	31.3793i	−0.671917	+	1.16379i	−0.977360	+	0.211583i	$0.932138\pi$
$728$		0			0
$729$	5.00000	−	26.5330i	0.185185	−	0.982704i
$730$	26.4891	−	45.8805i	0.980407	−	1.69811i
$731$	11.1386			0.411976
$732$	3.69702	+	3.93398i	0.136646	+	0.145404i
$733$	41.1168			1.51869			0.759343	−	0.650691i	$-0.225521\pi$
$733$	41.1168			1.51869			0.759343	+	0.650691i	$0.225521\pi$
$734$	6.11684	+	10.5947i	0.225777	+	0.391057i
$735$		0			0
$736$	−0.813859	+	1.40965i	−0.0299993	+	0.0519602i
$737$	−1.45245	+	2.51572i	−0.0535018	+	0.0926678i
$738$	−11.5693	−	7.67420i	−0.425872	−	0.282491i
$739$	4.05842	+	7.02939i	0.149291	+	0.258580i	0.930966	−	0.365106i	$-0.118967\pi$
$739$	4.05842	+	7.02939i	0.149291	+	0.258580i	−0.781674	+	0.623687i	$0.785634\pi$
$740$	4.37228	+	7.57301i	0.160728	+	0.278390i
$741$	−11.8614	−	12.6217i	−0.435740	−	0.463669i
$742$		0			0
$743$	6.86141	+	11.8843i	0.251721	+	0.435993i	0.964000	−	0.265904i	$-0.0856703\pi$
$743$	6.86141	+	11.8843i	0.251721	+	0.435993i	−0.712279	+	0.701896i	$0.752337\pi$
$744$	3.37228	−	0.792287i	0.123634	−	0.0290467i
$745$	−14.2337			−0.521482
$746$	−5.00000	−	8.66025i	−0.183063	−	0.317074i
$747$	43.7228	+	29.0024i	1.59973	+	1.06114i
$748$	1.88316			0.0688550
$749$		0			0
$750$	−19.9307	+	66.1027i	−0.727766	+	2.41373i
$751$	−17.1168			−0.624603			−0.312301	−	0.949983i	$-0.601100\pi$
$751$	−17.1168			−0.624603			−0.312301	+	0.949983i	$0.601100\pi$
$752$		0			0
$753$	−10.6753	−	11.3595i	−0.389028	−	0.413964i
$754$	8.74456	+	15.1460i	0.318458	+	0.551586i
$755$	−39.8614			−1.45071
$756$		0			0
$757$	46.2337			1.68039			0.840196	−	0.542283i	$-0.182440\pi$
$757$	46.2337			1.68039			0.840196	+	0.542283i	$0.182440\pi$
$758$	−4.05842	−	7.02939i	−0.147409	−	0.255319i
$759$	−2.64947	−	2.81929i	−0.0961696	−	0.102334i
$760$	10.9307	−	18.9325i	0.396498	−	0.686755i
$761$	−35.4891			−1.28648			−0.643240	−	0.765665i	$-0.722410\pi$
$761$	−35.4891			−1.28648			−0.643240	+	0.765665i	$0.722410\pi$
$762$	1.55842	−	5.16870i	0.0564557	−	0.187242i
$763$		0			0
$764$	−19.1168			−0.691623
$765$	16.1168	−	8.01544i	0.582706	−	0.289799i
$766$	16.3723	+	28.3576i	0.591555	+	1.02460i
$767$	−20.2337			−0.730596
$768$	1.68614	−	0.396143i	0.0608434	−	0.0142946i
$769$	−5.00000	−	8.66025i	−0.180305	−	0.312297i	0.761680	−	0.647954i	$-0.224375\pi$
$769$	−5.00000	−	8.66025i	−0.180305	−	0.312297i	−0.941984	+	0.335657i	$0.891042\pi$
$770$		0			0
$771$	−8.13859	−	8.66025i	−0.293104	−	0.311891i
$772$	3.50000	+	6.06218i	0.125968	+	0.218183i
$773$	−19.9307	−	34.5210i	−0.716858	−	1.24163i	−0.962239	−	0.272207i	$-0.912246\pi$
$773$	−19.9307	−	34.5210i	−0.716858	−	1.24163i	0.245381	−	0.969427i	$-0.421087\pi$
$774$	−1.51087	+	24.3036i	−0.0543073	+	0.873575i
