LMFDB - Embedded newform 1710.2.l.j.1261.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1710,2,Mod(1261,1710)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1710, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1710.1261");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1710.l (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:	$13.6544187456$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 7x^{2} + 49 $ x^4 + 7*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 570)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1261.1
Root			$1.32288 + 2.29129i$ of defining polynomial
Character	$\chi$	$=$	1710.1261
Dual form			1710.2.l.j.1531.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -2.64575 q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -2.64575 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{10} +6.29150 q^{11} +(1.32288 + 2.29129i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.82288 - 4.88936i) q^{17} +(-1.67712 + 4.02334i) q^{19} +1.00000 q^{20} +(-3.14575 - 5.44860i) q^{22} +(0.500000 - 0.866025i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(1.32288 - 2.29129i) q^{28} +(-1.82288 + 3.15731i) q^{29} +7.29150 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.82288 + 4.88936i) q^{34} +(1.32288 + 2.29129i) q^{35} +8.29150 q^{37} +(4.32288 - 0.559237i) q^{38} +(-0.500000 - 0.866025i) q^{40} +(-4.32288 - 7.48744i) q^{41} +(-3.00000 - 5.19615i) q^{43} +(-3.14575 + 5.44860i) q^{44} -1.00000 q^{46} +(6.29150 - 10.8972i) q^{47} +1.00000 q^{50} +(-2.32288 + 4.02334i) q^{53} +(-3.14575 - 5.44860i) q^{55} -2.64575 q^{56} +3.64575 q^{58} +(2.64575 + 4.58258i) q^{59} +(-3.46863 + 6.00784i) q^{61} +(-3.64575 - 6.31463i) q^{62} +1.00000 q^{64} +(4.82288 - 8.35347i) q^{67} +5.64575 q^{68} +(1.32288 - 2.29129i) q^{70} +(-6.82288 - 11.8176i) q^{71} +(-6.82288 - 11.8176i) q^{73} +(-4.14575 - 7.18065i) q^{74} +(-2.64575 - 3.46410i) q^{76} -16.6458 q^{77} +(-2.64575 - 4.58258i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-4.32288 + 7.48744i) q^{82} -16.5830 q^{83} +(-2.82288 + 4.88936i) q^{85} +(-3.00000 + 5.19615i) q^{86} +6.29150 q^{88} +(6.61438 - 11.4564i) q^{89} +(0.500000 + 0.866025i) q^{92} -12.5830 q^{94} +(4.32288 - 0.559237i) q^{95} +(0.822876 + 1.42526i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{4} - 2 q^{5} + 4 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 + 4 * q^8	$ 4 q - 2 q^{2} - 2 q^{4} - 2 q^{5} + 4 q^{8} - 2 q^{10} + 4 q^{11} - 2 q^{16} - 6 q^{17} - 12 q^{19} + 4 q^{20} - 2 q^{22} + 2 q^{23} - 2 q^{25} - 2 q^{29} + 8 q^{31} - 2 q^{32} - 6 q^{34} + 12 q^{37} + 12 q^{38} - 2 q^{40} - 12 q^{41} - 12 q^{43} - 2 q^{44} - 4 q^{46} + 4 q^{47} + 4 q^{50} - 4 q^{53} - 2 q^{55} + 4 q^{58} + 2 q^{61} - 4 q^{62} + 4 q^{64} + 14 q^{67} + 12 q^{68} - 22 q^{71} - 22 q^{73} - 6 q^{74} - 56 q^{77} - 2 q^{80} - 12 q^{82} - 24 q^{83} - 6 q^{85} - 12 q^{86} + 4 q^{88} + 2 q^{92} - 8 q^{94} + 12 q^{95} - 2 q^{97}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 + 4 * q^8 - 2 * q^10 + 4 * q^11 - 2 * q^16 - 6 * q^17 - 12 * q^19 + 4 * q^20 - 2 * q^22 + 2 * q^23 - 2 * q^25 - 2 * q^29 + 8 * q^31 - 2 * q^32 - 6 * q^34 + 12 * q^37 + 12 * q^38 - 2 * q^40 - 12 * q^41 - 12 * q^43 - 2 * q^44 - 4 * q^46 + 4 * q^47 + 4 * q^50 - 4 * q^53 - 2 * q^55 + 4 * q^58 + 2 * q^61 - 4 * q^62 + 4 * q^64 + 14 * q^67 + 12 * q^68 - 22 * q^71 - 22 * q^73 - 6 * q^74 - 56 * q^77 - 2 * q^80 - 12 * q^82 - 24 * q^83 - 6 * q^85 - 12 * q^86 + 4 * q^88 + 2 * q^92 - 8 * q^94 + 12 * q^95 - 2 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times$.

$n$	$191$	$1027$	$1351$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	−2.64575			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$7$	−2.64575			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	6.29150			1.89696			0.948480	−	0.316838i	$-0.102621\pi$
$11$	6.29150			1.89696			0.948480	+	0.316838i	$0.102621\pi$
$12$		0			0
$13$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$13$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$14$	1.32288	+	2.29129i	0.353553	+	0.612372i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.82288	−	4.88936i	−0.684648	−	1.18584i	−0.973547	−	0.228486i	$-0.926623\pi$
$17$	−2.82288	−	4.88936i	−0.684648	−	1.18584i	0.288899	−	0.957359i	$-0.406711\pi$
$18$		0			0
$19$	−1.67712	+	4.02334i	−0.384759	+	0.923017i
$19$	−1.67712	+	4.02334i	−0.384759	+	0.923017i
$20$	1.00000			0.223607
$21$		0			0
$22$	−3.14575	−	5.44860i	−0.670676	−	1.16165i
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i	−0.809177	−	0.587565i	$-0.800087\pi$
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i	0.913434	+	0.406986i	$0.133420\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$		0			0
$28$	1.32288	−	2.29129i	0.250000	−	0.433013i
$29$	−1.82288	+	3.15731i	−0.338500	+	0.586298i	−0.984151	−	0.177334i	$-0.943253\pi$
$29$	−1.82288	+	3.15731i	−0.338500	+	0.586298i	0.645651	+	0.763632i	$0.276586\pi$
$30$		0			0
$31$	7.29150			1.30959			0.654796	−	0.755805i	$-0.272754\pi$
$31$	7.29150			1.30959			0.654796	+	0.755805i	$0.272754\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	−2.82288	+	4.88936i	−0.484119	+	0.838519i
$35$	1.32288	+	2.29129i	0.223607	+	0.387298i
$36$		0			0
$37$	8.29150			1.36311			0.681557	−	0.731765i	$-0.261303\pi$
$37$	8.29150			1.36311			0.681557	+	0.731765i	$0.261303\pi$
$38$	4.32288	−	0.559237i	0.701263	−	0.0907202i
$39$		0			0
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	−4.32288	−	7.48744i	−0.675120	−	1.16934i	−0.976434	−	0.215817i	$-0.930759\pi$
$41$	−4.32288	−	7.48744i	−0.675120	−	1.16934i	0.301314	−	0.953525i	$-0.402575\pi$
$42$		0			0
$43$	−3.00000	−	5.19615i	−0.457496	−	0.792406i	0.541332	−	0.840809i	$-0.317920\pi$
$43$	−3.00000	−	5.19615i	−0.457496	−	0.792406i	−0.998828	+	0.0484030i	$0.984587\pi$
$44$	−3.14575	+	5.44860i	−0.474240	+	0.821408i
$45$		0			0
$46$	−1.00000			−0.147442
$47$	6.29150	−	10.8972i	0.917710	−	1.58952i	0.114825	−	0.993386i	$-0.463369\pi$
$47$	6.29150	−	10.8972i	0.917710	−	1.58952i	0.802884	−	0.596135i	$-0.203298\pi$
$48$		0			0
$49$		0			0
$50$	1.00000			0.141421
$51$		0			0
$52$		0			0
$53$	−2.32288	+	4.02334i	−0.319072	+	0.552648i	−0.980295	−	0.197541i	$-0.936704\pi$
$53$	−2.32288	+	4.02334i	−0.319072	+	0.552648i	0.661223	+	0.750189i	$0.270038\pi$
$54$		0			0
$55$	−3.14575	−	5.44860i	−0.424173	−	0.734689i
$56$	−2.64575			−0.353553
$57$		0			0
$58$	3.64575			0.478711
$59$	2.64575	+	4.58258i	0.344447	+	0.596601i	0.985253	−	0.171103i	$-0.0547329\pi$
$59$	2.64575	+	4.58258i	0.344447	+	0.596601i	−0.640806	+	0.767703i	$0.721400\pi$
$60$		0			0
$61$	−3.46863	+	6.00784i	−0.444112	+	0.769225i	−0.997990	−	0.0633732i	$-0.979814\pi$
$61$	−3.46863	+	6.00784i	−0.444112	+	0.769225i	0.553878	+	0.832598i	$0.313147\pi$
$62$	−3.64575	−	6.31463i	−0.463011	−	0.801958i
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	4.82288	−	8.35347i	0.589208	−	1.02054i	−0.405128	−	0.914260i	$-0.632773\pi$
