LMFDB - Embedded newform 1710.2.l.j.1531.2

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			1531.2
Root			$-1.32288 + 2.29129i$ of defining polynomial
Character	$\chi$	$=$	1710.1531
Dual form			1710.2.l.j.1261.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +2.64575 q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +2.64575 q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{10} -4.29150 q^{11} +(-1.32288 + 2.29129i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.177124 + 0.306788i) q^{17} +(-4.32288 + 0.559237i) q^{19} +1.00000 q^{20} +(2.14575 - 3.71655i) q^{22} +(0.500000 + 0.866025i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-1.32288 - 2.29129i) q^{28} +(0.822876 + 1.42526i) q^{29} -3.29150 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.177124 - 0.306788i) q^{34} +(-1.32288 + 2.29129i) q^{35} -2.29150 q^{37} +(1.67712 - 4.02334i) q^{38} +(-0.500000 + 0.866025i) q^{40} +(-1.67712 + 2.90486i) q^{41} +(-3.00000 + 5.19615i) q^{43} +(2.14575 + 3.71655i) q^{44} -1.00000 q^{46} +(-4.29150 - 7.43310i) q^{47} +1.00000 q^{50} +(0.322876 + 0.559237i) q^{53} +(2.14575 - 3.71655i) q^{55} +2.64575 q^{56} -1.64575 q^{58} +(-2.64575 + 4.58258i) q^{59} +(4.46863 + 7.73989i) q^{61} +(1.64575 - 2.85052i) q^{62} +1.00000 q^{64} +(2.17712 + 3.77089i) q^{67} +0.354249 q^{68} +(-1.32288 - 2.29129i) q^{70} +(-4.17712 + 7.23499i) q^{71} +(-4.17712 + 7.23499i) q^{73} +(1.14575 - 1.98450i) q^{74} +(2.64575 + 3.46410i) q^{76} -11.3542 q^{77} +(2.64575 - 4.58258i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-1.67712 - 2.90486i) q^{82} +4.58301 q^{83} +(-0.177124 - 0.306788i) q^{85} +(-3.00000 - 5.19615i) q^{86} -4.29150 q^{88} +(-6.61438 - 11.4564i) q^{89} +(0.500000 - 0.866025i) q^{92} +8.58301 q^{94} +(1.67712 - 4.02334i) q^{95} +(-1.82288 + 3.15731i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times$.

$n$	$191$	$1027$	$1351$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$		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	$-0.333333\pi$
$7$	2.64575			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	−4.29150			−1.29394			−0.646968	−	0.762517i	$-0.723963\pi$
$11$	−4.29150			−1.29394			−0.646968	+	0.762517i	$0.723963\pi$
$12$		0			0
$13$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$13$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$14$	−1.32288	+	2.29129i	−0.353553	+	0.612372i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.177124	+	0.306788i	−0.0429590	+	0.0744071i	−0.886705	−	0.462335i	$-0.847012\pi$
$17$	−0.177124	+	0.306788i	−0.0429590	+	0.0744071i	0.843746	+	0.536742i	$0.180345\pi$
$18$		0			0
$19$	−4.32288	+	0.559237i	−0.991736	+	0.128298i
$19$	−4.32288	+	0.559237i	−0.991736	+	0.128298i
$20$	1.00000			0.223607
$21$		0			0
$22$	2.14575	−	3.71655i	0.457476	−	0.792371i
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i	0.913434	−	0.406986i	$-0.133420\pi$
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i	−0.809177	+	0.587565i	$0.800087\pi$
$24$		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
$29$	0.822876	+	1.42526i	0.152804	+	0.264665i	0.932257	−	0.361796i	$-0.117836\pi$
$29$	0.822876	+	1.42526i	0.152804	+	0.264665i	−0.779453	+	0.626461i	$0.784503\pi$
$30$		0			0
$31$	−3.29150			−0.591171			−0.295586	−	0.955316i	$-0.595515\pi$
$31$	−3.29150			−0.591171			−0.295586	+	0.955316i	$0.595515\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	−0.177124	−	0.306788i	−0.0303766	−	0.0526138i
$35$	−1.32288	+	2.29129i	−0.223607	+	0.387298i
$36$		0			0
$37$	−2.29150			−0.376721			−0.188360	−	0.982100i	$-0.560317\pi$
$37$	−2.29150			−0.376721			−0.188360	+	0.982100i	$0.560317\pi$
$38$	1.67712	−	4.02334i	0.272065	−	0.652672i
$39$		0			0
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	−1.67712	+	2.90486i	−0.261923	+	0.453664i	−0.966753	−	0.255713i	$-0.917690\pi$
$41$	−1.67712	+	2.90486i	−0.261923	+	0.453664i	0.704830	+	0.709376i	$0.251023\pi$
$42$		0			0
$43$	−3.00000	+	5.19615i	−0.457496	+	0.792406i	−0.998828	−	0.0484030i	$-0.984587\pi$
$43$	−3.00000	+	5.19615i	−0.457496	+	0.792406i	0.541332	+	0.840809i	$0.317920\pi$
$44$	2.14575	+	3.71655i	0.323484	+	0.560291i
$45$		0			0
$46$	−1.00000			−0.147442
$47$	−4.29150	−	7.43310i	−0.625980	−	1.08423i	−0.988350	−	0.152195i	$-0.951366\pi$
$47$	−4.29150	−	7.43310i	−0.625980	−	1.08423i	0.362370	−	0.932034i	$-0.381968\pi$
$48$		0			0
$49$		0			0
$50$	1.00000			0.141421
$51$		0			0
$52$		0			0
$53$	0.322876	+	0.559237i	0.0443504	+	0.0768171i	0.887348	−	0.461099i	$-0.152545\pi$
$53$	0.322876	+	0.559237i	0.0443504	+	0.0768171i	−0.842998	+	0.537917i	$0.819212\pi$
$54$		0			0
$55$	2.14575	−	3.71655i	0.289333	−	0.501140i
$56$	2.64575			0.353553
$57$		0			0
$58$	−1.64575			−0.216098
$59$	−2.64575	+	4.58258i	−0.344447	+	0.596601i	−0.985253	−	0.171103i	$-0.945267\pi$
$59$	−2.64575	+	4.58258i	−0.344447	+	0.596601i	0.640806	+	0.767703i	$0.278600\pi$