$775$	14.1168	−	24.4511i	0.507092	−	0.878309i
$776$	4.05842	−	7.02939i	0.145689	−	0.252341i
$777$		0			0
$778$	5.48913	+	9.50744i	0.196795	+	0.340858i
$779$	23.1386			0.829026
$780$	−10.3723	−	11.0371i	−0.371387	−	0.395192i
$781$	9.76631			0.349466
$782$	1.11684	−	1.93443i	0.0399383	−	0.0691751i
$783$	−7.62772	−	44.7933i	−0.272592	−	1.60078i
$784$		0			0
$785$	−19.9307	+	34.5210i	−0.711357	+	1.23211i
$786$	0.813859	−	2.69927i	0.0290294	−	0.0962796i
$787$	−2.00000	+	3.46410i	−0.0712923	+	0.123482i	−0.899468	−	0.436987i	$-0.856046\pi$
$787$	−2.00000	+	3.46410i	−0.0712923	+	0.123482i	0.828176	+	0.560469i	$0.189379\pi$
$788$	3.00000	−	5.19615i	0.106871	−	0.185105i
$789$	−9.04755	−	9.62747i	−0.322101	−	0.342747i
$790$	11.1861	−	19.3750i	0.397985	−	0.689330i
$791$		0			0
$792$	−0.255437	+	4.10891i	−0.00907657	+	0.146004i
$793$	−3.11684	+	5.39853i	−0.110682	+	0.191707i
$794$	−22.0000			−0.780751
$795$	−19.1168	+	63.4034i	−0.678005	+	2.24869i
$796$	10.0000			0.354441
$797$	−4.06930	−	7.04823i	−0.144142	−	0.249661i	0.784911	−	0.619609i	$-0.212709\pi$
$797$	−4.06930	−	7.04823i	−0.144142	−	0.249661i	−0.929052	+	0.369948i	$0.879376\pi$
$798$		0			0
$799$		0			0
$800$	7.05842	−	12.2255i	0.249553	−	0.432238i
$801$	36.8614	+	24.4511i	1.30243	+	0.863937i
$802$	−5.87228	−	10.1711i	−0.207357	−	0.359154i
$803$	−8.31386	−	14.4000i	−0.293390	−	0.508166i
$804$	1.05842	−	3.51039i	0.0373277	−	0.123802i
$805$		0			0
$806$	2.00000	+	3.46410i	0.0704470	+	0.122018i
$807$	−0.813859	+	2.69927i	−0.0286492	+	0.0950187i
$808$	1.62772			0.0572629
$809$	3.43070	+	5.94215i	0.120617	+	0.208915i	0.920011	−	0.391892i	$-0.128179\pi$
$809$	3.43070	+	5.94215i	0.120617	+	0.208915i	−0.799394	+	0.600807i	$0.794846\pi$
$810$	15.3030	+	36.2530i	0.537692	+	1.27380i
$811$	−42.1168			−1.47892			−0.739461	−	0.673199i	$-0.764920\pi$
$811$	−42.1168			−1.47892			−0.739461	+	0.673199i	$0.764920\pi$
$812$		0			0
$813$	−27.3723	+	6.43087i	−0.959988	+	0.225540i
$814$	2.74456			0.0961969
$815$	−39.8614	+	69.0420i	−1.39628	+	2.41844i
$816$	−2.31386	+	0.543620i	−0.0810013	+	0.0190305i
$817$	−20.2921	−	35.1470i	−0.709931	−	1.22964i
$818$	−22.3505			−0.781468
$819$		0			0
$820$	20.2337			0.706591
$821$	1.88316	+	3.26172i	0.0657226	+	0.113835i	0.897014	−	0.442002i	$-0.145731\pi$
$821$	1.88316	+	3.26172i	0.0657226	+	0.113835i	−0.831292	+	0.555836i	$0.812398\pi$
$822$	5.31386	−	17.6241i	0.185342	−	0.614710i
$823$	6.11684	−	10.5947i	0.213220	−	0.369307i	−0.739501	−	0.673156i	$-0.764938\pi$
$823$	6.11684	−	10.5947i	0.213220	−	0.369307i	0.952720	+	0.303848i	$0.0982716\pi$
$824$	−10.0000			−0.348367
$825$	22.9783	+	24.4511i	0.800000	+	0.851278i
$826$		0			0
$827$	12.0000			0.417281			0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000			0.417281			0.208640	+	0.977992i	$0.433096\pi$