$67$	4.82288	−	8.35347i	0.589208	−	1.02054i	0.994336	−	0.106278i	$-0.0338935\pi$
$68$	5.64575			0.684648
$69$		0			0
$70$	1.32288	−	2.29129i	0.158114	−	0.273861i
$71$	−6.82288	−	11.8176i	−0.809726	−	1.40249i	−0.913054	−	0.407840i	$-0.866282\pi$
$71$	−6.82288	−	11.8176i	−0.809726	−	1.40249i	0.103327	−	0.994647i	$-0.467051\pi$
$72$		0			0
$73$	−6.82288	−	11.8176i	−0.798557	−	1.38314i	−0.920556	−	0.390611i	$-0.872264\pi$
$73$	−6.82288	−	11.8176i	−0.798557	−	1.38314i	0.121998	−	0.992530i	$-0.461070\pi$
$74$	−4.14575	−	7.18065i	−0.481934	−	0.834734i
$75$		0			0
$76$	−2.64575	−	3.46410i	−0.303488	−	0.397360i
$77$	−16.6458			−1.89696
$78$		0			0
$79$	−2.64575	−	4.58258i	−0.297670	−	0.515580i	0.677932	−	0.735124i	$-0.262876\pi$
$79$	−2.64575	−	4.58258i	−0.297670	−	0.515580i	−0.975603	+	0.219544i	$0.929543\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$		0			0
$82$	−4.32288	+	7.48744i	−0.477382	+	0.826849i
$83$	−16.5830			−1.82022			−0.910111	−	0.414365i	$-0.864004\pi$
$83$	−16.5830			−1.82022			−0.910111	+	0.414365i	$0.864004\pi$
$84$		0			0
$85$	−2.82288	+	4.88936i	−0.306184	+	0.530326i
$86$	−3.00000	+	5.19615i	−0.323498	+	0.560316i
$87$		0			0
$88$	6.29150			0.670676
$89$	6.61438	−	11.4564i	0.701123	−	1.21438i	−0.266950	−	0.963710i	$-0.586016\pi$
$89$	6.61438	−	11.4564i	0.701123	−	1.21438i	0.968073	−	0.250670i	$-0.0806508\pi$
$90$		0			0
$91$		0			0
$92$	0.500000	+	0.866025i	0.0521286	+	0.0902894i
$93$		0			0
$94$	−12.5830			−1.29784
$95$	4.32288	−	0.559237i	0.443518	−	0.0573765i
$96$		0			0
$97$	0.822876	+	1.42526i	0.0835504	+	0.144713i	0.904773	−	0.425895i	$-0.140041\pi$
$97$	0.822876	+	1.42526i	0.0835504	+	0.144713i	−0.821222	+	0.570609i	$0.806707\pi$
$98$		0			0
$99$		0			0
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	5.93725	−	10.2836i	0.590779	−	1.02326i	−0.403349	−	0.915046i	$-0.632154\pi$
$101$	5.93725	−	10.2836i	0.590779	−	1.02326i	0.994128	−	0.108213i	$-0.0345128\pi$
$102$		0			0
$103$	1.93725			0.190883			0.0954417	−	0.995435i	$-0.469574\pi$
$103$	1.93725			0.190883			0.0954417	+	0.995435i	$0.469574\pi$
$104$		0			0
$105$		0			0
$106$	4.64575			0.451235
$107$	−4.35425			−0.420941			−0.210471	−	0.977600i	$-0.567500\pi$
$107$	−4.35425			−0.420941			−0.210471	+	0.977600i	$0.567500\pi$
$108$		0			0
$109$	0.177124	+	0.306788i	0.0169654	+	0.0293850i	0.874383	−	0.485236i	$-0.161266\pi$
$109$	0.177124	+	0.306788i	0.0169654	+	0.0293850i	−0.857418	+	0.514621i	$0.827933\pi$
$110$	−3.14575	+	5.44860i	−0.299936	+	0.519504i
$111$		0			0
$112$	1.32288	+	2.29129i	0.125000	+	0.216506i
$113$	5.64575			0.531108			0.265554	−	0.964096i	$-0.414445\pi$
$113$	5.64575			0.531108			0.265554	+	0.964096i	$0.414445\pi$
$114$		0			0
$115$	−1.00000			−0.0932505
$116$	−1.82288	−	3.15731i	−0.169250	−	0.293149i
$117$		0			0
$118$	2.64575	−	4.58258i	0.243561	−	0.421860i
$119$	7.46863	+	12.9360i	0.684648	+	1.18584i
$120$		0			0
$121$	28.5830			2.59846
$122$	6.93725			0.628069
$123$		0			0
$124$	−3.64575	+	6.31463i	−0.327398	+	0.567070i
$125$	1.00000			0.0894427
$126$		0			0
$127$	5.61438	−	9.72439i	0.498196	−	0.862900i	−0.501802	−	0.864982i	$-0.667330\pi$
$127$	5.61438	−	9.72439i	0.498196	−	0.862900i	0.999998	+	0.00208239i	$0.000662847\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$		0			0
$131$	−3.85425	−	6.67575i	−0.336747	−	0.583263i	0.647072	−	0.762429i	$-0.275993\pi$
$131$	−3.85425	−	6.67575i	−0.336747	−	0.583263i	−0.983819	+	0.179166i	$0.942660\pi$
$132$		0			0
$133$	4.43725	−	10.6448i	0.384759	−	0.923017i
$134$	−9.64575			−0.833266
$135$		0			0
$136$	−2.82288	−	4.88936i	−0.242060	−	0.419260i
$137$	−6.00000	+	10.3923i	−0.512615	+	0.887875i	0.487278	+	0.873247i	$0.337990\pi$
$137$	−6.00000	+	10.3923i	−0.512615	+	0.887875i	−0.999893	+	0.0146279i	$0.995344\pi$
$138$		0			0
$139$	−1.64575	+	2.85052i	−0.139591	+	0.241778i	−0.927342	−	0.374215i	$-0.877912\pi$
$139$	−1.64575	+	2.85052i	−0.139591	+	0.241778i	0.787751	+	0.615994i	$0.211245\pi$
$140$	−2.64575			−0.223607
$141$		0			0
$142$	−6.82288	+	11.8176i	−0.572563	+	0.991708i
$143$		0			0
$144$		0			0
$145$	3.64575			0.302763
$146$	−6.82288	+	11.8176i	−0.564665	+	0.978029i
$147$		0			0
$148$	−4.14575	+	7.18065i	−0.340779	+	0.590246i
$149$	−8.11438	−	14.0545i	−0.664756	−	1.15139i	−0.979351	−	0.202165i	$-0.935202\pi$
$149$	−8.11438	−	14.0545i	−0.664756	−	1.15139i	0.314596	−	0.949226i	$-0.398131\pi$
$150$		0			0
$151$	−20.2288			−1.64619			−0.823096	−	0.567902i	$-0.807755\pi$
$151$	−20.2288			−1.64619			−0.823096	+	0.567902i	$0.807755\pi$
$152$	−1.67712	+	4.02334i	−0.136033	+	0.326336i
$153$		0			0
$154$	8.32288	+	14.4156i	0.670676	+	1.16165i
$155$	−3.64575	−	6.31463i	−0.292834	−	0.507203i
$156$		0			0
$157$	6.43725	+	11.1497i	0.513749	+	0.889839i	0.999873	+	0.0159492i	$0.00507700\pi$
$157$	6.43725	+	11.1497i	0.513749	+	0.889839i	−0.486124	+	0.873890i	$0.661590\pi$
$158$	−2.64575	+	4.58258i	−0.210485	+	0.364570i
$159$		0			0
$160$	1.00000			0.0790569
$161$	−1.32288	+	2.29129i	−0.104257	+	0.180579i
$162$		0			0
$163$	−2.70850			−0.212146			−0.106073	−	0.994358i	$-0.533828\pi$
$163$	−2.70850			−0.212146			−0.106073	+	0.994358i	$0.533828\pi$
$164$	8.64575			0.675120
$165$		0			0
$166$	8.29150	+	14.3613i	0.643545	+	1.11465i
$167$	8.79150	−	15.2273i	0.680307	−	1.17833i	−0.294580	−	0.955627i	$-0.595180\pi$
$167$	8.79150	−	15.2273i	0.680307	−	1.17833i	0.974887	−	0.222699i	$-0.0714868\pi$
$168$		0			0
$169$	6.50000	+	11.2583i	0.500000	+	0.866025i
$170$	5.64575			0.433009
$171$		0			0
$172$	6.00000			0.457496
$173$	3.96863	+	6.87386i	0.301729	+	0.522610i	0.976528	−	0.215392i	$-0.0691028\pi$
$173$	3.96863	+	6.87386i	0.301729	+	0.522610i	−0.674799	+	0.738002i	$0.735770\pi$
$174$		0			0
$175$	1.32288	−	2.29129i	0.100000	−	0.173205i
$176$	−3.14575	−	5.44860i	−0.237120	−	0.410704i
$177$		0			0
$178$	−13.2288			−0.991537
$179$	−3.58301			−0.267806			−0.133903	−	0.990994i	$-0.542751\pi$
$179$	−3.58301			−0.267806			−0.133903	+	0.990994i	$0.542751\pi$
$180$		0			0
$181$	7.17712	−	12.4311i	0.533471	−	0.924000i	−0.465764	−	0.884909i	$-0.654221\pi$
$181$	7.17712	−	12.4311i	0.533471	−	0.924000i	0.999236	−	0.0390908i	$-0.0124462\pi$
$182$		0			0
$183$		0			0
$184$	0.500000	−	0.866025i	0.0368605	−	0.0638442i
$185$	−4.14575	−	7.18065i	−0.304802	−	0.527932i
$186$		0			0
$187$	−17.7601	−	30.7614i	−1.29875	−	2.24950i
$188$	6.29150	+	10.8972i	0.458855	+	0.794760i
$189$		0			0
$190$	−2.64575	−	3.46410i	−0.191943	−	0.251312i
$191$	4.58301			0.331615			0.165807	−	0.986158i	$-0.446977\pi$
$191$	4.58301			0.331615			0.165807	+	0.986158i	$0.446977\pi$
$192$		0			0
$193$	−5.82288	−	10.0855i	−0.419140	−	0.725971i	0.576713	−	0.816947i	$-0.304335\pi$
$193$	−5.82288	−	10.0855i	−0.419140	−	0.725971i	−0.995853	+	0.0909752i	$0.971002\pi$
$194$	0.822876	−	1.42526i	0.0590790	−	0.102328i
$195$		0			0
$196$		0			0
$197$	2.64575			0.188502			0.0942510	−	0.995548i	$-0.469954\pi$
$197$	2.64575			0.188502			0.0942510	+	0.995548i	$0.469954\pi$