$60$		0			0
$61$	4.46863	+	7.73989i	0.572149	+	0.990991i	0.996345	+	0.0854208i	$0.0272235\pi$
$61$	4.46863	+	7.73989i	0.572149	+	0.990991i	−0.424196	+	0.905570i	$0.639443\pi$
$62$	1.64575	−	2.85052i	0.209011	−	0.362017i
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	2.17712	+	3.77089i	0.265978	+	0.460688i	0.967819	−	0.251646i	$-0.0809718\pi$
$67$	2.17712	+	3.77089i	0.265978	+	0.460688i	−0.701841	+	0.712333i	$0.747638\pi$
$68$	0.354249			0.0429590
$69$		0			0
$70$	−1.32288	−	2.29129i	−0.158114	−	0.273861i
$71$	−4.17712	+	7.23499i	−0.495733	+	0.858636i	−0.999988	−	0.00491959i	$-0.998434\pi$
$71$	−4.17712	+	7.23499i	−0.495733	+	0.858636i	0.504254	+	0.863555i	$0.331767\pi$
$72$		0			0
$73$	−4.17712	+	7.23499i	−0.488895	+	0.846792i	−0.999918	−	0.0127753i	$-0.995933\pi$
$73$	−4.17712	+	7.23499i	−0.488895	+	0.846792i	0.511023	+	0.859567i	$0.329267\pi$
$74$	1.14575	−	1.98450i	0.133191	−	0.230693i
$75$		0			0
$76$	2.64575	+	3.46410i	0.303488	+	0.397360i
$77$	−11.3542			−1.29394
$78$		0			0
$79$	2.64575	−	4.58258i	0.297670	−	0.515580i	−0.677932	−	0.735124i	$-0.737124\pi$
$79$	2.64575	−	4.58258i	0.297670	−	0.515580i	0.975603	+	0.219544i	$0.0704571\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$		0			0
$82$	−1.67712	−	2.90486i	−0.185207	−	0.320789i
$83$	4.58301			0.503050			0.251525	−	0.967851i	$-0.419068\pi$
$83$	4.58301			0.503050			0.251525	+	0.967851i	$0.419068\pi$
$84$		0			0
$85$	−0.177124	−	0.306788i	−0.0192118	−	0.0332759i
$86$	−3.00000	−	5.19615i	−0.323498	−	0.560316i
$87$		0			0
$88$	−4.29150			−0.457476
$89$	−6.61438	−	11.4564i	−0.701123	−	1.21438i	−0.968073	−	0.250670i	$-0.919349\pi$
$89$	−6.61438	−	11.4564i	−0.701123	−	1.21438i	0.266950	−	0.963710i	$-0.413984\pi$
$90$		0			0
$91$		0			0
$92$	0.500000	−	0.866025i	0.0521286	−	0.0902894i
$93$		0			0
$94$	8.58301			0.885269
$95$	1.67712	−	4.02334i	0.172069	−	0.412786i
$96$		0			0
$97$	−1.82288	+	3.15731i	−0.185085	+	0.320577i	−0.943605	−	0.331073i	$-0.892589\pi$
$97$	−1.82288	+	3.15731i	−0.185085	+	0.320577i	0.758520	+	0.651650i	$0.225923\pi$
$98$		0			0
$99$		0			0
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−9.93725	−	17.2118i	−0.988794	−	1.71264i	−0.623684	−	0.781676i	$-0.714365\pi$
$101$	−9.93725	−	17.2118i	−0.988794	−	1.71264i	−0.365109	−	0.930965i	$-0.618968\pi$
$102$		0			0
$103$	−13.9373			−1.37328			−0.686639	−	0.726998i	$-0.740915\pi$
$103$	−13.9373			−1.37328			−0.686639	+	0.726998i	$0.740915\pi$
$104$		0			0
$105$		0			0
$106$	−0.645751			−0.0627209
$107$	−9.64575			−0.932490			−0.466245	−	0.884656i	$-0.654393\pi$
$107$	−9.64575			−0.932490			−0.466245	+	0.884656i	$0.654393\pi$
$108$		0			0
$109$	2.82288	−	4.88936i	0.270382	−	0.468316i	−0.698577	−	0.715535i	$-0.746183\pi$
$109$	2.82288	−	4.88936i	0.270382	−	0.468316i	0.968960	+	0.247218i	$0.0795165\pi$
$110$	2.14575	+	3.71655i	0.204589	+	0.354359i
$111$		0			0
$112$	−1.32288	+	2.29129i	−0.125000	+	0.216506i
$113$	0.354249			0.0333249			0.0166625	−	0.999861i	$-0.494696\pi$
$113$	0.354249			0.0333249			0.0166625	+	0.999861i	$0.494696\pi$
$114$		0			0
$115$	−1.00000			−0.0932505
$116$	0.822876	−	1.42526i	0.0764021	−	0.132332i
$117$		0			0
$118$	−2.64575	−	4.58258i	−0.243561	−	0.421860i
$119$	−0.468627	+	0.811686i	−0.0429590	+	0.0744071i
$120$		0			0
$121$	7.41699			0.674272
$122$	−8.93725			−0.809141
$123$		0			0
$124$	1.64575	+	2.85052i	0.147793	+	0.255985i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−7.61438	−	13.1885i	−0.675667	−	1.17029i	−0.976274	−	0.216541i	$-0.930522\pi$
$127$	−7.61438	−	13.1885i	−0.675667	−	1.17029i	0.300607	−	0.953748i	$-0.402811\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$		0			0
$131$	−9.14575	+	15.8409i	−0.799068	+	1.38403i	0.121156	+	0.992634i	$0.461340\pi$
$131$	−9.14575	+	15.8409i	−0.799068	+	1.38403i	−0.920224	+	0.391393i	$0.871993\pi$
$132$		0			0
$133$	−11.4373	+	1.47960i	−0.991736	+	0.128298i
$134$	−4.35425			−0.376150
$135$		0			0
$136$	−0.177124	+	0.306788i	−0.0151883	+	0.0263069i
$137$	−6.00000	−	10.3923i	−0.512615	−	0.887875i	−0.999893	−	0.0146279i	$-0.995344\pi$
$137$	−6.00000	−	10.3923i	−0.512615	−	0.887875i	0.487278	−	0.873247i	$-0.337990\pi$
$138$		0			0
$139$	3.64575	+	6.31463i	0.309229	+	0.535600i	0.978194	−	0.207694i	$-0.0665958\pi$
$139$	3.64575	+	6.31463i	0.309229	+	0.535600i	−0.668965	+	0.743294i	$0.733263\pi$
$140$	2.64575			0.223607
$141$		0			0
$142$	−4.17712	−	7.23499i	−0.350536	−	0.607147i
$143$		0			0
$144$		0			0
$145$	−1.64575			−0.136672
$146$	−4.17712	−	7.23499i	−0.345701	−	0.598772i
$147$		0			0
$148$	1.14575	+	1.98450i	0.0941802	+	0.163125i
$149$	5.11438	−	8.85836i	0.418986	−	0.725705i	−0.576852	−	0.816849i	$-0.695719\pi$
$149$	5.11438	−	8.85836i	0.418986	−	0.725705i	0.995838	+	0.0911436i	$0.0290522\pi$
$150$		0			0
$151$	6.22876			0.506889			0.253445	−	0.967350i	$-0.418436\pi$