$828$	4.06930	+	2.69927i	0.141418	+	0.0938060i
$829$	−6.88316	−	11.9220i	−0.239062	−	0.414067i	0.721383	−	0.692536i	$-0.243507\pi$
$829$	−6.88316	−	11.9220i	−0.239062	−	0.414067i	−0.960445	+	0.278468i	$0.910173\pi$
$830$	−76.4674			−2.65422
$831$	14.5109	+	15.4410i	0.503377	+	0.535642i
$832$	1.00000	+	1.73205i	0.0346688	+	0.0600481i
$833$		0			0
$834$	22.3139	−	5.24244i	0.772666	−	0.181531i
$835$	12.0000	+	20.7846i	0.415277	+	0.719281i
$836$	−3.43070	−	5.94215i	−0.118653	−	0.205514i
$837$	−1.74456	−	10.2448i	−0.0603009	−	0.354113i
$838$	6.30298	−	10.9171i	0.217733	−	0.377125i
$839$	2.74456	−	4.75372i	0.0947528	−	0.164117i	−0.814753	−	0.579809i	$-0.803127\pi$
$839$	2.74456	−	4.75372i	0.0947528	−	0.164117i	0.909505	+	0.415692i	$0.136461\pi$
$840$		0			0
$841$	−23.7337	−	41.1080i	−0.818403	−	1.41752i
$842$	−34.2337			−1.17977
$843$	27.6060	−	6.48577i	0.950800	−	0.223382i
$844$	−16.0000			−0.550743
$845$	−19.6753	+	34.0786i	−0.676850	+	1.17234i
$846$		0			0
$847$		0			0
$848$	4.37228	−	7.57301i	0.150145	−	0.260058i
$849$	−45.7228	+	10.7422i	−1.56920	+	0.368670i
$850$	−9.68614	+	16.7769i	−0.332232	+	0.575443i
$851$	1.62772	−	2.81929i	0.0557975	−	0.0966441i
$852$	−12.0000	+	2.81929i	−0.411113	+	0.0965873i
$853$	−17.5584	+	30.4121i	−0.601189	+	1.04129i	0.391452	+	0.920198i	$0.371973\pi$
$853$	−17.5584	+	30.4121i	−0.601189	+	1.04129i	−0.992641	+	0.121091i	$0.961361\pi$
$854$		0			0
$855$	−54.6535	−	36.2530i	−1.86911	−	1.23983i
$856$	−3.68614	+	6.38458i	−0.125990	+	0.218221i
$857$	39.9565			1.36489			0.682444	−	0.730938i	$-0.260917\pi$
$857$	39.9565			1.36489			0.682444	+	0.730938i	$0.260917\pi$
$858$	−4.62772	+	1.08724i	−0.157988	+	0.0371178i
$859$	−33.8832			−1.15608			−0.578039	−	0.816009i	$-0.696182\pi$
$859$	−33.8832			−1.15608			−0.578039	+	0.816009i	$0.696182\pi$
$860$	−17.7446	−	30.7345i	−0.605085	−	1.04804i
$861$		0			0
$862$	−3.25544	+	5.63858i	−0.110881	+	0.192051i
$863$	−4.93070	+	8.54023i	−0.167843	+	0.290713i	−0.937661	−	0.347550i	$-0.887014\pi$
$863$	−4.93070	+	8.54023i	−0.167843	+	0.290713i	0.769818	+	0.638263i	$0.220347\pi$
$864$	−0.872281	−	5.12241i	−0.0296756	−	0.174268i
$865$	13.1168	+	22.7190i	0.445986	+	0.772471i
$866$	10.0584	+	17.4217i	0.341799	+	0.592013i
$867$	−25.4891	+	5.98844i	−0.865656	+	0.203378i
$868$		0			0
$869$	−3.51087	−	6.08101i	−0.119098	−	0.206284i
$870$	45.3505	+	48.2574i	1.53753	+	1.63608i
$871$	4.23369			0.143453
$872$	7.00000	+	12.1244i	0.237050	+	0.410582i
$873$	−20.2921	−	13.4603i	−0.686784	−	0.455561i
$874$	−8.13859			−0.275292
$875$		0			0
$876$	14.3723	+	15.2935i	0.485594	+	0.516720i
$877$	−58.7011			−1.98219			−0.991097	−	0.133141i	$-0.957494\pi$