$198$		0			0
$199$	−1.53137	+	2.65242i	−0.108556	+	0.188025i	−0.915186	−	0.403033i	$-0.867956\pi$
$199$	−1.53137	+	2.65242i	−0.108556	+	0.188025i	0.806629	+	0.591058i	$0.201289\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$		0			0
$202$	−11.8745			−0.835487
$203$	4.82288	−	8.35347i	0.338500	−	0.586298i
$204$		0			0
$205$	−4.32288	+	7.48744i	−0.301923	+	0.522946i
$206$	−0.968627	−	1.67771i	−0.0674874	−	0.116892i
$207$		0			0
$208$		0			0
$209$	−10.5516	+	25.3128i	−0.729872	+	1.75093i
$210$		0			0
$211$	9.26013	+	16.0390i	0.637494	+	1.10417i	0.985981	+	0.166858i	$0.0533621\pi$
$211$	9.26013	+	16.0390i	0.637494	+	1.10417i	−0.348487	+	0.937313i	$0.613305\pi$
$212$	−2.32288	−	4.02334i	−0.159536	−	0.276324i
$213$		0			0
$214$	2.17712	+	3.77089i	0.148825	+	0.257773i
$215$	−3.00000	+	5.19615i	−0.204598	+	0.354375i
$216$		0			0
$217$	−19.2915			−1.30959
$218$	0.177124	−	0.306788i	0.0119964	−	0.0207783i
$219$		0			0
$220$	6.29150			0.424173
$221$		0			0
$222$		0			0
$223$	−3.32288	−	5.75539i	−0.222516	−	0.385409i	0.733055	−	0.680169i	$-0.238094\pi$
$223$	−3.32288	−	5.75539i	−0.222516	−	0.385409i	−0.955571	+	0.294760i	$0.904760\pi$
$224$	1.32288	−	2.29129i	0.0883883	−	0.153093i
$225$		0			0
$226$	−2.82288	−	4.88936i	−0.187775	−	0.325236i
$227$	−22.8118			−1.51407			−0.757035	−	0.653374i	$-0.773353\pi$
$227$	−22.8118			−1.51407			−0.757035	+	0.653374i	$0.773353\pi$
$228$		0			0
$229$	14.7085			0.971965			0.485982	−	0.873969i	$-0.338462\pi$
$229$	14.7085			0.971965			0.485982	+	0.873969i	$0.338462\pi$
$230$	0.500000	+	0.866025i	0.0329690	+	0.0571040i
$231$		0			0
$232$	−1.82288	+	3.15731i	−0.119678	+	0.207288i
$233$	10.2915	+	17.8254i	0.674219	+	1.16778i	0.976697	+	0.214625i	$0.0688528\pi$
$233$	10.2915	+	17.8254i	0.674219	+	1.16778i	−0.302478	+	0.953156i	$0.597814\pi$
$234$		0			0
$235$	−12.5830			−0.820825
$236$	−5.29150			−0.344447
$237$		0			0
$238$	7.46863	−	12.9360i	0.484119	−	0.838519i
$239$	24.0000			1.55243			0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000			1.55243			0.776215	+	0.630468i	$0.217137\pi$
$240$		0			0
$241$	−0.708497	+	1.22715i	−0.0456383	+	0.0790479i	−0.887942	−	0.459955i	$-0.847866\pi$
$241$	−0.708497	+	1.22715i	−0.0456383	+	0.0790479i	0.842304	+	0.539003i	$0.181199\pi$
$242$	−14.2915	−	24.7536i	−0.918693	−	1.59122i
$243$		0			0
$244$	−3.46863	−	6.00784i	−0.222056	−	0.384612i
$245$		0			0
$246$		0			0
$247$		0			0
$248$	7.29150			0.463011
$249$		0			0
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	−1.29150	+	2.23695i	−0.0815189	+	0.141195i	−0.903903	−	0.427738i	$-0.859310\pi$
$251$	−1.29150	+	2.23695i	−0.0815189	+	0.141195i	0.822384	+	0.568933i	$0.192644\pi$
$252$		0			0
$253$	3.14575	−	5.44860i	0.197772	−	0.342551i
$254$	−11.2288			−0.704555
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	3.00000	−	5.19615i	0.187135	−	0.324127i	−0.757159	−	0.653231i	$-0.773413\pi$
$257$	3.00000	−	5.19615i	0.187135	−	0.324127i	0.944294	+	0.329104i	$0.106747\pi$
$258$		0			0
$259$	−21.9373			−1.36311
$260$		0			0
$261$		0			0
$262$	−3.85425	+	6.67575i	−0.238116	+	0.412429i
$263$	2.14575	+	3.71655i	0.132313	+	0.229172i	0.924568	−	0.381018i	$-0.124426\pi$
$263$	2.14575	+	3.71655i	0.132313	+	0.229172i	−0.792255	+	0.610190i	$0.791093\pi$
$264$		0			0
$265$	4.64575			0.285386
$266$	−11.4373	+	1.47960i	−0.701263	+	0.0907202i
$267$		0			0
$268$	4.82288	+	8.35347i	0.294604	+	0.510269i
$269$	6.46863	+	11.2040i	0.394399	+	0.683119i	0.993024	−	0.117910i	$-0.0376194\pi$
$269$	6.46863	+	11.2040i	0.394399	+	0.683119i	−0.598625	+	0.801029i	$0.704286\pi$
$270$		0			0
$271$	−5.93725	−	10.2836i	−0.360662	−	0.624686i	0.627408	−	0.778691i	$-0.284116\pi$
$271$	−5.93725	−	10.2836i	−0.360662	−	0.624686i	−0.988070	+	0.154005i	$0.950783\pi$
$272$	−2.82288	+	4.88936i	−0.171162	+	0.296461i
$273$		0			0
$274$	12.0000			0.724947
$275$	−3.14575	+	5.44860i	−0.189696	+	0.328563i
$276$		0			0
$277$	−8.00000			−0.480673			−0.240337	−	0.970690i	$-0.577258\pi$
$277$	−8.00000			−0.480673			−0.240337	+	0.970690i	$0.577258\pi$
$278$	3.29150			0.197411
$279$		0			0
$280$	1.32288	+	2.29129i	0.0790569	+	0.136931i
$281$	−9.90588	+	17.1575i	−0.590935	+	1.02353i	0.403171	+	0.915124i	$0.367908\pi$
$281$	−9.90588	+	17.1575i	−0.590935	+	1.02353i	−0.994107	+	0.108406i	$0.965426\pi$
$282$		0			0
$283$	−9.93725	−	17.2118i	−0.590708	−	1.02314i	−0.994137	−	0.108126i	$-0.965515\pi$
$283$	−9.93725	−	17.2118i	−0.590708	−	1.02314i	0.403429	−	0.915011i	$-0.367818\pi$
$284$	13.6458			0.809726
$285$		0			0
$286$		0			0
$287$	11.4373	+	19.8099i	0.675120	+	1.16934i
$288$		0			0
$289$	−7.43725	+	12.8817i	−0.437486	+	0.757747i
$290$	−1.82288	−	3.15731i	−0.107043	−	0.185404i
$291$		0			0
$292$	13.6458			0.798557
$293$	9.35425			0.546481			0.273241	−	0.961946i	$-0.411905\pi$
$293$	9.35425			0.546481			0.273241	+	0.961946i	$0.411905\pi$
$294$		0			0
$295$	2.64575	−	4.58258i	0.154042	−	0.266808i
$296$	8.29150			0.481934
$297$		0			0
$298$	−8.11438	+	14.0545i	−0.470053	+	0.814156i
$299$		0			0
$300$		0			0
$301$	7.93725	+	13.7477i	0.457496	+	0.792406i
$302$	10.1144	+	17.5186i	0.582017	+	1.00808i
$303$		0			0
$304$	4.32288	−	0.559237i	0.247934	−	0.0320744i
$305$	6.93725			0.397226
$306$		0			0
$307$	12.7601	+	22.1012i	0.728259	+	1.26138i	0.957618	+	0.288040i	$0.0930036\pi$
$307$	12.7601	+	22.1012i	0.728259	+	1.26138i	−0.229359	+	0.973342i	$0.573663\pi$
$308$	8.32288	−	14.4156i	0.474240	−	0.821408i
$309$		0			0
$310$	−3.64575	+	6.31463i	−0.207065	+	0.358647i
$311$	25.1660			1.42703			0.713517	−	0.700638i	$-0.247101\pi$
$311$	25.1660			1.42703			0.713517	+	0.700638i	$0.247101\pi$
$312$		0			0
$313$	1.29150	−	2.23695i	0.0730000	−	0.126440i	−0.827215	−	0.561886i	$-0.810076\pi$
$313$	1.29150	−	2.23695i	0.0730000	−	0.126440i	0.900215	+	0.435446i	$0.143409\pi$
$314$	6.43725	−	11.1497i	0.363275	−	0.629211i
$315$		0			0
$316$	5.29150			0.297670
$317$	2.03137	−	3.51844i	0.114093	−	0.197615i	−0.803324	−	0.595543i	$-0.796937\pi$
$317$	2.03137	−	3.51844i	0.114093	−	0.197615i	0.917417	+	0.397927i	$0.130270\pi$
$318$		0			0
$319$	−11.4686	+	19.8642i	−0.642120	+	1.11218i
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$		0			0
$322$	2.64575			0.147442
$323$	24.4059	−	3.15731i	1.35798	−	0.175678i
$324$		0			0
$325$		0			0
$326$	1.35425	+	2.34563i	0.0750049	+	0.129912i
$327$		0			0
$328$	−4.32288	−	7.48744i	−0.238691	−	0.413425i
$329$	−16.6458	+	28.8313i	−0.917710	+	1.58952i
$330$		0			0
$331$	−18.6458			−1.02486			−0.512432	−	0.858728i	$-0.671255\pi$
$331$	−18.6458			−1.02486			−0.512432	+	0.858728i	$0.671255\pi$
$332$	8.29150	−	14.3613i	0.455055	−	0.788179i
$333$		0			0
$334$	−17.5830			−0.962099
$335$	−9.64575			−0.527004
$336$		0			0
$337$	−3.35425	−	5.80973i	−0.182718	−	0.316476i	0.760087	−	0.649821i	$-0.225156\pi$
$337$	−3.35425	−	5.80973i	−0.182718	−	0.316476i	−0.942805	+	0.333345i	$0.891823\pi$
$338$	6.50000	−	11.2583i	0.353553	−	0.612372i
$339$		0			0