$151$	6.22876			0.506889			0.253445	+	0.967350i	$0.418436\pi$
$152$	−4.32288	+	0.559237i	−0.350632	+	0.0453601i
$153$		0			0
$154$	5.67712	−	9.83307i	0.457476	−	0.792371i
$155$	1.64575	−	2.85052i	0.132190	−	0.228960i
$156$		0			0
$157$	−9.43725	+	16.3458i	−0.753175	+	1.30454i	0.193102	+	0.981179i	$0.438145\pi$
$157$	−9.43725	+	16.3458i	−0.753175	+	1.30454i	−0.946277	+	0.323358i	$0.895188\pi$
$158$	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
$163$	−13.2915			−1.04107			−0.520535	−	0.853840i	$-0.674268\pi$
$163$	−13.2915			−1.04107			−0.520535	+	0.853840i	$0.674268\pi$
$164$	3.35425			0.261923
$165$		0			0
$166$	−2.29150	+	3.96900i	−0.177855	+	0.308054i
$167$	−1.79150	−	3.10297i	−0.138631	−	0.240115i	0.788348	−	0.615230i	$-0.210937\pi$
$167$	−1.79150	−	3.10297i	−0.138631	−	0.240115i	−0.926979	+	0.375114i	$0.877603\pi$
$168$		0			0
$169$	6.50000	−	11.2583i	0.500000	−	0.866025i
$170$	0.354249			0.0271696
$171$		0			0
$172$	6.00000			0.457496
$173$	−3.96863	+	6.87386i	−0.301729	+	0.522610i	−0.976528	−	0.215392i	$-0.930897\pi$
$173$	−3.96863	+	6.87386i	−0.301729	+	0.522610i	0.674799	+	0.738002i	$0.264230\pi$
$174$		0			0
$175$	−1.32288	−	2.29129i	−0.100000	−	0.173205i
$176$	2.14575	−	3.71655i	0.161742	−	0.280146i
$177$		0			0
$178$	13.2288			0.991537
$179$	17.5830			1.31422			0.657108	−	0.753797i	$-0.271780\pi$
$179$	17.5830			1.31422			0.657108	+	0.753797i	$0.271780\pi$
$180$		0			0
$181$	9.82288	+	17.0137i	0.730129	+	1.26462i	0.956828	+	0.290655i	$0.0938732\pi$
$181$	9.82288	+	17.0137i	0.730129	+	1.26462i	−0.226699	+	0.973965i	$0.572793\pi$
$182$		0			0
$183$		0			0
$184$	0.500000	+	0.866025i	0.0368605	+	0.0638442i
$185$	1.14575	−	1.98450i	0.0842373	−	0.145903i
$186$		0			0
$187$	0.760130	−	1.31658i	0.0555862	−	0.0962781i
$188$	−4.29150	+	7.43310i	−0.312990	+	0.542115i
$189$		0			0
$190$	2.64575	+	3.46410i	0.191943	+	0.251312i
$191$	−16.5830			−1.19990			−0.599952	−	0.800036i	$-0.704814\pi$
$191$	−16.5830			−1.19990			−0.599952	+	0.800036i	$0.704814\pi$
$192$		0			0
$193$	−3.17712	+	5.50294i	−0.228694	+	0.396110i	−0.957421	−	0.288694i	$-0.906779\pi$
$193$	−3.17712	+	5.50294i	−0.228694	+	0.396110i	0.728727	+	0.684804i	$0.240112\pi$
$194$	−1.82288	−	3.15731i	−0.130875	−	0.226682i
$195$		0			0
$196$		0			0
$197$	−2.64575			−0.188502			−0.0942510	−	0.995548i	$-0.530046\pi$
$197$	−2.64575			−0.188502			−0.0942510	+	0.995548i	$0.530046\pi$
$198$		0			0
$199$	−9.46863	−	16.4001i	−0.671213	−	1.16258i	−0.977560	−	0.210655i	$-0.932440\pi$
$199$	−9.46863	−	16.4001i	−0.671213	−	1.16258i	0.306347	−	0.951920i	$-0.400893\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$		0			0
$202$	19.8745			1.39837
$203$	2.17712	+	3.77089i	0.152804	+	0.264665i
$204$		0			0
$205$	−1.67712	−	2.90486i	−0.117135	−	0.202885i
$206$	6.96863	−	12.0700i	0.485527	−	0.840958i
$207$		0			0
$208$		0			0
$209$	18.5516	−	2.39997i	1.28324	−	0.166009i
$210$		0			0
$211$	−9.26013	+	16.0390i	−0.637494	+	1.10417i	0.348487	+	0.937313i	$0.386695\pi$
$211$	−9.26013	+	16.0390i	−0.637494	+	1.10417i	−0.985981	+	0.166858i	$0.946638\pi$
$212$	0.322876	−	0.559237i	0.0221752	−	0.0384086i
$213$		0			0
$214$	4.82288	−	8.35347i	0.329685	−	0.571031i
$215$	−3.00000	−	5.19615i	−0.204598	−	0.354375i
$216$		0			0
$217$	−8.70850			−0.591171
$218$	2.82288	+	4.88936i	0.191189	+	0.331150i
$219$		0			0
$220$	−4.29150			−0.289333
$221$		0			0
$222$		0			0
$223$	−0.677124	+	1.17281i	−0.0453436	+	0.0785374i	−0.887806	−	0.460217i	$-0.847772\pi$
$223$	−0.677124	+	1.17281i	−0.0453436	+	0.0785374i	0.842463	+	0.538754i	$0.181105\pi$
$224$	−1.32288	−	2.29129i	−0.0883883	−	0.153093i
$225$		0			0
$226$	−0.177124	+	0.306788i	−0.0117821	+	0.0204073i
$227$	24.8118			1.64681			0.823407	−	0.567451i	$-0.192070\pi$
$227$	24.8118			1.64681			0.823407	+	0.567451i	$0.192070\pi$
$228$		0			0
$229$	25.2915			1.67131			0.835655	−	0.549255i	$-0.185088\pi$
$229$	25.2915			1.67131			0.835655	+	0.549255i	$0.185088\pi$
$230$	0.500000	−	0.866025i	0.0329690	−	0.0571040i
$231$		0			0
$232$	0.822876	+	1.42526i	0.0540244	+	0.0935731i
$233$	−0.291503	+	0.504897i	−0.0190970	+	0.0330769i	−0.875416	−	0.483370i	$-0.839412\pi$
$233$	−0.291503	+	0.504897i	−0.0190970	+	0.0330769i	0.856319	+	0.516447i	$0.172746\pi$
$234$		0			0
$235$	8.58301			0.559894
$236$	5.29150			0.344447
$237$		0			0
$238$	−0.468627	−	0.811686i	−0.0303766	−	0.0526138i
$239$	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
$241$	−11.2915	−	19.5575i	−0.727350	−	1.25981i	−0.958000	−	0.286770i	$-0.907419\pi$
$241$	−11.2915	−	19.5575i	−0.727350	−	1.25981i	0.230650	−	0.973037i	$-0.425915\pi$
$242$	−3.70850	+	6.42331i	−0.238391	+	0.412906i
$243$		0			0
$244$	4.46863	−	7.73989i	0.286075	−	0.495496i
$245$		0			0
$246$		0			0
$247$		0			0
$248$	−3.29150			−0.209011
$249$		0			0
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	9.29150	+	16.0934i	0.586474	+	1.01580i	0.994690	+	0.102918i	$0.0328179\pi$