$877$	−58.7011			−1.98219			−0.991097	+	0.133141i	$0.957494\pi$
$878$	−4.00000	+	6.92820i	−0.134993	+	0.233816i
$879$	−5.18614	+	17.2005i	−0.174924	+	0.580158i
$880$	−3.00000	−	5.19615i	−0.101130	−	0.175162i
$881$	20.2337			0.681690			0.340845	−	0.940119i	$-0.389287\pi$
$881$	20.2337			0.681690			0.340845	+	0.940119i	$0.389287\pi$
$882$		0			0
$883$	−40.3505			−1.35790			−0.678952	−	0.734183i	$-0.737565\pi$
$883$	−40.3505			−1.35790			−0.678952	+	0.734183i	$0.737565\pi$
$884$	−1.37228	−	2.37686i	−0.0461548	−	0.0799425i
$885$	−74.5842	+	17.5229i	−2.50712	+	0.589025i
$886$	−20.0584	+	34.7422i	−0.673876	+	1.16719i
$887$	−25.7228			−0.863688			−0.431844	−	0.901948i	$-0.642137\pi$
$887$	−25.7228			−0.863688			−0.431844	+	0.901948i	$0.642137\pi$
$888$	−3.37228	+	0.792287i	−0.113166	+	0.0265874i
$889$		0			0
$890$	−64.4674			−2.16095
$891$	12.2554	+	1.52967i	0.410573	+	0.0512459i
$892$	−2.00000	−	3.46410i	−0.0669650	−	0.115987i
$893$		0			0
$894$	1.62772	−	5.39853i	0.0544391	−	0.180554i
$895$	7.11684	+	12.3267i	0.237890	+	0.412037i
$896$		0			0
$897$	−1.62772	+	5.39853i	−0.0543479	+	0.180252i
$898$	16.5000	+	28.5788i	0.550612	+	0.953688i
$899$	−8.74456	−	15.1460i	−0.291647	−	0.505148i
$900$	−35.2921	−	23.4101i	−1.17640	−	0.780338i
$901$	−6.00000	+	10.3923i	−0.199889	+	0.346218i
$902$	3.17527	−	5.49972i	0.105725	−	0.183121i
$903$		0			0
$904$	−2.18614	−	3.78651i	−0.0727100	−	0.125937i
$905$	3.86141			0.128357
$906$	4.55842	−	15.1186i	0.151443	−	0.502281i
$907$	−26.1168			−0.867196			−0.433598	−	0.901107i	$-0.642756\pi$
$907$	−26.1168			−0.867196			−0.433598	+	0.901107i	$0.642756\pi$
$908$	−6.12772	+	10.6135i	−0.203355	+	0.352222i
$909$	0.302985	−	4.87375i	0.0100494	−	0.161652i
$910$		0			0
$911$	18.8139	−	32.5866i	0.623331	−	1.07964i	−0.365530	−	0.930800i	$-0.619112\pi$
$911$	18.8139	−	32.5866i	0.623331	−	1.07964i	0.988861	−	0.148841i	$-0.0475544\pi$
$912$	5.93070	+	6.31084i	0.196385	+	0.208973i
$913$	−12.0000	+	20.7846i	−0.397142	+	0.687870i
$914$	−17.7337	+	30.7156i	−0.586578	+	1.01598i
$915$	−6.81386	+	22.5990i	−0.225259	+	0.747100i
$916$	−1.44158	+	2.49689i	−0.0476311	+	0.0824994i
$917$		0			0
$918$	1.19702	+	7.02939i	0.0395074	+	0.232005i
$919$	23.5584	−	40.8044i	0.777121	−	1.34601i	−0.156474	−	0.987682i	$-0.550013\pi$
$919$	23.5584	−	40.8044i	0.777121	−	1.34601i	0.933595	−	0.358330i	$-0.116654\pi$
$920$	−7.11684			−0.234635
$921$	−15.4198	−	16.4082i	−0.508101	−	0.540668i
$922$	2.13859			0.0704308
$923$	−7.11684	−	12.3267i	−0.234254	−	0.405739i
$924$		0			0
$925$	−14.1168	+	24.4511i	−0.464159	+	0.803947i
$926$	−11.5584	+	20.0198i	−0.379833	+	0.657891i
$927$	−1.86141	+	29.9422i	−0.0611366	+	0.983431i
$928$	−4.37228	−	7.57301i	−0.143527	−	0.248596i