$340$	−2.82288	−	4.88936i	−0.153092	−	0.265163i
$341$	45.8745			2.48424
$342$		0			0
$343$	18.5203			1.00000
$344$	−3.00000	−	5.19615i	−0.161749	−	0.280158i
$345$		0			0
$346$	3.96863	−	6.87386i	0.213355	−	0.369541i
$347$	6.29150	+	10.8972i	0.337746	+	0.584992i	0.984008	−	0.178122i	$-0.0570023\pi$
$347$	6.29150	+	10.8972i	0.337746	+	0.584992i	−0.646263	+	0.763115i	$0.723669\pi$
$348$		0			0
$349$	17.0627			0.913348			0.456674	−	0.889634i	$-0.349041\pi$
$349$	17.0627			0.913348			0.456674	+	0.889634i	$0.349041\pi$
$350$	−2.64575			−0.141421
$351$		0			0
$352$	−3.14575	+	5.44860i	−0.167669	+	0.290411i
$353$	7.06275			0.375912			0.187956	−	0.982177i	$-0.439814\pi$
$353$	7.06275			0.375912			0.187956	+	0.982177i	$0.439814\pi$
$354$		0			0
$355$	−6.82288	+	11.8176i	−0.362121	+	0.627211i
$356$	6.61438	+	11.4564i	0.350561	+	0.607190i
$357$		0			0
$358$	1.79150	+	3.10297i	0.0946839	+	0.163997i
$359$	2.46863	+	4.27579i	0.130289	+	0.225667i	0.923788	−	0.382904i	$-0.125076\pi$
$359$	2.46863	+	4.27579i	0.130289	+	0.225667i	−0.793499	+	0.608572i	$0.791743\pi$
$360$		0			0
$361$	−13.3745	−	13.4953i	−0.703921	−	0.710278i
$362$	−14.3542			−0.754443
$363$		0			0
$364$		0			0
$365$	−6.82288	+	11.8176i	−0.357126	+	0.618560i
$366$		0			0
$367$	0.937254	−	1.62337i	0.0489243	−	0.0847393i	−0.840526	−	0.541771i	$-0.817754\pi$
$367$	0.937254	−	1.62337i	0.0489243	−	0.0847393i	0.889450	+	0.457032i	$0.151087\pi$
$368$	−1.00000			−0.0521286
$369$		0			0
$370$	−4.14575	+	7.18065i	−0.215527	+	0.373304i
$371$	6.14575	−	10.6448i	0.319072	−	0.552648i
$372$		0			0
$373$	18.2915			0.947098			0.473549	−	0.880767i	$-0.342973\pi$
$373$	18.2915			0.947098			0.473549	+	0.880767i	$0.342973\pi$
$374$	−17.7601	+	30.7614i	−0.918354	+	1.59064i
$375$		0			0
$376$	6.29150	−	10.8972i	0.324459	−	0.561980i
$377$		0			0
$378$		0			0
$379$	17.8745			0.918152			0.459076	−	0.888397i	$-0.348181\pi$
$379$	17.8745			0.918152			0.459076	+	0.888397i	$0.348181\pi$
$380$	−1.67712	+	4.02334i	−0.0860347	+	0.206393i
$381$		0			0
$382$	−2.29150	−	3.96900i	−0.117243	−	0.203072i
$383$	−18.2915	−	31.6818i	−0.934652	−	1.61886i	−0.775253	−	0.631651i	$-0.782378\pi$
$383$	−18.2915	−	31.6818i	−0.934652	−	1.61886i	−0.159399	−	0.987214i	$-0.550956\pi$
$384$		0			0
$385$	8.32288	+	14.4156i	0.424173	+	0.734689i
$386$	−5.82288	+	10.0855i	−0.296377	+	0.513339i
$387$		0			0
$388$	−1.64575			−0.0835504
$389$	−8.76013	+	15.1730i	−0.444156	+	0.769301i	−0.997993	−	0.0633241i	$-0.979830\pi$
$389$	−8.76013	+	15.1730i	−0.444156	+	0.769301i	0.553837	+	0.832625i	$0.313163\pi$
$390$		0			0
$391$	−5.64575			−0.285518
$392$		0			0
$393$		0			0
$394$	−1.32288	−	2.29129i	−0.0666455	−	0.115433i
$395$	−2.64575	+	4.58258i	−0.133122	+	0.230574i
$396$		0			0
$397$	13.7288	+	23.7789i	0.689027	+	1.19343i	0.972153	+	0.234346i	$0.0752950\pi$
$397$	13.7288	+	23.7789i	0.689027	+	1.19343i	−0.283127	+	0.959083i	$0.591372\pi$
$398$	3.06275			0.153522
$399$		0			0
$400$	1.00000			0.0500000
$401$	3.00000	+	5.19615i	0.149813	+	0.259483i	0.931158	−	0.364615i	$-0.118800\pi$
$401$	3.00000	+	5.19615i	0.149813	+	0.259483i	−0.781345	+	0.624099i	$0.785466\pi$
$402$		0			0
$403$		0			0
$404$	5.93725	+	10.2836i	0.295389	+	0.511629i
$405$		0			0
$406$	−9.64575			−0.478711
$407$	52.1660			2.58577
$408$		0			0
$409$	9.20850	−	15.9496i	0.455331	−	0.788656i	−0.543376	−	0.839489i	$-0.682854\pi$
$409$	9.20850	−	15.9496i	0.455331	−	0.788656i	0.998707	+	0.0508330i	$0.0161876\pi$
$410$	8.64575			0.426983
$411$		0			0
$412$	−0.968627	+	1.67771i	−0.0477208	+	0.0826549i
$413$	−7.00000	−	12.1244i	−0.344447	−	0.596601i
$414$		0			0
$415$	8.29150	+	14.3613i	0.407014	+	0.704969i
$416$		0			0
$417$		0			0
$418$	27.1974	−	3.51844i	1.33027	−	0.172093i
$419$	−38.1660			−1.86453			−0.932266	−	0.361774i	$-0.882171\pi$
$419$	−38.1660			−1.86453			−0.932266	+	0.361774i	$0.882171\pi$
$420$		0			0
$421$	9.46863	+	16.4001i	0.461473	+	0.799294i	0.999035	−	0.0439302i	$-0.0139879\pi$
$421$	9.46863	+	16.4001i	0.461473	+	0.799294i	−0.537562	+	0.843224i	$0.680655\pi$
$422$	9.26013	−	16.0390i	0.450776	−	0.780767i
$423$		0			0
$424$	−2.32288	+	4.02334i	−0.112809	+	0.195391i
$425$	5.64575			0.273859
$426$		0			0
$427$	9.17712	−	15.8952i	0.444112	−	0.769225i
$428$	2.17712	−	3.77089i	0.105235	−	0.182273i
$429$		0			0
$430$	6.00000			0.289346
$431$	14.1771	−	24.5555i	0.682888	−	1.18280i	−0.291207	−	0.956660i	$-0.594057\pi$
$431$	14.1771	−	24.5555i	0.682888	−	1.18280i	0.974096	−	0.226137i	$-0.0726097\pi$
$432$		0			0
$433$	−2.46863	+	4.27579i	−0.118635	+	0.205481i	−0.919227	−	0.393728i	$-0.871185\pi$
$433$	−2.46863	+	4.27579i	−0.118635	+	0.205481i	0.800592	+	0.599210i	$0.204518\pi$
$434$	9.64575	+	16.7069i	0.463011	+	0.801958i
$435$		0			0
$436$	−0.354249			−0.0169654
$437$	2.64575	+	3.46410i	0.126563	+	0.165710i
$438$		0			0
$439$	1.53137	+	2.65242i	0.0730884	+	0.126593i	0.900253	−	0.435366i	$-0.143381\pi$
$439$	1.53137	+	2.65242i	0.0730884	+	0.126593i	−0.827165	+	0.561959i	$0.810048\pi$
$440$	−3.14575	−	5.44860i	−0.149968	−	0.259752i
$441$		0			0
$442$		0			0
$443$	−12.5314	+	21.7050i	−0.595384	+	1.03123i	0.398109	+	0.917338i	$0.369667\pi$
$443$	−12.5314	+	21.7050i	−0.595384	+	1.03123i	−0.993493	+	0.113896i	$0.963667\pi$
$444$		0			0
$445$	−13.2288			−0.627103
$446$	−3.32288	+	5.75539i	−0.157343	+	0.272526i
$447$		0			0
$448$	−2.64575			−0.125000
$449$	17.3542			0.818998			0.409499	−	0.912311i	$-0.365704\pi$
$449$	17.3542			0.818998			0.409499	+	0.912311i	$0.365704\pi$
$450$		0			0
$451$	−27.1974	−	47.1073i	−1.28067	−	2.21819i
$452$	−2.82288	+	4.88936i	−0.132777	+	0.229976i
$453$		0			0
$454$	11.4059	+	19.7556i	0.535305	+	0.927175i
$455$		0			0
$456$		0			0
$457$	1.77124			0.0828553			0.0414276	−	0.999142i	$-0.486809\pi$
$457$	1.77124			0.0828553			0.0414276	+	0.999142i	$0.486809\pi$
$458$	−7.35425	−	12.7379i	−0.343641	−	0.595204i
$459$		0			0
$460$	0.500000	−	0.866025i	0.0233126	−	0.0403786i
$461$	−17.5830	−	30.4547i	−0.818922	−	1.41841i	−0.906477	−	0.422255i	$-0.861239\pi$
$461$	−17.5830	−	30.4547i	−0.818922	−	1.41841i	0.0875548	−	0.996160i	$-0.472095\pi$
$462$		0			0
$463$	29.3542			1.36421			0.682104	−	0.731255i	$-0.261065\pi$
$463$	29.3542			1.36421			0.682104	+	0.731255i	$0.261065\pi$
$464$	3.64575			0.169250
$465$		0			0
$466$	10.2915	−	17.8254i	0.476745	−	0.825746i
$467$	−15.5203			−0.718192			−0.359096	−	0.933301i	$-0.616915\pi$
$467$	−15.5203			−0.718192			−0.359096	+	0.933301i	$0.616915\pi$
$468$		0			0
$469$	−12.7601	+	22.1012i	−0.589208	+	1.02054i
$470$	6.29150	+	10.8972i	0.290205	+	0.502650i
$471$		0			0
$472$	2.64575	+	4.58258i	0.121781	+	0.210930i
$473$	−18.8745	−	32.6916i	−0.867851	−	1.50316i
$474$		0			0
$475$	−2.64575	−	3.46410i	−0.121395	−	0.158944i
$476$	−14.9373			−0.684648
$477$		0			0
$478$	−12.0000	−	20.7846i	−0.548867	−	0.950666i
$479$	2.46863	−	4.27579i	0.112794	−	0.195366i	−0.804102	−	0.594492i	$-0.797353\pi$
$479$	2.46863	−	4.27579i	0.112794	−	0.195366i	0.916896	+	0.399126i	$0.130687\pi$