$251$	9.29150	+	16.0934i	0.586474	+	1.01580i	−0.408215	+	0.912886i	$0.633849\pi$
$252$		0			0
$253$	−2.14575	−	3.71655i	−0.134902	−	0.233658i
$254$	15.2288			0.955537
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.00000	+	5.19615i	0.187135	+	0.324127i	0.944294	−	0.329104i	$-0.106747\pi$
$257$	3.00000	+	5.19615i	0.187135	+	0.324127i	−0.757159	+	0.653231i	$0.773413\pi$
$258$		0			0
$259$	−6.06275			−0.376721
$260$		0			0
$261$		0			0
$262$	−9.14575	−	15.8409i	−0.565026	−	0.978654i
$263$	−3.14575	+	5.44860i	−0.193975	+	0.335975i	−0.946564	−	0.322516i	$-0.895472\pi$
$263$	−3.14575	+	5.44860i	−0.193975	+	0.335975i	0.752589	+	0.658491i	$0.228805\pi$
$264$		0			0
$265$	−0.645751			−0.0396682
$266$	4.43725	−	10.6448i	0.272065	−	0.652672i
$267$		0			0
$268$	2.17712	−	3.77089i	0.132989	−	0.230344i
$269$	−1.46863	+	2.54374i	−0.0895438	+	0.155094i	−0.907318	−	0.420444i	$-0.861874\pi$
$269$	−1.46863	+	2.54374i	−0.0895438	+	0.155094i	0.817775	+	0.575539i	$0.195208\pi$
$270$		0			0
$271$	9.93725	−	17.2118i	0.603645	−	1.04554i	−0.388619	−	0.921399i	$-0.627048\pi$
$271$	9.93725	−	17.2118i	0.603645	−	1.04554i	0.992264	−	0.124146i	$-0.0396190\pi$
$272$	−0.177124	−	0.306788i	−0.0107397	−	0.0186018i
$273$		0			0
$274$	12.0000			0.724947
$275$	2.14575	+	3.71655i	0.129394	+	0.224116i
$276$		0			0
$277$	−8.00000			−0.480673			−0.240337	−	0.970690i	$-0.577258\pi$
$277$	−8.00000			−0.480673			−0.240337	+	0.970690i	$0.577258\pi$
$278$	−7.29150			−0.437315
$279$		0			0
$280$	−1.32288	+	2.29129i	−0.0790569	+	0.136931i
$281$	13.9059	+	24.0857i	0.829555	+	1.43683i	0.898388	+	0.439204i	$0.144739\pi$
$281$	13.9059	+	24.0857i	0.829555	+	1.43683i	−0.0688322	+	0.997628i	$0.521927\pi$
$282$		0			0
$283$	5.93725	−	10.2836i	0.352933	−	0.611298i	−0.633829	−	0.773473i	$-0.718518\pi$
$283$	5.93725	−	10.2836i	0.352933	−	0.611298i	0.986762	+	0.162175i	$0.0518510\pi$
$284$	8.35425			0.495733
$285$		0			0
$286$		0			0
$287$	−4.43725	+	7.68555i	−0.261923	+	0.453664i
$288$		0			0
$289$	8.43725	+	14.6138i	0.496309	+	0.859632i
$290$	0.822876	−	1.42526i	0.0483209	−	0.0836943i
$291$		0			0
$292$	8.35425			0.488895
$293$	14.6458			0.855614			0.427807	−	0.903870i	$-0.359286\pi$
$293$	14.6458			0.855614			0.427807	+	0.903870i	$0.359286\pi$
$294$		0			0
$295$	−2.64575	−	4.58258i	−0.154042	−	0.266808i
$296$	−2.29150			−0.133191
$297$		0			0
$298$	5.11438	+	8.85836i	0.296268	+	0.513151i
$299$		0			0
$300$		0			0
$301$	−7.93725	+	13.7477i	−0.457496	+	0.792406i
$302$	−3.11438	+	5.39426i	−0.179212	+	0.310405i
$303$		0			0
$304$	1.67712	−	4.02334i	0.0961897	−	0.230754i
$305$	−8.93725			−0.511746
$306$		0			0
$307$	−5.76013	+	9.97684i	−0.328748	+	0.569408i	−0.982264	−	0.187505i	$-0.939960\pi$
$307$	−5.76013	+	9.97684i	−0.328748	+	0.569408i	0.653516	+	0.756913i	$0.273293\pi$
$308$	5.67712	+	9.83307i	0.323484	+	0.560291i
$309$		0			0
$310$	1.64575	+	2.85052i	0.0934724	+	0.161899i
$311$	−17.1660			−0.973395			−0.486698	−	0.873571i	$-0.661799\pi$
$311$	−17.1660			−0.973395			−0.486698	+	0.873571i	$0.661799\pi$
$312$		0			0
$313$	−9.29150	−	16.0934i	−0.525187	−	0.909650i	−0.999570	−	0.0293316i	$-0.990662\pi$
$313$	−9.29150	−	16.0934i	−0.525187	−	0.909650i	0.474383	−	0.880319i	$-0.342671\pi$
$314$	−9.43725	−	16.3458i	−0.532575	−	0.922447i
$315$		0			0
$316$	−5.29150			−0.297670
$317$	9.96863	+	17.2662i	0.559894	+	0.969765i	0.997505	+	0.0706001i	$0.0224914\pi$
$317$	9.96863	+	17.2662i	0.559894	+	0.969765i	−0.437611	+	0.899164i	$0.644175\pi$
$318$		0			0
$319$	−3.53137	−	6.11652i	−0.197719	−	0.342459i
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$		0			0
$322$	−2.64575			−0.147442
$323$	0.594119	−	1.42526i	0.0330577	−	0.0793037i
$324$		0			0
$325$		0			0
$326$	6.64575	−	11.5108i	0.368074	−	0.637523i
$327$		0			0
$328$	−1.67712	+	2.90486i	−0.0926037	+	0.160394i
$329$	−11.3542	−	19.6661i	−0.625980	−	1.08423i
$330$		0			0
$331$	−13.3542			−0.734016			−0.367008	−	0.930218i	$-0.619618\pi$
$331$	−13.3542			−0.734016			−0.367008	+	0.930218i	$0.619618\pi$
$332$	−2.29150	−	3.96900i	−0.125763	−	0.217827i
$333$		0			0
$334$	3.58301			0.196053
$335$	−4.35425			−0.237898
$336$		0			0
$337$	−8.64575	+	14.9749i	−0.470964	+	0.815734i	−0.999448	−	0.0332093i	$-0.989427\pi$
$337$	−8.64575	+	14.9749i	−0.470964	+	0.815734i	0.528484	+	0.848943i	$0.322761\pi$
$338$	6.50000	+	11.2583i	0.353553	+	0.612372i
$339$		0			0
$340$	−0.177124	+	0.306788i	−0.00960592	+	0.0166379i
$341$	14.1255			0.764938
$342$		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
$347$	−4.29150	+	7.43310i	−0.230380	+	0.399030i	−0.957920	−	0.287036i	$-0.907330\pi$
$347$	−4.29150	+	7.43310i	−0.230380	+	0.399030i	0.727540	+	0.686065i	$0.240664\pi$
$348$		0			0
$349$	32.9373			1.76309			0.881545	−	0.472099i	$-0.156504\pi$
$349$	32.9373			1.76309			0.881545	+	0.472099i	$0.156504\pi$