$929$	22.1168	+	38.3075i	0.725630	+	1.25683i	0.958714	+	0.284372i	$0.0917850\pi$
$929$	22.1168	+	38.3075i	0.725630	+	1.25683i	−0.233084	+	0.972457i	$0.574882\pi$
$930$	10.3723	+	11.0371i	0.340121	+	0.361921i
$931$		0			0
$932$	0.127719	+	0.221215i	0.00418356	+	0.00724615i
$933$	−13.8832	+	3.26172i	−0.454514	+	0.106784i
$934$	33.0951			1.08290
$935$	4.11684	+	7.13058i	0.134635	+	0.233195i
$936$	5.37228	−	2.67181i	0.175599	−	0.0873310i
$937$	−30.4674			−0.995326			−0.497663	−	0.867371i	$-0.665808\pi$
$937$	−30.4674			−0.995326			−0.497663	+	0.867371i	$0.665808\pi$
$938$		0			0
$939$	−10.0584	+	33.3600i	−0.328244	+	1.08866i
$940$		0			0
$941$	9.55842	−	16.5557i	0.311596	−	0.539699i	−0.667112	−	0.744957i	$-0.732470\pi$
$941$	9.55842	−	16.5557i	0.311596	−	0.539699i	0.978708	+	0.205258i	$0.0658032\pi$
$942$	−10.8139	−	11.5070i	−0.352335	−	0.374918i
$943$	−3.76631	−	6.52344i	−0.122648	−	0.212433i
$944$	10.1168			0.329275
$945$		0			0
$946$	−11.1386			−0.362147
$947$	−17.0584	−	29.5461i	−0.554324	−	0.960118i	−0.997956	−	0.0639085i	$-0.979643\pi$
$947$	−17.0584	−	29.5461i	−0.554324	−	0.960118i	0.443632	−	0.896209i	$-0.353690\pi$
$948$	6.06930	+	6.45832i	0.197122	+	0.209757i
$949$	−12.1168	+	20.9870i	−0.393329	+	0.681267i
$950$	70.5842			2.29005
$951$	3.00000	−	9.94987i	0.0972817	−	0.322647i
$952$		0			0
$953$	28.1168			0.910794			0.455397	−	0.890288i	$-0.349497\pi$
$953$	28.1168			0.910794			0.455397	+	0.890288i	$0.349497\pi$
$954$	−21.8614	−	14.5012i	−0.707789	−	0.469494i
$955$	−41.7921	−	72.3861i	−1.35236	−	2.34236i
$956$	9.86141			0.318941
$957$	20.2337	−	4.75372i	0.654062	−	0.153666i
$958$	−16.3723	−	28.3576i	−0.528964	−	0.916193i
$959$		0			0
$960$	5.18614	+	5.51856i	0.167382	+	0.178111i
$961$	13.5000	+	23.3827i	0.435484	+	0.754280i
$962$	−2.00000	−	3.46410i	−0.0644826	−	0.111687i
$963$	18.4307	+	12.2255i	0.593921	+	0.393963i
$964$	9.05842	−	15.6896i	0.291752	−	0.505330i
$965$	−15.3030	+	26.5055i	−0.492621	+	0.853244i
$966$		0			0
$967$	−15.4416	−	26.7456i	−0.496568	−	0.860080i	0.503424	−	0.864039i	$-0.332073\pi$
$967$	−15.4416	−	26.7456i	−0.496568	−	0.860080i	−0.999992	+	0.00395879i	$0.998740\pi$
$968$	9.11684			0.293026
$969$	−8.13859	−	8.66025i	−0.261449	−	0.278207i
$970$	35.4891			1.13949
$971$	0.813859	−	1.40965i	0.0261180	−	0.0452377i	−0.852671	−	0.522448i	$-0.825019\pi$
$971$	0.813859	−	1.40965i	0.0261180	−	0.0452377i	0.878789	+	0.477211i	$0.158352\pi$
$972$	−15.5000	+	1.65831i	−0.497163	+	0.0531904i
$973$		0			0
$974$	17.6753	−	30.6145i	0.566352	−	0.980951i
$975$	14.1168	−	46.8203i	0.452101	−	1.49945i
$976$	1.55842	−	2.69927i	0.0498839	−	0.0864014i
$977$	−20.0584	+	34.7422i	−0.641726	+	1.11150i	0.343322	+	0.939218i	$0.388448\pi$
$977$	−20.0584	+	34.7422i	−0.641726	+	1.11150i	−0.985047	+	0.172284i	$0.944885\pi$