$480$		0			0
$481$		0			0
$482$	1.41699			0.0645423
$483$		0			0
$484$	−14.2915	+	24.7536i	−0.649614	+	1.12516i
$485$	0.822876	−	1.42526i	0.0373649	−	0.0647178i
$486$		0			0
$487$	20.6458			0.935548			0.467774	−	0.883848i	$-0.345056\pi$
$487$	20.6458			0.935548			0.467774	+	0.883848i	$0.345056\pi$
$488$	−3.46863	+	6.00784i	−0.157017	+	0.271962i
$489$		0			0
$490$		0			0
$491$	19.7288	+	34.1712i	0.890346	+	1.54213i	0.839461	+	0.543421i	$0.182871\pi$
$491$	19.7288	+	34.1712i	0.890346	+	1.54213i	0.0508857	+	0.998704i	$0.483796\pi$
$492$		0			0
$493$	20.5830			0.927012
$494$		0			0
$495$		0			0
$496$	−3.64575	−	6.31463i	−0.163699	−	0.283535i
$497$	18.0516	+	31.2663i	0.809726	+	1.40249i
$498$		0			0
$499$	−3.67712	−	6.36897i	−0.164611	−	0.285114i	0.771906	−	0.635736i	$-0.219303\pi$
$499$	−3.67712	−	6.36897i	−0.164611	−	0.285114i	−0.936517	+	0.350622i	$0.885970\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$		0			0
$502$	2.58301			0.115285
$503$	13.3745	−	23.1653i	0.596340	−	1.03289i	−0.397016	−	0.917811i	$-0.629954\pi$
$503$	13.3745	−	23.1653i	0.596340	−	1.03289i	0.993356	−	0.115079i	$-0.0367122\pi$
$504$		0			0
$505$	−11.8745			−0.528409
$506$	−6.29150			−0.279691
$507$		0			0
$508$	5.61438	+	9.72439i	0.249098	+	0.431450i
$509$	−1.35425	+	2.34563i	−0.0600260	+	0.103968i	−0.894477	−	0.447114i	$-0.852452\pi$
$509$	−1.35425	+	2.34563i	−0.0600260	+	0.103968i	0.834451	+	0.551082i	$0.185785\pi$
$510$		0			0
$511$	18.0516	+	31.2663i	0.798557	+	1.38314i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−6.00000			−0.264649
$515$	−0.968627	−	1.67771i	−0.0426828	−	0.0739288i
$516$		0			0
$517$	39.5830	−	68.5598i	1.74086	−	3.01526i
$518$	10.9686	+	18.9982i	0.481934	+	0.834734i
$519$		0			0
$520$		0			0
$521$	−22.4575			−0.983882			−0.491941	−	0.870629i	$-0.663712\pi$
$521$	−22.4575			−0.983882			−0.491941	+	0.870629i	$0.663712\pi$
$522$		0			0
$523$	6.88562	−	11.9262i	0.301087	−	0.521498i	−0.675295	−	0.737547i	$-0.735984\pi$
$523$	6.88562	−	11.9262i	0.301087	−	0.521498i	0.976382	+	0.216049i	$0.0693171\pi$
$524$	7.70850			0.336747
$525$		0			0
$526$	2.14575	−	3.71655i	0.0935592	−	0.162049i
$527$	−20.5830	−	35.6508i	−0.896610	−	1.55297i
$528$		0			0
$529$	11.0000	+	19.0526i	0.478261	+	0.828372i
$530$	−2.32288	−	4.02334i	−0.100899	−	0.174763i
$531$		0			0
$532$	7.00000	+	9.16515i	0.303488	+	0.397360i
$533$		0			0
$534$		0			0
$535$	2.17712	+	3.77089i	0.0941253	+	0.163030i
$536$	4.82288	−	8.35347i	0.208316	−	0.360815i
$537$		0			0
$538$	6.46863	−	11.2040i	0.278882	−	0.483038i
$539$		0			0
$540$		0			0
$541$	−8.93725	+	15.4798i	−0.384243	+	0.665528i	−0.991664	−	0.128852i	$-0.958871\pi$
$541$	−8.93725	+	15.4798i	−0.384243	+	0.665528i	0.607421	+	0.794380i	$0.292204\pi$
$542$	−5.93725	+	10.2836i	−0.255027	+	0.441720i
$543$		0			0
$544$	5.64575			0.242060
$545$	0.177124	−	0.306788i	0.00758717	−	0.0131414i
$546$		0			0
$547$	−9.35425	+	16.2020i	−0.399959	+	0.692749i	−0.993720	−	0.111892i	$-0.964309\pi$
$547$	−9.35425	+	16.2020i	−0.399959	+	0.692749i	0.593762	+	0.804641i	$0.297642\pi$
$548$	−6.00000	−	10.3923i	−0.256307	−	0.443937i
$549$		0			0
$550$	6.29150			0.268271
$551$	−9.64575	−	12.6293i	−0.410923	−	0.538024i
$552$		0			0
$553$	7.00000	+	12.1244i	0.297670	+	0.515580i
$554$	4.00000	+	6.92820i	0.169944	+	0.294351i
$555$		0			0
$556$	−1.64575	−	2.85052i	−0.0697954	−	0.120889i
$557$	−12.2601	+	21.2352i	−0.519478	+	0.899763i	0.480265	+	0.877123i	$0.340540\pi$
$557$	−12.2601	+	21.2352i	−0.519478	+	0.899763i	−0.999744	+	0.0226397i	$0.992793\pi$
$558$		0			0
$559$		0			0
$560$	1.32288	−	2.29129i	0.0559017	−	0.0968246i
$561$		0			0
$562$	19.8118			0.835709
$563$	−21.4170			−0.902619			−0.451309	−	0.892368i	$-0.649043\pi$
$563$	−21.4170			−0.902619			−0.451309	+	0.892368i	$0.649043\pi$
$564$		0			0
$565$	−2.82288	−	4.88936i	−0.118759	−	0.205697i
$566$	−9.93725	+	17.2118i	−0.417694	+	0.723467i
$567$		0			0
$568$	−6.82288	−	11.8176i	−0.286282	−	0.495854i
$569$	−5.35425			−0.224462			−0.112231	−	0.993682i	$-0.535800\pi$
$569$	−5.35425			−0.224462			−0.112231	+	0.993682i	$0.535800\pi$
$570$		0			0
$571$	26.4575			1.10721			0.553606	−	0.832779i	$-0.313251\pi$
$571$	26.4575			1.10721			0.553606	+	0.832779i	$0.313251\pi$
$572$		0			0
$573$		0			0
$574$	11.4373	−	19.8099i	0.477382	−	0.826849i
$575$	0.500000	+	0.866025i	0.0208514	+	0.0361158i
$576$		0			0
$577$	2.93725			0.122279			0.0611397	−	0.998129i	$-0.480526\pi$
$577$	2.93725			0.122279			0.0611397	+	0.998129i	$0.480526\pi$
$578$	14.8745			0.618698
$579$		0			0
$580$	−1.82288	+	3.15731i	−0.0756908	+	0.131100i
$581$	43.8745			1.82022
$582$		0			0
$583$	−14.6144	+	25.3128i	−0.605266	+	1.04835i
$584$	−6.82288	−	11.8176i	−0.282333	−	0.489014i
$585$		0			0
$586$	−4.67712	−	8.10102i	−0.193210	−	0.334650i
$587$	16.3542	+	28.3264i	0.675012	+	1.16916i	0.976465	+	0.215674i	$0.0691949\pi$
$587$	16.3542	+	28.3264i	0.675012	+	1.16916i	−0.301453	+	0.953481i	$0.597472\pi$
$588$		0			0
$589$	−12.2288	+	29.3362i	−0.503877	+	1.20878i
$590$	−5.29150			−0.217848
$591$		0			0
$592$	−4.14575	−	7.18065i	−0.170389	−	0.295123i
$593$	−17.8229	+	30.8701i	−0.731898	+	1.26768i	0.224173	+	0.974549i	$0.428032\pi$
$593$	−17.8229	+	30.8701i	−0.731898	+	1.26768i	−0.956071	+	0.293135i	$0.905302\pi$
$594$		0			0
$595$	7.46863	−	12.9360i	0.306184	−	0.530326i
$596$	16.2288			0.664756
$597$		0			0
$598$		0			0
$599$	−8.76013	+	15.1730i	−0.357929	+	0.619952i	−0.987615	−	0.156899i	$-0.949850\pi$
$599$	−8.76013	+	15.1730i	−0.357929	+	0.619952i	0.629686	+	0.776850i	$0.283184\pi$
$600$		0			0
$601$	−16.2915			−0.664544			−0.332272	−	0.943184i	$-0.607815\pi$
$601$	−16.2915			−0.664544			−0.332272	+	0.943184i	$0.607815\pi$
$602$	7.93725	−	13.7477i	0.323498	−	0.560316i
$603$		0			0
$604$	10.1144	−	17.5186i	0.411548	−	0.712822i
$605$	−14.2915	−	24.7536i	−0.581032	−	1.00638i
$606$		0			0
$607$	−7.22876			−0.293406			−0.146703	−	0.989181i	$-0.546866\pi$
$607$	−7.22876			−0.293406			−0.146703	+	0.989181i	$0.546866\pi$
$608$	−2.64575	−	3.46410i	−0.107299	−	0.140488i
$609$		0			0
$610$	−3.46863	−	6.00784i	−0.140441	−	0.243250i
$611$		0			0
$612$		0			0
$613$	14.4373	+	25.0061i	0.583115	+	1.00999i	0.995108	+	0.0987978i	$0.0314997\pi$
$613$	14.4373	+	25.0061i	0.583115	+	1.00999i	−0.411992	+	0.911187i	$0.635167\pi$
$614$	12.7601	−	22.1012i	0.514957	−	0.891932i
$615$		0			0
$616$	−16.6458			−0.670676
$617$	−1.29150	+	2.23695i	−0.0519939	+	0.0900561i	−0.890851	−	0.454296i	$-0.849891\pi$
$617$	−1.29150	+	2.23695i	−0.0519939	+	0.0900561i	0.838857	+	0.544352i	$0.183224\pi$
$618$		0			0
$619$	−18.0627			−0.726003			−0.363002	−	0.931789i	$-0.618248\pi$
$619$	−18.0627			−0.726003			−0.363002	+	0.931789i	$0.618248\pi$
$620$	7.29150			0.292834
$621$		0			0
$622$	−12.5830	−	21.7944i	−0.504533	−	0.873876i
$623$	−17.5000	+	30.3109i	−0.701123	+	1.21438i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−2.58301			−0.103238
$627$		0			0