$350$	2.64575			0.141421
$351$		0			0
$352$	2.14575	+	3.71655i	0.114369	+	0.198093i
$353$	22.9373			1.22083			0.610413	−	0.792083i	$-0.291003\pi$
$353$	22.9373			1.22083			0.610413	+	0.792083i	$0.291003\pi$
$354$		0			0
$355$	−4.17712	−	7.23499i	−0.221699	−	0.383993i
$356$	−6.61438	+	11.4564i	−0.350561	+	0.607190i
$357$		0			0
$358$	−8.79150	+	15.2273i	−0.464645	+	0.804789i
$359$	−5.46863	+	9.47194i	−0.288623	+	0.499910i	−0.973481	−	0.228766i	$-0.926531\pi$
$359$	−5.46863	+	9.47194i	−0.288623	+	0.499910i	0.684858	+	0.728676i	$0.259864\pi$
$360$		0			0
$361$	18.3745	−	4.83502i	0.967079	−	0.254475i
$362$	−19.6458			−1.03256
$363$		0			0
$364$		0			0
$365$	−4.17712	−	7.23499i	−0.218641	−	0.378697i
$366$		0			0
$367$	−14.9373	−	25.8721i	−0.779718	−	1.35051i	−0.932104	−	0.362191i	$-0.882029\pi$
$367$	−14.9373	−	25.8721i	−0.779718	−	1.35051i	0.152386	−	0.988321i	$-0.451304\pi$
$368$	−1.00000			−0.0521286
$369$		0			0
$370$	1.14575	+	1.98450i	0.0595648	+	0.103169i
$371$	0.854249	+	1.47960i	0.0443504	+	0.0768171i
$372$		0			0
$373$	7.70850			0.399131			0.199565	−	0.979885i	$-0.436047\pi$
$373$	7.70850			0.399131			0.199565	+	0.979885i	$0.436047\pi$
$374$	0.760130	+	1.31658i	0.0393054	+	0.0680789i
$375$		0			0
$376$	−4.29150	−	7.43310i	−0.221317	−	0.383333i
$377$		0			0
$378$		0			0
$379$	−13.8745			−0.712686			−0.356343	−	0.934355i	$-0.615976\pi$
$379$	−13.8745			−0.712686			−0.356343	+	0.934355i	$0.615976\pi$
$380$	−4.32288	+	0.559237i	−0.221759	+	0.0286883i
$381$		0			0
$382$	8.29150	−	14.3613i	0.424230	−	0.734788i
$383$	−7.70850	+	13.3515i	−0.393886	+	0.682230i	−0.992958	−	0.118465i	$-0.962203\pi$
$383$	−7.70850	+	13.3515i	−0.393886	+	0.682230i	0.599072	+	0.800695i	$0.295536\pi$
$384$		0			0
$385$	5.67712	−	9.83307i	0.289333	−	0.501140i
$386$	−3.17712	−	5.50294i	−0.161711	−	0.280092i
$387$		0			0
$388$	3.64575			0.185085
$389$	9.76013	+	16.9050i	0.494858	+	0.857120i	0.999982	−	0.00592708i	$-0.00188666\pi$
$389$	9.76013	+	16.9050i	0.494858	+	0.857120i	−0.505124	+	0.863047i	$0.668553\pi$
$390$		0			0
$391$	−0.354249			−0.0179151
$392$		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
$397$	−12.7288	+	22.0469i	−0.638838	+	1.10650i	0.346850	+	0.937921i	$0.387251\pi$
$397$	−12.7288	+	22.0469i	−0.638838	+	1.10650i	−0.985688	+	0.168579i	$0.946082\pi$
$398$	18.9373			0.949239
$399$		0			0
$400$	1.00000			0.0500000
$401$	3.00000	−	5.19615i	0.149813	−	0.259483i	−0.781345	−	0.624099i	$-0.785466\pi$
$401$	3.00000	−	5.19615i	0.149813	−	0.259483i	0.931158	+	0.364615i	$0.118800\pi$
$402$		0			0
$403$		0			0
$404$	−9.93725	+	17.2118i	−0.494397	+	0.856320i
$405$		0			0
$406$	−4.35425			−0.216098
$407$	9.83399			0.487453
$408$		0			0
$409$	19.7915	+	34.2799i	0.978627	+	1.69503i	0.667407	+	0.744694i	$0.267404\pi$
$409$	19.7915	+	34.2799i	0.978627	+	1.69503i	0.311220	+	0.950338i	$0.399262\pi$
$410$	3.35425			0.165655
$411$		0			0
$412$	6.96863	+	12.0700i	0.343320	+	0.594647i
$413$	−7.00000	+	12.1244i	−0.344447	+	0.596601i
$414$		0			0
$415$	−2.29150	+	3.96900i	−0.112485	+	0.194830i
$416$		0			0
$417$		0			0
$418$	−7.19738	+	17.2662i	−0.352036	+	0.844516i
$419$	4.16601			0.203523			0.101761	−	0.994809i	$-0.467552\pi$
$419$	4.16601			0.203523			0.101761	+	0.994809i	$0.467552\pi$
$420$		0			0
$421$	1.53137	−	2.65242i	0.0746346	−	0.129271i	−0.826293	−	0.563241i	$-0.809554\pi$
$421$	1.53137	−	2.65242i	0.0746346	−	0.129271i	0.900927	+	0.433970i	$0.142888\pi$
$422$	−9.26013	−	16.0390i	−0.450776	−	0.780767i
$423$		0			0
$424$	0.322876	+	0.559237i	0.0156802	+	0.0271590i
$425$	0.354249			0.0171836
$426$		0			0
$427$	11.8229	+	20.4778i	0.572149	+	0.990991i
$428$	4.82288	+	8.35347i	0.233122	+	0.403780i
$429$		0			0
$430$	6.00000			0.289346
$431$	16.8229	+	29.1381i	0.810329	+	1.40353i	0.912634	+	0.408779i	$0.134045\pi$
$431$	16.8229	+	29.1381i	0.810329	+	1.40353i	−0.102304	+	0.994753i	$0.532622\pi$
$432$		0			0
$433$	5.46863	+	9.47194i	0.262805	+	0.455192i	0.966986	−	0.254828i	$-0.0820189\pi$
$433$	5.46863	+	9.47194i	0.262805	+	0.455192i	−0.704181	+	0.710021i	$0.748686\pi$
$434$	4.35425	−	7.54178i	0.209011	−	0.362017i
$435$		0			0
$436$	−5.64575			−0.270382
$437$	−2.64575	−	3.46410i	−0.126563	−	0.165710i
$438$		0			0
$439$	9.46863	−	16.4001i	0.451913	−	0.782736i	−0.546592	−	0.837399i	$-0.684075\pi$
$439$	9.46863	−	16.4001i	0.451913	−	0.782736i	0.998505	+	0.0546630i	$0.0174084\pi$
$440$	2.14575	−	3.71655i	0.102295	−	0.177180i
$441$		0			0
$442$		0			0
$443$	−20.4686	−	35.4527i	−0.972494	−	1.68441i	−0.687969	−	0.725740i	$-0.741498\pi$
$443$	−20.4686	−	35.4527i	−0.972494	−	1.68441i	−0.284525	−	0.958669i	$-0.591836\pi$
$444$		0			0
$445$	13.2288			0.627103
$446$	−0.677124	−	1.17281i	−0.0320628	−	0.0555343i
$447$		0			0
$448$	2.64575			0.125000
$449$	22.6458			1.06872			0.534360	−	0.845257i	$-0.320553\pi$