$978$	−21.6277	−	23.0140i	−0.691578	−	0.735906i
$979$	−10.1168	+	17.5229i	−0.323336	+	0.560034i
$980$		0			0
$981$	37.6060	−	18.7027i	1.20067	−	0.597131i
$982$	−12.6861	+	21.9730i	−0.404831	+	0.701188i
$983$	39.2554			1.25205			0.626027	−	0.779801i	$-0.284680\pi$
$983$	39.2554			1.25205			0.626027	+	0.779801i	$0.284680\pi$
$984$	−2.31386	+	7.67420i	−0.0737631	+	0.244645i
$985$	26.2337			0.835875
$986$	6.00000	+	10.3923i	0.191079	+	0.330958i
$987$		0			0
$988$	−5.00000	+	8.66025i	−0.159071	+	0.275519i
$989$	−6.60597	+	11.4419i	−0.210058	+	0.363830i
$990$	−16.1168	+	8.01544i	−0.512227	+	0.254748i
$991$	−24.2337	−	41.9740i	−0.769808	−	1.33335i	−0.937667	−	0.347536i	$-0.887018\pi$
$991$	−24.2337	−	41.9740i	−0.769808	−	1.33335i	0.167858	−	0.985811i	$-0.446315\pi$
$992$	−1.00000	−	1.73205i	−0.0317500	−	0.0549927i
$993$	−11.1168	+	36.8704i	−0.352782	+	1.17005i
$994$		0			0
$995$	21.8614	+	37.8651i	0.693053	+	1.20040i
$996$	8.74456	−	29.0024i	0.277082	−	0.918977i
$997$	5.11684			0.162052			0.0810260	−	0.996712i	$-0.474180\pi$
$997$	5.11684			0.162052			0.0810260	+	0.996712i	$0.474180\pi$
$998$	9.05842	+	15.6896i	0.286739	+	0.496647i
$999$	1.74456	+	10.2448i	0.0551955	+	0.324132i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.h.n.79.1		4
3.2	odd	2		2646.2.h.l.667.2		4
7.2	even	3		882.2.f.k.295.2		4
7.3	odd	6		882.2.e.l.655.1		4
7.4	even	3		882.2.e.k.655.2		4
7.5	odd	6		126.2.f.d.43.1	✓	4
7.6	odd	2		882.2.h.m.79.2		4
9.4	even	3		882.2.e.k.373.1		4
9.5	odd	6		2646.2.e.m.1549.1		4
21.2	odd	6		2646.2.f.j.883.1		4
21.5	even	6		378.2.f.c.127.2		4
21.11	odd	6		2646.2.e.m.2125.1		4
21.17	even	6		2646.2.e.n.2125.2		4
21.20	even	2		2646.2.h.k.667.1		4
28.19	even	6		1008.2.r.f.673.2		4
63.2	odd	6		7938.2.a.bs.1.2		2
63.4	even	3	inner	882.2.h.n.67.1		4
63.5	even	6		378.2.f.c.253.2		4
63.13	odd	6		882.2.e.l.373.2		4
63.16	even	3		7938.2.a.bh.1.1		2
63.23	odd	6		2646.2.f.j.1765.1		4
63.31	odd	6		882.2.h.m.67.2		4
63.32	odd	6		2646.2.h.l.361.2		4
63.40	odd	6		126.2.f.d.85.1	yes	4
63.41	even	6		2646.2.e.n.1549.2		4
63.47	even	6		1134.2.a.n.1.1		2
63.58	even	3		882.2.f.k.589.2		4
63.59	even	6		2646.2.h.k.361.1		4
63.61	odd	6		1134.2.a.k.1.2		2
84.47	odd	6		3024.2.r.f.2017.2		4
252.47	odd	6		9072.2.a.bb.1.1		2
252.103	even	6		1008.2.r.f.337.2		4
252.131	odd	6		3024.2.r.f.1009.2		4
252.187	even	6		9072.2.a.bm.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.f.d.43.1	✓	4	7.5	odd	6
126.2.f.d.85.1	yes	4	63.40	odd	6
378.2.f.c.127.2		4	21.5	even	6
378.2.f.c.253.2		4	63.5	even	6
882.2.e.k.373.1		4	9.4	even	3
882.2.e.k.655.2		4	7.4	even	3
882.2.e.l.373.2		4	63.13	odd	6
882.2.e.l.655.1		4	7.3	odd	6
882.2.f.k.295.2		4	7.2	even	3
882.2.f.k.589.2		4	63.58	even	3