$628$	−12.8745			−0.513749
$629$	−23.4059	−	40.5402i	−0.933254	−	1.61644i
$630$		0			0
$631$	−8.17712	+	14.1632i	−0.325526	+	0.563828i	−0.981619	−	0.190853i	$-0.938875\pi$
$631$	−8.17712	+	14.1632i	−0.325526	+	0.563828i	0.656093	+	0.754680i	$0.272208\pi$
$632$	−2.64575	−	4.58258i	−0.105242	−	0.182285i
$633$		0			0
$634$	−4.06275			−0.161352
$635$	−11.2288			−0.445600
$636$		0			0
$637$		0			0
$638$	22.9373			0.908095
$639$		0			0
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	−10.6458	−	18.4390i	−0.420482	−	0.728296i	0.575505	−	0.817798i	$-0.304806\pi$
$641$	−10.6458	−	18.4390i	−0.420482	−	0.728296i	−0.995987	+	0.0895025i	$0.971472\pi$
$642$		0			0
$643$	−0.594119	−	1.02904i	−0.0234298	−	0.0405816i	0.854073	−	0.520154i	$-0.174125\pi$
$643$	−0.594119	−	1.02904i	−0.0234298	−	0.0405816i	−0.877503	+	0.479572i	$0.840792\pi$
$644$	−1.32288	−	2.29129i	−0.0521286	−	0.0902894i
$645$		0			0
$646$	−14.9373	−	19.5575i	−0.587698	−	0.769478i
$647$	−36.8745			−1.44969			−0.724843	−	0.688914i	$-0.758088\pi$
$647$	−36.8745			−1.44969			−0.724843	+	0.688914i	$0.758088\pi$
$648$		0			0
$649$	16.6458	+	28.8313i	0.653403	+	1.13173i
$650$		0			0
$651$		0			0
$652$	1.35425	−	2.34563i	0.0530365	−	0.0918619i
$653$	−25.9373			−1.01500			−0.507502	−	0.861651i	$-0.669431\pi$
$653$	−25.9373			−1.01500			−0.507502	+	0.861651i	$0.669431\pi$
$654$		0			0
$655$	−3.85425	+	6.67575i	−0.150598	+	0.260843i
$656$	−4.32288	+	7.48744i	−0.168780	+	0.292335i
$657$		0			0
$658$	33.2915			1.29784
$659$	4.79150	−	8.29913i	0.186650	−	0.323288i	−0.757481	−	0.652857i	$-0.773570\pi$
$659$	4.79150	−	8.29913i	0.186650	−	0.323288i	0.944131	+	0.329569i	$0.106903\pi$
$660$		0			0
$661$	17.2915	−	29.9498i	0.672562	−	1.16491i	−0.304614	−	0.952476i	$-0.598527\pi$
$661$	17.2915	−	29.9498i	0.672562	−	1.16491i	0.977175	−	0.212435i	$-0.0681393\pi$
$662$	9.32288	+	16.1477i	0.362344	+	0.627598i
$663$		0			0
$664$	−16.5830			−0.643545
$665$	−11.4373	+	1.47960i	−0.443518	+	0.0573765i
$666$		0			0
$667$	1.82288	+	3.15731i	0.0705820	+	0.122252i
$668$	8.79150	+	15.2273i	0.340153	+	0.589163i
$669$		0			0
$670$	4.82288	+	8.35347i	0.186324	+	0.322723i
$671$	−21.8229	+	37.7983i	−0.842463	+	1.45919i
$672$		0			0
$673$	−37.8745			−1.45995			−0.729977	−	0.683471i	$-0.760469\pi$
$673$	−37.8745			−1.45995			−0.729977	+	0.683471i	$0.760469\pi$
$674$	−3.35425	+	5.80973i	−0.129201	+	0.223782i
$675$		0			0
$676$	−13.0000			−0.500000
$677$	14.7712			0.567705			0.283853	−	0.958868i	$-0.408387\pi$
$677$	14.7712			0.567705			0.283853	+	0.958868i	$0.408387\pi$
$678$		0			0
$679$	−2.17712	−	3.77089i	−0.0835504	−	0.144713i
$680$	−2.82288	+	4.88936i	−0.108252	+	0.187499i
$681$		0			0
$682$	−22.9373	−	39.7285i	−0.878313	−	1.52128i
$683$	−13.0627			−0.499832			−0.249916	−	0.968268i	$-0.580403\pi$
$683$	−13.0627			−0.499832			−0.249916	+	0.968268i	$0.580403\pi$
$684$		0			0
$685$	12.0000			0.458496
$686$	−9.26013	−	16.0390i	−0.353553	−	0.612372i
$687$		0			0
$688$	−3.00000	+	5.19615i	−0.114374	+	0.198101i
$689$		0			0
$690$		0			0
$691$	33.8118			1.28626			0.643130	−	0.765757i	$-0.277635\pi$
$691$	33.8118			1.28626			0.643130	+	0.765757i	$0.277635\pi$
$692$	−7.93725			−0.301729
$693$		0			0
$694$	6.29150	−	10.8972i	0.238822	−	0.413652i
$695$	3.29150			0.124854
$696$		0			0
$697$	−24.4059	+	42.2722i	−0.924439	+	1.60117i
$698$	−8.53137	−	14.7768i	−0.322917	−	0.559309i
$699$		0			0
$700$	1.32288	+	2.29129i	0.0500000	+	0.0866025i
$701$	22.1660	+	38.3927i	0.837199	+	1.45007i	0.892228	+	0.451586i	$0.149142\pi$
$701$	22.1660	+	38.3927i	0.837199	+	1.45007i	−0.0550290	+	0.998485i	$0.517525\pi$
$702$		0			0
$703$	−13.9059	+	33.3595i	−0.524470	+	1.25818i
$704$	6.29150			0.237120
$705$		0			0
$706$	−3.53137	−	6.11652i	−0.132905	−	0.230198i
$707$	−15.7085	+	27.2079i	−0.590779	+	1.02326i
$708$		0			0
$709$	−4.53137	+	7.84857i	−0.170179	+	0.294759i	−0.938482	−	0.345327i	$-0.887768\pi$
$709$	−4.53137	+	7.84857i	−0.170179	+	0.294759i	0.768303	+	0.640086i	$0.221101\pi$
$710$	13.6458			0.512116
$711$		0			0
$712$	6.61438	−	11.4564i	0.247884	−	0.429348i
$713$	3.64575	−	6.31463i	0.136534	−	0.236485i
$714$		0			0
$715$		0			0
$716$	1.79150	−	3.10297i	0.0669516	−	0.115964i
$717$		0			0
$718$	2.46863	−	4.27579i	0.0921283	−	0.159571i
$719$	−6.35425	−	11.0059i	−0.236973	−	0.410450i	0.722871	−	0.690983i	$-0.242822\pi$
$719$	−6.35425	−	11.0059i	−0.236973	−	0.410450i	−0.959844	+	0.280533i	$0.909489\pi$
$720$		0			0
$721$	−5.12549			−0.190883
$722$	−5.00000	+	18.3303i	−0.186081	+	0.682183i
$723$		0			0
$724$	7.17712	+	12.4311i	0.266736	+	0.462000i
$725$	−1.82288	−	3.15731i	−0.0676999	−	0.117260i
$726$		0			0
$727$	−5.93725	−	10.2836i	−0.220201	−	0.381399i	0.734668	−	0.678427i	$-0.237338\pi$
$727$	−5.93725	−	10.2836i	−0.220201	−	0.381399i	−0.954869	+	0.297028i	$0.904005\pi$
$728$		0			0
$729$		0			0
$730$	13.6458			0.505052
$731$	−16.9373	+	29.3362i	−0.626447	+	1.08504i
$732$		0			0
$733$	−12.2915			−0.453997			−0.226999	−	0.973895i	$-0.572891\pi$
$733$	−12.2915			−0.453997			−0.226999	+	0.973895i	$0.572891\pi$
$734$	−1.87451			−0.0691893
$735$		0			0
$736$	0.500000	+	0.866025i	0.0184302	+	0.0319221i
$737$	30.3431	−	52.5559i	1.11770	−	1.93592i
$738$		0			0
$739$	−19.4889	−	33.7557i	−0.716910	−	1.24173i	−0.962218	−	0.272280i	$-0.912222\pi$
$739$	−19.4889	−	33.7557i	−0.716910	−	1.24173i	0.245308	−	0.969445i	$-0.421111\pi$
$740$	8.29150			0.304802
$741$		0			0
$742$	−12.2915			−0.451235
$743$	−20.7915	−	36.0119i	−0.762766	−	1.32115i	−0.941419	−	0.337238i	$-0.890507\pi$
$743$	−20.7915	−	36.0119i	−0.762766	−	1.32115i	0.178653	−	0.983912i	$-0.442826\pi$
$744$		0			0
$745$	−8.11438	+	14.0545i	−0.297288	+	0.514918i
$746$	−9.14575	−	15.8409i	−0.334850	−	0.579977i
$747$		0			0
$748$	35.5203			1.29875
$749$	11.5203			0.420941
$750$		0			0
$751$	22.0000	−	38.1051i	0.802791	−	1.39048i	−0.114981	−	0.993368i	$-0.536681\pi$
$751$	22.0000	−	38.1051i	0.802791	−	1.39048i	0.917772	−	0.397108i	$-0.129986\pi$
$752$	−12.5830			−0.458855
$753$		0			0
$754$		0			0
$755$	10.1144	+	17.5186i	0.368100	+	0.637568i
$756$		0			0
$757$	−11.7288	−	20.3148i	−0.426289	−	0.738354i	0.570251	−	0.821471i	$-0.306846\pi$
$757$	−11.7288	−	20.3148i	−0.426289	−	0.738354i	−0.996540	+	0.0831165i	$0.973513\pi$
$758$	−8.93725	−	15.4798i	−0.324616	−	0.562251i
$759$		0			0
$760$	4.32288	−	0.559237i	0.156807	−	0.0202857i
$761$	20.5203			0.743859			0.371929	−	0.928261i	$-0.378696\pi$
$761$	20.5203			0.743859			0.371929	+	0.928261i	$0.378696\pi$
$762$		0			0
$763$	−0.468627	−	0.811686i	−0.0169654	−	0.0293850i
$764$	−2.29150	+	3.96900i	−0.0829037	+	0.143593i
$765$		0			0
$766$	−18.2915	+	31.6818i	−0.660899	+	1.14471i
$767$		0			0
$768$		0			0
$769$	−9.64575	+	16.7069i	−0.347835	+	0.602467i	−0.985865	−	0.167544i	$-0.946416\pi$
$769$	−9.64575	+	16.7069i	−0.347835	+	0.602467i	0.638030	+	0.770012i	$0.279750\pi$
$770$	8.32288	−	14.4156i	0.299936	−	0.519504i
$771$		0			0
$772$	11.6458			0.419140