$449$	22.6458			1.06872			0.534360	+	0.845257i	$0.320553\pi$
$450$		0			0
$451$	7.19738	−	12.4662i	0.338912	−	0.587012i
$452$	−0.177124	−	0.306788i	−0.00833123	−	0.0144301i
$453$		0			0
$454$	−12.4059	+	21.4876i	−0.582237	+	1.00846i
$455$		0			0
$456$		0			0
$457$	28.2288			1.32049			0.660243	−	0.751052i	$-0.270453\pi$
$457$	28.2288			1.32049			0.660243	+	0.751052i	$0.270453\pi$
$458$	−12.6458	+	21.9031i	−0.590897	+	1.02346i
$459$		0			0
$460$	0.500000	+	0.866025i	0.0233126	+	0.0403786i
$461$	3.58301	−	6.20595i	0.166877	−	0.289040i	−0.770443	−	0.637509i	$-0.779965\pi$
$461$	3.58301	−	6.20595i	0.166877	−	0.289040i	0.937320	+	0.348469i	$0.113298\pi$
$462$		0			0
$463$	34.6458			1.61012			0.805062	−	0.593190i	$-0.202132\pi$
$463$	34.6458			1.61012			0.805062	+	0.593190i	$0.202132\pi$
$464$	−1.64575			−0.0764021
$465$		0			0
$466$	−0.291503	−	0.504897i	−0.0135036	−	0.0233889i
$467$	21.5203			0.995839			0.497919	−	0.867223i	$-0.334098\pi$
$467$	21.5203			0.995839			0.497919	+	0.867223i	$0.334098\pi$
$468$		0			0
$469$	5.76013	+	9.97684i	0.265978	+	0.460688i
$470$	−4.29150	+	7.43310i	−0.197952	+	0.342863i
$471$		0			0
$472$	−2.64575	+	4.58258i	−0.121781	+	0.210930i
$473$	12.8745	−	22.2993i	0.591971	−	1.02532i
$474$		0			0
$475$	2.64575	+	3.46410i	0.121395	+	0.158944i
$476$	0.937254			0.0429590
$477$		0			0
$478$	−12.0000	+	20.7846i	−0.548867	+	0.950666i
$479$	−5.46863	−	9.47194i	−0.249868	−	0.432784i	0.713621	−	0.700532i	$-0.247054\pi$
$479$	−5.46863	−	9.47194i	−0.249868	−	0.432784i	−0.963489	+	0.267748i	$0.913721\pi$
$480$		0			0
$481$		0			0
$482$	22.5830			1.02863
$483$		0			0
$484$	−3.70850	−	6.42331i	−0.168568	−	0.291968i
$485$	−1.82288	−	3.15731i	−0.0827725	−	0.143366i
$486$		0			0
$487$	15.3542			0.695767			0.347884	−	0.937538i	$-0.386900\pi$
$487$	15.3542			0.695767			0.347884	+	0.937538i	$0.386900\pi$
$488$	4.46863	+	7.73989i	0.202285	+	0.350368i
$489$		0			0
$490$		0			0
$491$	−6.72876	+	11.6545i	−0.303665	+	0.525962i	−0.976963	−	0.213408i	$-0.931544\pi$
$491$	−6.72876	+	11.6545i	−0.303665	+	0.525962i	0.673299	+	0.739371i	$0.264877\pi$
$492$		0			0
$493$	−0.583005			−0.0262572
$494$		0			0
$495$		0			0
$496$	1.64575	−	2.85052i	0.0738964	−	0.127992i
$497$	−11.0516	+	19.1420i	−0.495733	+	0.858636i
$498$		0			0
$499$	−6.32288	+	10.9515i	−0.283051	+	0.490258i	−0.972135	−	0.234423i	$-0.924680\pi$
$499$	−6.32288	+	10.9515i	−0.283051	+	0.490258i	0.689084	+	0.724682i	$0.258013\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$		0			0
$502$	−18.5830			−0.829400
$503$	−18.3745	−	31.8256i	−0.819279	−	1.41903i	−0.906214	−	0.422819i	$-0.861041\pi$
$503$	−18.3745	−	31.8256i	−0.819279	−	1.41903i	0.0869355	−	0.996214i	$-0.472293\pi$
$504$		0			0
$505$	19.8745			0.884404
$506$	4.29150			0.190781
$507$		0			0
$508$	−7.61438	+	13.1885i	−0.337833	+	0.585145i
$509$	−6.64575	−	11.5108i	−0.294568	−	0.510206i	0.680317	−	0.732918i	$-0.261842\pi$
$509$	−6.64575	−	11.5108i	−0.294568	−	0.510206i	−0.974884	+	0.222712i	$0.928509\pi$
$510$		0			0
$511$	−11.0516	+	19.1420i	−0.488895	+	0.846792i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−6.00000			−0.264649
$515$	6.96863	−	12.0700i	0.307074	−	0.531868i
$516$		0			0
$517$	18.4170	+	31.8992i	0.809979	+	1.40292i
$518$	3.03137	−	5.25049i	0.133191	−	0.230693i
$519$		0			0
$520$		0			0
$521$	30.4575			1.33437			0.667184	−	0.744893i	$-0.267499\pi$
$521$	30.4575			1.33437			0.667184	+	0.744893i	$0.267499\pi$
$522$		0			0
$523$	20.1144	+	34.8391i	0.879540	+	1.52341i	0.851846	+	0.523792i	$0.175483\pi$
$523$	20.1144	+	34.8391i	0.879540	+	1.52341i	0.0276942	+	0.999616i	$0.491184\pi$
$524$	18.2915			0.799068
$525$		0			0
$526$	−3.14575	−	5.44860i	−0.137161	−	0.237570i
$527$	0.583005	−	1.00979i	0.0253961	−	0.0439873i
$528$		0			0
$529$	11.0000	−	19.0526i	0.478261	−	0.828372i
$530$	0.322876	−	0.559237i	0.0140248	−	0.0242917i
$531$		0			0
$532$	7.00000	+	9.16515i	0.303488	+	0.397360i
$533$		0			0
$534$		0			0
$535$	4.82288	−	8.35347i	0.208511	−	0.361152i
$536$	2.17712	+	3.77089i	0.0940374	+	0.162878i
$537$		0			0
$538$	−1.46863	−	2.54374i	−0.0633170	−	0.109668i
$539$		0			0
$540$		0			0
$541$	6.93725	+	12.0157i	0.298256	+	0.516594i	0.975737	−	0.218946i	$-0.0702618\pi$
$541$	6.93725	+	12.0157i	0.298256	+	0.516594i	−0.677481	+	0.735540i	$0.736928\pi$
$542$	9.93725	+	17.2118i	0.426842	+	0.739311i
$543$		0			0
$544$	0.354249			0.0151883
$545$	2.82288	+	4.88936i	0.120919	+	0.209437i
$546$		0			0
$547$	−14.6458	−	25.3672i	−0.626207	−	1.08462i	−0.988306	−	0.152483i	$-0.951273\pi$
$547$	−14.6458	−	25.3672i	−0.626207	−	1.08462i	0.362099	−	0.932140i	$-0.382060\pi$
$548$	−6.00000	+	10.3923i	−0.256307	+	0.443937i
$549$		0			0
$550$	−4.29150			−0.182990
$551$	−4.35425	−	5.70105i	−0.185497	−	0.242873i
$552$		0			0
$553$	7.00000	−	12.1244i	0.297670	−	0.515580i
$554$	4.00000	−	6.92820i	0.169944	−	0.294351i
$555$		0			0