882.2.h.m.67.2		4	63.31	odd	6
882.2.h.m.79.2		4	7.6	odd	2
882.2.h.n.67.1		4	63.4	even	3	inner
882.2.h.n.79.1		4	1.1	even	1	trivial
1008.2.r.f.337.2		4	252.103	even	6
1008.2.r.f.673.2		4	28.19	even	6
1134.2.a.k.1.2		2	63.61	odd	6
1134.2.a.n.1.1		2	63.47	even	6
2646.2.e.m.1549.1		4	9.5	odd	6
2646.2.e.m.2125.1		4	21.11	odd	6
2646.2.e.n.1549.2		4	63.41	even	6
2646.2.e.n.2125.2		4	21.17	even	6
2646.2.f.j.883.1		4	21.2	odd	6
2646.2.f.j.1765.1		4	63.23	odd	6
2646.2.h.k.361.1		4	63.59	even	6
2646.2.h.k.667.1		4	21.20	even	2
2646.2.h.l.361.2		4	63.32	odd	6
2646.2.h.l.667.2		4	3.2	odd	2
3024.2.r.f.1009.2		4	252.131	odd	6
3024.2.r.f.2017.2		4	84.47	odd	6
7938.2.a.bh.1.1		2	63.16	even	3
7938.2.a.bs.1.2		2	63.2	odd	6
9072.2.a.bb.1.1		2	252.47	odd	6
9072.2.a.bm.1.2		2	252.187	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.18614 - 1.26217i) q^{3} +(-0.500000 + 0.866025i) q^{4} -4.37228 q^{5} +(0.500000 - 1.65831i) q^{6} -1.00000 q^{8} +(-0.186141 + 2.99422i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.18614 - 1.26217i) q^{3} +(-0.500000 + 0.866025i) q^{4} -4.37228 q^{5} +(0.500000 - 1.65831i) q^{6} -1.00000 q^{8} +(-0.186141 + 2.99422i) q^{9} +(-2.18614 - 3.78651i) q^{10} -1.37228 q^{11} +(1.68614 - 0.396143i) q^{12} +(1.00000 + 1.73205i) q^{13} +(5.18614 + 5.51856i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.686141 + 1.18843i) q^{17} +(-2.68614 + 1.33591i) q^{18} +(2.50000 - 4.33013i) q^{19} +(2.18614 - 3.78651i) q^{20} +(-0.686141 - 1.18843i) q^{22} -1.62772 q^{23} +(1.18614 + 1.26217i) q^{24} +14.1168 q^{25} +(-1.00000 + 1.73205i) q^{26} +(4.00000 - 3.31662i) q^{27} +(4.37228 - 7.57301i) q^{29} +(-2.18614 + 7.25061i) q^{30} +(1.00000 - 1.73205i) q^{31} +(0.500000 - 0.866025i) q^{32} +(1.62772 + 1.73205i) q^{33} +(-0.686141 + 1.18843i) q^{34} +(-2.50000 - 1.65831i) q^{36} +(-1.00000 + 1.73205i) q^{37} +5.00000 q^{38} +(1.00000 - 3.31662i) q^{39} +4.37228 q^{40} +(2.31386 + 4.00772i) q^{41} +(4.05842 - 7.02939i) q^{43} +(0.686141 - 1.18843i) q^{44} +(0.813859 - 13.0916i) q^{45} +(-0.813859 - 1.40965i) q^{46} +(-0.500000 + 1.65831i) q^{48} +(7.05842 + 12.2255i) q^{50} +(0.686141 - 2.27567i) q^{51} -2.00000 q^{52} +(4.37228 + 7.57301i) q^{53} +(4.87228 + 1.80579i) q^{54} +6.00000 q^{55} +(-8.43070 + 1.98072i) q^{57} +8.74456 q^{58} +(-5.05842 + 8.76144i) q^{59} +(-7.37228 + 1.73205i) q^{60} +(1.55842 + 2.69927i) q^{61} +2.00000 q^{62} +1.00000 q^{64} +(-4.37228 - 7.57301i) q^{65} +(-0.686141 + 2.27567i) q^{66} +(1.05842 - 1.83324i) q^{67} -1.37228 q^{68} +(1.93070 + 2.05446i) q^{69} -7.11684 q^{71} +(0.186141 - 2.99422i) q^{72} +(6.05842 + 10.4935i) q^{73} -2.00000 q^{74} +(-16.7446 - 17.8178i) q^{75} +(2.50000 + 4.33013i) q^{76} +(3.37228 - 0.792287i) q^{78} +(2.55842 + 4.43132i) q^{79} +(2.18614 + 3.78651i) q^{80} +(-8.93070 - 1.11469i) q^{81} +(-2.31386 + 4.00772i) q^{82} +(8.74456 - 15.1460i) q^{83} +(-3.00000 - 5.19615i) q^{85} +8.11684 q^{86} +(-14.7446 + 3.46410i) q^{87} +1.37228 q^{88} +(7.37228 - 12.7692i) q^{89} +(11.7446 - 5.84096i) q^{90} +(0.813859 - 1.40965i) q^{92} +(-3.37228 + 0.792287i) q^{93} +(-10.9307 + 18.9325i) q^{95} +(-1.68614 + 0.396143i) q^{96} +(-4.05842 + 7.02939i) q^{97} +(0.255437 - 4.10891i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} - 4 q^{8} + 5 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 + q^3 - 2 * q^4 - 6 * q^5 + 2 * q^6 - 4 * q^8 + 5 * q^9	\( 4 q + 2 q^{2} + q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} - 4 q^{8} + 5 q^{9} - 3 q^{10} + 6 q^{11} + q^{12} + 4 q^{13} + 15 q^{15} - 2 q^{16} - 3 q^{17} - 5 q^{18} + 10 q^{19} + 3 q^{20} + 3 q^{22} - 18 q^{23} - q^{24} + 22 q^{25} - 4 q^{26} + 16 q^{27} + 6 q^{29} - 3 q^{30} + 4 q^{31} + 2 q^{32} + 18 q^{33} + 3 q^{34} - 10 q^{36} - 4 q^{37} + 20 q^{38} + 4 q^{39} + 6 q^{40} + 15 q^{41} - q^{43} - 3 q^{44} + 9 q^{45} - 9 q^{46} - 2 q^{48} + 11 q^{50} - 3 q^{51} - 8 q^{52} + 6 q^{53} + 8 q^{54} + 24 q^{55} - 5 q^{57} + 12 q^{58} - 3 q^{59} - 18 q^{60} - 11 q^{61} + 8 q^{62} + 4 q^{64} - 6 q^{65} + 3 q^{66} - 13 q^{67} + 6 q^{68} - 21 q^{69} + 6 q^{71} - 5 q^{72} + 7 q^{73} - 8 q^{74} - 44 q^{75} + 10 q^{76} + 2 q^{78} - 7 q^{79} + 3 q^{80} - 7 q^{81} - 15 q^{82} + 12 q^{83} - 12 q^{85} - 2 q^{86} - 36 q^{87} - 6 q^{88} + 18 q^{89} + 24 q^{90} + 9 q^{92} - 2 q^{93} - 15 q^{95} - q^{96} + q^{97} + 24 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + q^3 - 2 * q^4 - 6 * q^5 + 2 * q^6 - 4 * q^8 + 5 * q^9 - 3 * q^10 + 6 * q^11 + q^12 + 4 * q^13 + 15 * q^15 - 2 * q^16 - 3 * q^17 - 5 * q^18 + 10 * q^19 + 3 * q^20 + 3 * q^22 - 18 * q^23 - q^24 + 22 * q^25 - 4 * q^26 + 16 * q^27 + 6 * q^29 - 3 * q^30 + 4 * q^31 + 2 * q^32 + 18 * q^33 + 3 * q^34 - 10 * q^36 - 4 * q^37 + 20 * q^38 + 4 * q^39 + 6 * q^40 + 15 * q^41 - q^43 - 3 * q^44 + 9 * q^45 - 9 * q^46 - 2 * q^48 + 11 * q^50 - 3 * q^51 - 8 * q^52 + 6 * q^53 + 8 * q^54 + 24 * q^55 - 5 * q^57 + 12 * q^58 - 3 * q^59 - 18 * q^60 - 11 * q^61 + 8 * q^62 + 4 * q^64 - 6 * q^65 + 3 * q^66 - 13 * q^67 + 6 * q^68 - 21 * q^69 + 6 * q^71 - 5 * q^72 + 7 * q^73 - 8 * q^74 - 44 * q^75 + 10 * q^76 + 2 * q^78 - 7 * q^79 + 3 * q^80 - 7 * q^81 - 15 * q^82 + 12 * q^83 - 12 * q^85 - 2 * q^86 - 36 * q^87 - 6 * q^88 + 18 * q^89 + 24 * q^90 + 9 * q^92 - 2 * q^93 - 15 * q^95 - q^96 + q^97 + 24 * q^99

Introduction

L-functions

Modular forms

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Database

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