$773$	−0.968627	+	1.67771i	−0.0348391	+	0.0603431i	−0.882919	−	0.469525i	$-0.844425\pi$
$773$	−0.968627	+	1.67771i	−0.0348391	+	0.0603431i	0.848080	+	0.529868i	$0.177759\pi$
$774$		0			0
$775$	−3.64575	+	6.31463i	−0.130959	+	0.226828i
$776$	0.822876	+	1.42526i	0.0295395	+	0.0511639i
$777$		0			0
$778$	17.5203			0.628132
$779$	37.3745	−	4.83502i	1.33908	−	0.173233i
$780$		0			0
$781$	−42.9261	−	74.3503i	−1.53602	−	2.66046i
$782$	2.82288	+	4.88936i	0.100946	+	0.174843i
$783$		0			0
$784$		0			0
$785$	6.43725	−	11.1497i	0.229755	−	0.397948i
$786$		0			0
$787$	8.10326			0.288850			0.144425	−	0.989516i	$-0.453867\pi$
$787$	8.10326			0.288850			0.144425	+	0.989516i	$0.453867\pi$
$788$	−1.32288	+	2.29129i	−0.0471255	+	0.0816237i
$789$		0			0
$790$	5.29150			0.188263
$791$	−14.9373			−0.531108
$792$		0			0
$793$		0			0
$794$	13.7288	−	23.7789i	0.487215	−	0.843882i
$795$		0			0
$796$	−1.53137	−	2.65242i	−0.0542781	−	0.0940124i
$797$	37.6863			1.33492			0.667458	−	0.744647i	$-0.267382\pi$
$797$	37.6863			1.33492			0.667458	+	0.744647i	$0.267382\pi$
$798$		0			0
$799$	−71.0405			−2.51323
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$		0			0
$802$	3.00000	−	5.19615i	0.105934	−	0.183483i
$803$	−42.9261	−	74.3503i	−1.51483	−	2.62376i
$804$		0			0
$805$	2.64575			0.0932505
$806$		0			0
$807$		0			0
$808$	5.93725	−	10.2836i	0.208872	−	0.361777i
$809$	24.0000			0.843795			0.421898	−	0.906644i	$-0.361364\pi$
$809$	24.0000			0.843795			0.421898	+	0.906644i	$0.361364\pi$
$810$		0			0
$811$	−13.6771	+	23.6895i	−0.480269	+	0.831850i	−0.999744	−	0.0226357i	$-0.992794\pi$
$811$	−13.6771	+	23.6895i	−0.480269	+	0.831850i	0.519475	+	0.854486i	$0.326128\pi$
$812$	4.82288	+	8.35347i	0.169250	+	0.293149i
$813$		0			0
$814$	−26.0830	−	45.1771i	−0.914209	−	1.58346i
$815$	1.35425	+	2.34563i	0.0474373	+	0.0821637i
$816$		0			0
$817$	25.9373	−	3.35542i	0.907430	−	0.117391i
$818$	−18.4170			−0.643935
$819$		0			0
$820$	−4.32288	−	7.48744i	−0.150961	−	0.261473i
$821$	−10.2915	+	17.8254i	−0.359176	+	0.622111i	−0.987823	−	0.155579i	$-0.950276\pi$
$821$	−10.2915	+	17.8254i	−0.359176	+	0.622111i	0.628647	+	0.777690i	$0.283609\pi$
$822$		0			0
$823$	−15.6144	+	27.0449i	−0.544283	+	0.942726i	0.454369	+	0.890814i	$0.349865\pi$
$823$	−15.6144	+	27.0449i	−0.544283	+	0.942726i	−0.998652	+	0.0519121i	$0.983468\pi$
$824$	1.93725			0.0674874
$825$		0			0
$826$	−7.00000	+	12.1244i	−0.243561	+	0.421860i
$827$	15.5314	−	26.9011i	0.540079	−	0.935444i	−0.458820	−	0.888529i	$-0.651728\pi$
$827$	15.5314	−	26.9011i	0.540079	−	0.935444i	0.998899	−	0.0469147i	$-0.0149389\pi$
$828$		0			0
$829$	−52.4575			−1.82192			−0.910962	−	0.412489i	$-0.864659\pi$
$829$	−52.4575			−1.82192			−0.910962	+	0.412489i	$0.864659\pi$
$830$	8.29150	−	14.3613i	0.287802	−	0.498488i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−17.5830			−0.608485
$836$	−16.6458	−	21.7944i	−0.575705	−	0.753775i
$837$		0			0
$838$	19.0830	+	33.0527i	0.659211	+	1.14179i
$839$	7.93725	+	13.7477i	0.274024	+	0.474624i	0.969889	−	0.243549i	$-0.0783117\pi$
$839$	7.93725	+	13.7477i	0.274024	+	0.474624i	−0.695864	+	0.718173i	$0.744978\pi$
$840$		0			0
$841$	7.85425	+	13.6040i	0.270836	+	0.469102i
$842$	9.46863	−	16.4001i	0.326310	−	0.565186i
$843$		0			0
$844$	−18.5203			−0.637494
$845$	6.50000	−	11.2583i	0.223607	−	0.387298i
$846$		0			0
$847$	−75.6235			−2.59846
$848$	4.64575			0.159536
$849$		0			0
$850$	−2.82288	−	4.88936i	−0.0968238	−	0.167704i
$851$	4.14575	−	7.18065i	0.142115	−	0.246150i
$852$		0			0
$853$	7.70850	+	13.3515i	0.263934	+	0.457147i	0.967284	−	0.253697i	$-0.0816466\pi$
$853$	7.70850	+	13.3515i	0.263934	+	0.457147i	−0.703350	+	0.710844i	$0.748313\pi$
$854$	−18.3542			−0.628069
$855$		0			0
$856$	−4.35425			−0.148825
$857$	−6.00000	−	10.3923i	−0.204956	−	0.354994i	0.745163	−	0.666883i	$-0.232372\pi$
$857$	−6.00000	−	10.3923i	−0.204956	−	0.354994i	−0.950119	+	0.311888i	$0.899038\pi$
$858$		0			0
$859$	6.26013	−	10.8429i	0.213593	−	0.369954i	−0.739243	−	0.673438i	$-0.764817\pi$
$859$	6.26013	−	10.8429i	0.213593	−	0.369954i	0.952836	+	0.303485i	$0.0981501\pi$
$860$	−3.00000	−	5.19615i	−0.102299	−	0.177187i
$861$		0			0
$862$	−28.3542			−0.965750
$863$	−20.4170			−0.695003			−0.347501	−	0.937680i	$-0.612970\pi$
$863$	−20.4170			−0.695003			−0.347501	+	0.937680i	$0.612970\pi$
$864$		0			0
$865$	3.96863	−	6.87386i	0.134937	−	0.233718i
$866$	4.93725			0.167775
$867$		0			0
$868$	9.64575	−	16.7069i	0.327398	−	0.567070i
$869$	−16.6458	−	28.8313i	−0.564668	−	0.978034i
$870$		0			0
$871$		0			0
$872$	0.177124	+	0.306788i	0.00599819	+	0.0103892i
$873$		0			0
$874$	1.67712	−	4.02334i	0.0567296	−	0.136091i
$875$	−2.64575			−0.0894427
$876$		0			0
$877$	22.1458	+	38.3576i	0.747809	+	1.29524i	0.948871	+	0.315664i	$0.102227\pi$
$877$	22.1458	+	38.3576i	0.747809	+	1.29524i	−0.201062	+	0.979579i	$0.564439\pi$
$878$	1.53137	−	2.65242i	0.0516813	−	0.0895147i
$879$		0			0
$880$	−3.14575	+	5.44860i	−0.106043	+	0.183672i
$881$	35.3542			1.19111			0.595557	−	0.803313i	$-0.296931\pi$
$881$	35.3542			1.19111			0.595557	+	0.803313i	$0.296931\pi$
$882$		0			0
$883$	23.0516	−	39.9266i	0.775749	−	1.34364i	−0.158623	−	0.987339i	$-0.550706\pi$
$883$	23.0516	−	39.9266i	0.775749	−	1.34364i	0.934372	−	0.356298i	$-0.115961\pi$
$884$		0			0
$885$		0			0
$886$	25.0627			0.841999
$887$	−3.22876	+	5.59237i	−0.108411	+	0.187773i	−0.915127	−	0.403166i	$-0.867910\pi$
$887$	−3.22876	+	5.59237i	−0.108411	+	0.187773i	0.806716	+	0.590940i	$0.201243\pi$
$888$		0			0
$889$	−14.8542	+	25.7283i	−0.498196	+	0.862900i
$890$	6.61438	+	11.4564i	0.221714	+	0.384021i
$891$		0			0
$892$	6.64575			0.222516
$893$	33.2915	+	43.5888i	1.11406	+	1.45864i
$894$		0			0
$895$	1.79150	+	3.10297i	0.0598833	+	0.103721i
$896$	1.32288	+	2.29129i	0.0441942	+	0.0765466i
$897$		0			0
$898$	−8.67712	−	15.0292i	−0.289559	−	0.501532i
$899$	−13.2915	+	23.0216i	−0.443296	+	0.767812i
$900$		0			0
$901$	26.2288			0.873807
$902$	−27.1974	+	47.1073i	−0.905574	+	1.56850i
$903$		0			0
$904$	5.64575			0.187775
$905$	−14.3542			−0.477151
$906$		0			0
$907$	8.29150	+	14.3613i	0.275315	+	0.476859i	0.970215	−	0.242247i	$-0.0778846\pi$
$907$	8.29150	+	14.3613i	0.275315	+	0.476859i	−0.694900	+	0.719107i	$0.744551\pi$
$908$	11.4059	−	19.7556i	0.378517	−	0.655611i
$909$		0			0
$910$		0			0
$911$	−13.2915			−0.440367			−0.220184	−	0.975458i	$-0.570666\pi$
$911$	−13.2915			−0.440367			−0.220184	+	0.975458i	$0.570666\pi$
$912$		0			0
$913$	−104.332			−3.45289
$914$	−0.885622	−	1.53394i	−0.0292938	−	0.0507383i
$915$		0			0
$916$	−7.35425	+	12.7379i	−0.242991	+	0.420873i
$917$	10.1974	+	17.6624i	0.336747	+	0.583263i
$918$		0			0
$919$	10.2288			0.337416			0.168708	−	0.985666i	$-0.446041\pi$
$919$	10.2288			0.337416			0.168708	+	0.985666i	$0.446041\pi$
$920$	−1.00000			−0.0329690
$921$		0			0
$922$	−17.5830	+	30.4547i	−0.579065	+	1.00297i
$923$		0			0
$924$		0			0
$925$	−4.14575	+	7.18065i	−0.136311	+	0.236098i