$556$	3.64575	−	6.31463i	0.154614	−	0.267800i
$557$	6.26013	+	10.8429i	0.265250	+	0.459427i	0.967629	−	0.252376i	$-0.0812121\pi$
$557$	6.26013	+	10.8429i	0.265250	+	0.459427i	−0.702379	+	0.711803i	$0.747879\pi$
$558$		0			0
$559$		0			0
$560$	−1.32288	−	2.29129i	−0.0559017	−	0.0968246i
$561$		0			0
$562$	−27.8118			−1.17317
$563$	−42.5830			−1.79466			−0.897330	−	0.441361i	$-0.854496\pi$
$563$	−42.5830			−1.79466			−0.897330	+	0.441361i	$0.854496\pi$
$564$		0			0
$565$	−0.177124	+	0.306788i	−0.00745168	+	0.0129067i
$566$	5.93725	+	10.2836i	0.249561	+	0.432253i
$567$		0			0
$568$	−4.17712	+	7.23499i	−0.175268	+	0.303574i
$569$	−10.6458			−0.446293			−0.223147	−	0.974785i	$-0.571633\pi$
$569$	−10.6458			−0.446293			−0.223147	+	0.974785i	$0.571633\pi$
$570$		0			0
$571$	−26.4575			−1.10721			−0.553606	−	0.832779i	$-0.686749\pi$
$571$	−26.4575			−1.10721			−0.553606	+	0.832779i	$0.686749\pi$
$572$		0			0
$573$		0			0
$574$	−4.43725	−	7.68555i	−0.185207	−	0.320789i
$575$	0.500000	−	0.866025i	0.0208514	−	0.0361158i
$576$		0			0
$577$	−12.9373			−0.538585			−0.269292	−	0.963058i	$-0.586790\pi$
$577$	−12.9373			−0.538585			−0.269292	+	0.963058i	$0.586790\pi$
$578$	−16.8745			−0.701887
$579$		0			0
$580$	0.822876	+	1.42526i	0.0341681	+	0.0591808i
$581$	12.1255			0.503050
$582$		0			0
$583$	−1.38562	−	2.39997i	−0.0573866	−	0.0993965i
$584$	−4.17712	+	7.23499i	−0.172851	+	0.299386i
$585$		0			0
$586$	−7.32288	+	12.6836i	−0.302505	+	0.523954i
$587$	21.6458	−	37.4915i	0.893416	−	1.54744i	0.0576626	−	0.998336i	$-0.481635\pi$
$587$	21.6458	−	37.4915i	0.893416	−	1.54744i	0.835753	−	0.549105i	$-0.185031\pi$
$588$		0			0
$589$	14.2288	−	1.84073i	0.586286	−	0.0758460i
$590$	5.29150			0.217848
$591$		0			0
$592$	1.14575	−	1.98450i	0.0470901	−	0.0815624i
$593$	−15.1771	−	26.2876i	−0.623250	−	1.07950i	−0.988877	−	0.148739i	$-0.952479\pi$
$593$	−15.1771	−	26.2876i	−0.623250	−	1.07950i	0.365627	−	0.930762i	$-0.380855\pi$
$594$		0			0
$595$	−0.468627	−	0.811686i	−0.0192118	−	0.0332759i
$596$	−10.2288			−0.418986
$597$		0			0
$598$		0			0
$599$	9.76013	+	16.9050i	0.398788	+	0.690721i	0.993577	−	0.113161i	$-0.0360976\pi$
$599$	9.76013	+	16.9050i	0.398788	+	0.690721i	−0.594789	+	0.803882i	$0.702764\pi$
$600$		0			0
$601$	−5.70850			−0.232854			−0.116427	−	0.993199i	$-0.537144\pi$
$601$	−5.70850			−0.232854			−0.116427	+	0.993199i	$0.537144\pi$
$602$	−7.93725	−	13.7477i	−0.323498	−	0.560316i
$603$		0			0
$604$	−3.11438	−	5.39426i	−0.126722	−	0.219489i
$605$	−3.70850	+	6.42331i	−0.150772	+	0.261145i
$606$		0			0
$607$	19.2288			0.780471			0.390236	−	0.920715i	$-0.372394\pi$
$607$	19.2288			0.780471			0.390236	+	0.920715i	$0.372394\pi$
$608$	2.64575	+	3.46410i	0.107299	+	0.140488i
$609$		0			0
$610$	4.46863	−	7.73989i	0.180929	−	0.313379i
$611$		0			0
$612$		0			0
$613$	−1.43725	+	2.48940i	−0.0580501	+	0.100546i	−0.893590	−	0.448884i	$-0.851822\pi$
$613$	−1.43725	+	2.48940i	−0.0580501	+	0.100546i	0.835540	+	0.549430i	$0.185155\pi$
$614$	−5.76013	−	9.97684i	−0.232460	−	0.402632i
$615$		0			0
$616$	−11.3542			−0.457476
$617$	9.29150	+	16.0934i	0.374062	+	0.647894i	0.990186	−	0.139755i	$-0.0446315\pi$
$617$	9.29150	+	16.0934i	0.374062	+	0.647894i	−0.616124	+	0.787649i	$0.711298\pi$
$618$		0			0
$619$	−33.9373			−1.36405			−0.682027	−	0.731327i	$-0.738901\pi$
$619$	−33.9373			−1.36405			−0.682027	+	0.731327i	$0.738901\pi$
$620$	−3.29150			−0.132190
$621$		0			0
$622$	8.58301	−	14.8662i	0.344147	−	0.596080i
$623$	−17.5000	−	30.3109i	−0.701123	−	1.21438i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	18.5830			0.742726
$627$		0			0
$628$	18.8745			0.753175
$629$	0.405881	−	0.703006i	0.0161835	−	0.0280307i
$630$		0			0
$631$	−10.8229	−	18.7458i	−0.430852	−	0.746257i	0.566095	−	0.824340i	$-0.308454\pi$
$631$	−10.8229	−	18.7458i	−0.430852	−	0.746257i	−0.996947	+	0.0780827i	$0.975120\pi$
$632$	2.64575	−	4.58258i	0.105242	−	0.182285i
$633$		0			0
$634$	−19.9373			−0.791810
$635$	15.2288			0.604335
$636$		0			0
$637$		0			0
$638$	7.06275			0.279617
$639$		0			0
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	−5.35425	+	9.27383i	−0.211480	+	0.366294i	−0.952178	−	0.305544i	$-0.901162\pi$
$641$	−5.35425	+	9.27383i	−0.211480	+	0.366294i	0.740698	+	0.671838i	$0.234495\pi$
$642$		0			0
$643$	−24.4059	+	42.2722i	−0.962474	+	1.66705i	−0.246220	+	0.969214i	$0.579189\pi$
$643$	−24.4059	+	42.2722i	−0.962474	+	1.66705i	−0.716254	+	0.697840i	$0.754145\pi$
$644$	1.32288	−	2.29129i	0.0521286	−	0.0902894i
$645$		0			0
$646$	0.937254	+	1.22715i	0.0368758	+	0.0482817i
$647$	−5.12549			−0.201504			−0.100752	−	0.994912i	$-0.532125\pi$
$647$	−5.12549			−0.201504			−0.100752	+	0.994912i	$0.532125\pi$
$648$		0			0
$649$	11.3542	−	19.6661i	0.445693	−	0.771963i
$650$		0			0
$651$		0			0
$652$	6.64575	+	11.5108i	0.260268	+	0.450797i
$653$	−10.0627			−0.393786			−0.196893	−	0.980425i	$-0.563085\pi$