$926$	−14.6771	−	25.4215i	−0.482320	−	0.835403i
$927$		0			0
$928$	−1.82288	−	3.15731i	−0.0598388	−	0.103644i
$929$	−15.9686	−	27.6585i	−0.523914	−	0.907445i	−0.999612	−	0.0278368i	$-0.991138\pi$
$929$	−15.9686	−	27.6585i	−0.523914	−	0.907445i	0.475699	−	0.879608i	$-0.342195\pi$
$930$		0			0
$931$		0			0
$932$	−20.5830			−0.674219
$933$		0			0
$934$	7.76013	+	13.4409i	0.253919	+	0.439801i
$935$	−17.7601	+	30.7614i	−0.580818	+	1.00601i
$936$		0			0
$937$	−18.4686	+	31.9886i	−0.603344	+	1.04502i	0.388967	+	0.921252i	$0.372832\pi$
$937$	−18.4686	+	31.9886i	−0.603344	+	1.04502i	−0.992311	+	0.123770i	$0.960501\pi$
$938$	25.5203			0.833266
$939$		0			0
$940$	6.29150	−	10.8972i	0.205206	−	0.355428i
$941$	23.1144	−	40.0353i	0.753507	−	1.30511i	−0.192606	−	0.981276i	$-0.561694\pi$
$941$	23.1144	−	40.0353i	0.753507	−	1.30511i	0.946113	−	0.323837i	$-0.104973\pi$
$942$		0			0
$943$	−8.64575			−0.281544
$944$	2.64575	−	4.58258i	0.0861119	−	0.149150i
$945$		0			0
$946$	−18.8745	+	32.6916i	−0.613663	+	1.06290i
$947$	−21.6974	−	37.5810i	−0.705070	−	1.22122i	−0.966666	−	0.256040i	$-0.917582\pi$
$947$	−21.6974	−	37.5810i	−0.705070	−	1.22122i	0.261596	−	0.965177i	$-0.415751\pi$
$948$		0			0
$949$		0			0
$950$	−1.67712	+	4.02334i	−0.0544131	+	0.130534i
$951$		0			0
$952$	7.46863	+	12.9360i	0.242060	+	0.419260i
$953$	−14.5830	−	25.2585i	−0.472390	−	0.818203i	0.527111	−	0.849796i	$-0.323275\pi$
$953$	−14.5830	−	25.2585i	−0.472390	−	0.818203i	−0.999501	+	0.0315932i	$0.989942\pi$
$954$		0			0
$955$	−2.29150	−	3.96900i	−0.0741513	−	0.128434i
$956$	−12.0000	+	20.7846i	−0.388108	+	0.672222i
$957$		0			0
$958$	−4.93725			−0.159515
$959$	15.8745	−	27.4955i	0.512615	−	0.887875i
$960$		0			0
$961$	22.1660			0.715033
$962$		0			0
$963$		0			0
$964$	−0.708497	−	1.22715i	−0.0228192	−	0.0395240i
$965$	−5.82288	+	10.0855i	−0.187445	+	0.324664i
$966$		0			0
$967$	−16.9373	−	29.3362i	−0.544665	−	0.943388i	−0.998628	−	0.0523673i	$-0.983323\pi$
$967$	−16.9373	−	29.3362i	−0.544665	−	0.943388i	0.453963	−	0.891021i	$-0.350010\pi$
$968$	28.5830			0.918693
$969$		0			0
$970$	−1.64575			−0.0528419
$971$	−0.874508	−	1.51469i	−0.0280643	−	0.0486088i	0.851652	−	0.524107i	$-0.175601\pi$
$971$	−0.874508	−	1.51469i	−0.0280643	−	0.0486088i	−0.879716	+	0.475499i	$0.842268\pi$
$972$		0			0
$973$	4.35425	−	7.54178i	0.139591	−	0.241778i
$974$	−10.3229	−	17.8797i	−0.330766	−	0.572904i
$975$		0			0
$976$	6.93725			0.222056
$977$	1.06275			0.0340003			0.0170001	−	0.999855i	$-0.494588\pi$
$977$	1.06275			0.0340003			0.0170001	+	0.999855i	$0.494588\pi$
$978$		0			0
$979$	41.6144	−	72.0782i	1.33000	−	2.30363i
$980$		0			0
$981$		0			0
$982$	19.7288	−	34.1712i	0.629570	−	1.09045i
$983$	−24.4373	−	42.3266i	−0.779427	−	1.35001i	−0.932272	−	0.361758i	$-0.882177\pi$
$983$	−24.4373	−	42.3266i	−0.779427	−	1.35001i	0.152845	−	0.988250i	$-0.451157\pi$
$984$		0			0
$985$	−1.32288	−	2.29129i	−0.0421503	−	0.0730065i
$986$	−10.2915	−	17.8254i	−0.327748	−	0.567677i
$987$		0			0
$988$		0			0
$989$	−6.00000			−0.190789
$990$		0			0
$991$	5.82288	+	10.0855i	0.184970	+	0.320377i	0.943566	−	0.331184i	$-0.107448\pi$
$991$	5.82288	+	10.0855i	0.184970	+	0.320377i	−0.758597	+	0.651561i	$0.774115\pi$
$992$	−3.64575	+	6.31463i	−0.115753	+	0.200490i
$993$		0			0
$994$	18.0516	−	31.2663i	0.572563	−	0.991708i
$995$	3.06275			0.0970956
$996$		0			0
$997$	−5.50000	+	9.52628i	−0.174187	+	0.301700i	−0.939880	−	0.341506i	$-0.889063\pi$
$997$	−5.50000	+	9.52628i	−0.174187	+	0.301700i	0.765693	+	0.643206i	$0.222396\pi$
$998$	−3.67712	+	6.36897i	−0.116397	+	0.201606i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.l.j.1261.1		4
3.2	odd	2		570.2.i.i.121.1	✓	4
19.11	even	3	inner	1710.2.l.j.1531.1		4
57.11	odd	6		570.2.i.i.391.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.i.i.121.1	✓	4	3.2	odd	2
570.2.i.i.391.1	yes	4	57.11	odd	6
1710.2.l.j.1261.1		4	1.1	even	1	trivial
1710.2.l.j.1531.1		4	19.11	even	3	inner

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:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -2.64575 q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -2.64575 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{10} +6.29150 q^{11} +(1.32288 + 2.29129i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.82288 - 4.88936i) q^{17} +(-1.67712 + 4.02334i) q^{19} +1.00000 q^{20} +(-3.14575 - 5.44860i) q^{22} +(0.500000 - 0.866025i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(1.32288 - 2.29129i) q^{28} +(-1.82288 + 3.15731i) q^{29} +7.29150 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.82288 + 4.88936i) q^{34} +(1.32288 + 2.29129i) q^{35} +8.29150 q^{37} +(4.32288 - 0.559237i) q^{38} +(-0.500000 - 0.866025i) q^{40} +(-4.32288 - 7.48744i) q^{41} +(-3.00000 - 5.19615i) q^{43} +(-3.14575 + 5.44860i) q^{44} -1.00000 q^{46} +(6.29150 - 10.8972i) q^{47} +1.00000 q^{50} +(-2.32288 + 4.02334i) q^{53} +(-3.14575 - 5.44860i) q^{55} -2.64575 q^{56} +3.64575 q^{58} +(2.64575 + 4.58258i) q^{59} +(-3.46863 + 6.00784i) q^{61} +(-3.64575 - 6.31463i) q^{62} +1.00000 q^{64} +(4.82288 - 8.35347i) q^{67} +5.64575 q^{68} +(1.32288 - 2.29129i) q^{70} +(-6.82288 - 11.8176i) q^{71} +(-6.82288 - 11.8176i) q^{73} +(-4.14575 - 7.18065i) q^{74} +(-2.64575 - 3.46410i) q^{76} -16.6458 q^{77} +(-2.64575 - 4.58258i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-4.32288 + 7.48744i) q^{82} -16.5830 q^{83} +(-2.82288 + 4.88936i) q^{85} +(-3.00000 + 5.19615i) q^{86} +6.29150 q^{88} +(6.61438 - 11.4564i) q^{89} +(0.500000 + 0.866025i) q^{92} -12.5830 q^{94} +(4.32288 - 0.559237i) q^{95} +(0.822876 + 1.42526i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} - 2 q^{5} + 4 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 + 4 * q^8	\( 4 q - 2 q^{2} - 2 q^{4} - 2 q^{5} + 4 q^{8} - 2 q^{10} + 4 q^{11} - 2 q^{16} - 6 q^{17} - 12 q^{19} + 4 q^{20} - 2 q^{22} + 2 q^{23} - 2 q^{25} - 2 q^{29} + 8 q^{31} - 2 q^{32} - 6 q^{34} + 12 q^{37} + 12 q^{38} - 2 q^{40} - 12 q^{41} - 12 q^{43} - 2 q^{44} - 4 q^{46} + 4 q^{47} + 4 q^{50} - 4 q^{53} - 2 q^{55} + 4 q^{58} + 2 q^{61} - 4 q^{62} + 4 q^{64} + 14 q^{67} + 12 q^{68} - 22 q^{71} - 22 q^{73} - 6 q^{74} - 56 q^{77} - 2 q^{80} - 12 q^{82} - 24 q^{83} - 6 q^{85} - 12 q^{86} + 4 q^{88} + 2 q^{92} - 8 q^{94} + 12 q^{95} - 2 q^{97}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 + 4 * q^8 - 2 * q^10 + 4 * q^11 - 2 * q^16 - 6 * q^17 - 12 * q^19 + 4 * q^20 - 2 * q^22 + 2 * q^23 - 2 * q^25 - 2 * q^29 + 8 * q^31 - 2 * q^32 - 6 * q^34 + 12 * q^37 + 12 * q^38 - 2 * q^40 - 12 * q^41 - 12 * q^43 - 2 * q^44 - 4 * q^46 + 4 * q^47 + 4 * q^50 - 4 * q^53 - 2 * q^55 + 4 * q^58 + 2 * q^61 - 4 * q^62 + 4 * q^64 + 14 * q^67 + 12 * q^68 - 22 * q^71 - 22 * q^73 - 6 * q^74 - 56 * q^77 - 2 * q^80 - 12 * q^82 - 24 * q^83 - 6 * q^85 - 12 * q^86 + 4 * q^88 + 2 * q^92 - 8 * q^94 + 12 * q^95 - 2 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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