$653$	−10.0627			−0.393786			−0.196893	+	0.980425i	$0.563085\pi$
$654$		0			0
$655$	−9.14575	−	15.8409i	−0.357354	−	0.618955i
$656$	−1.67712	−	2.90486i	−0.0654807	−	0.113416i
$657$		0			0
$658$	22.7085			0.885269
$659$	−5.79150	−	10.0312i	−0.225605	−	0.390759i	0.730896	−	0.682489i	$-0.239103\pi$
$659$	−5.79150	−	10.0312i	−0.225605	−	0.390759i	−0.956501	+	0.291730i	$0.905769\pi$
$660$		0			0
$661$	6.70850	+	11.6195i	0.260930	+	0.451945i	0.966489	−	0.256707i	$-0.0826374\pi$
$661$	6.70850	+	11.6195i	0.260930	+	0.451945i	−0.705559	+	0.708651i	$0.749304\pi$
$662$	6.67712	−	11.5651i	0.259514	−	0.449491i
$663$		0			0
$664$	4.58301			0.177855
$665$	4.43725	−	10.6448i	0.172069	−	0.412786i
$666$		0			0
$667$	−0.822876	+	1.42526i	−0.0318619	+	0.0551864i
$668$	−1.79150	+	3.10297i	−0.0693153	+	0.120058i
$669$		0			0
$670$	2.17712	−	3.77089i	0.0841097	−	0.145682i
$671$	−19.1771	−	33.2158i	−0.740325	−	1.28228i
$672$		0			0
$673$	−6.12549			−0.236120			−0.118060	−	0.993006i	$-0.537668\pi$
$673$	−6.12549			−0.236120			−0.118060	+	0.993006i	$0.537668\pi$
$674$	−8.64575	−	14.9749i	−0.333022	−	0.576811i
$675$		0			0
$676$	−13.0000			−0.500000
$677$	41.2288			1.58455			0.792275	−	0.610164i	$-0.208897\pi$
$677$	41.2288			1.58455			0.792275	+	0.610164i	$0.208897\pi$
$678$		0			0
$679$	−4.82288	+	8.35347i	−0.185085	+	0.320577i
$680$	−0.177124	−	0.306788i	−0.00679241	−	0.0117648i
$681$		0			0
$682$	−7.06275	+	12.2330i	−0.270447	+	0.468427i
$683$	−28.9373			−1.10725			−0.553627	−	0.832765i	$-0.686757\pi$
$683$	−28.9373			−1.10725			−0.553627	+	0.832765i	$0.686757\pi$
$684$		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
$691$	−13.8118			−0.525424			−0.262712	−	0.964874i	$-0.584617\pi$
$691$	−13.8118			−0.525424			−0.262712	+	0.964874i	$0.584617\pi$
$692$	7.93725			0.301729
$693$		0			0
$694$	−4.29150	−	7.43310i	−0.162903	−	0.282157i
$695$	−7.29150			−0.276582
$696$		0			0
$697$	−0.594119	−	1.02904i	−0.0225039	−	0.0389778i
$698$	−16.4686	+	28.5245i	−0.623347	+	1.07967i
$699$		0			0
$700$	−1.32288	+	2.29129i	−0.0500000	+	0.0866025i
$701$	−20.1660	+	34.9286i	−0.761660	+	1.31923i	0.180335	+	0.983605i	$0.442282\pi$
$701$	−20.1660	+	34.9286i	−0.761660	+	1.31923i	−0.941995	+	0.335628i	$0.891051\pi$
$702$		0			0
$703$	9.90588	−	1.28149i	0.373607	−	0.0483324i
$704$	−4.29150			−0.161742
$705$		0			0
$706$	−11.4686	+	19.8642i	−0.431627	+	0.747601i
$707$	−26.2915	−	45.5382i	−0.988794	−	1.71264i
$708$		0			0
$709$	−12.4686	−	21.5963i	−0.468269	−	0.811066i	0.531073	−	0.847326i	$-0.321789\pi$
$709$	−12.4686	−	21.5963i	−0.468269	−	0.811066i	−0.999342	+	0.0362600i	$0.988456\pi$
$710$	8.35425			0.313529
$711$		0			0
$712$	−6.61438	−	11.4564i	−0.247884	−	0.429348i
$713$	−1.64575	−	2.85052i	−0.0616339	−	0.106753i
$714$		0			0
$715$		0			0
$716$	−8.79150	−	15.2273i	−0.328554	−	0.569072i
$717$		0			0
$718$	−5.46863	−	9.47194i	−0.204087	−	0.353490i
$719$	−11.6458	+	20.1710i	−0.434313	+	0.752253i	−0.997239	−	0.0742547i	$-0.976342\pi$
$719$	−11.6458	+	20.1710i	−0.434313	+	0.752253i	0.562926	+	0.826507i	$0.309676\pi$
$720$		0			0
$721$	−36.8745			−1.37328
$722$	−5.00000	+	18.3303i	−0.186081	+	0.682183i
$723$		0			0
$724$	9.82288	−	17.0137i	0.365064	−	0.632310i
$725$	0.822876	−	1.42526i	0.0305608	−	0.0529329i
$726$		0			0
$727$	9.93725	−	17.2118i	0.368552	−	0.638351i	−0.620787	−	0.783979i	$-0.713187\pi$
$727$	9.93725	−	17.2118i	0.368552	−	0.638351i	0.989339	+	0.145628i	$0.0465202\pi$
$728$		0			0
$729$		0			0
$730$	8.35425			0.309205
$731$	−1.06275	−	1.84073i	−0.0393071	−	0.0680819i
$732$		0			0
$733$	−1.70850			−0.0631048			−0.0315524	−	0.999502i	$-0.510045\pi$
$733$	−1.70850			−0.0631048			−0.0315524	+	0.999502i	$0.510045\pi$
$734$	29.8745			1.10269
$735$		0			0
$736$	0.500000	−	0.866025i	0.0184302	−	0.0319221i
$737$	−9.34313	−	16.1828i	−0.344159	−	0.596101i
$738$		0			0
$739$	25.4889	−	44.1480i	0.937624	−	1.62401i	0.167737	−	0.985832i	$-0.446354\pi$
$739$	25.4889	−	44.1480i	0.937624	−	1.62401i	0.769887	−	0.638180i	$-0.220313\pi$
$740$	−2.29150			−0.0842373
$741$		0			0
$742$	−1.70850			−0.0627209
$743$	−10.2085	+	17.6816i	−0.374513	+	0.648676i	−0.990254	−	0.139273i	$-0.955524\pi$
$743$	−10.2085	+	17.6816i	−0.374513	+	0.648676i	0.615741	+	0.787949i	$0.288857\pi$
$744$		0			0
$745$	5.11438	+	8.85836i	0.187376	+	0.324545i
$746$	−3.85425	+	6.67575i	−0.141114	+	0.244417i
$747$		0			0
$748$	−1.52026			−0.0555862
$749$	−25.5203			−0.932490
$750$		0			0
$751$	22.0000	+	38.1051i	0.802791	+	1.39048i	0.917772	+	0.397108i	$0.129986\pi$
$751$	22.0000	+	38.1051i	0.802791	+	1.39048i	−0.114981	+	0.993368i	$0.536681\pi$
$752$	8.58301			0.312990
$753$		0			0
$754$		0			0
$755$	−3.11438	+	5.39426i	−0.113344	+	0.196317i
$756$		0			0
$757$	14.7288	−	25.5110i	0.535326	−	0.927211i	−0.463822	−	0.885929i	$-0.653522\pi$
$757$	14.7288	−	25.5110i	0.535326	−	0.927211i	0.999147	−	0.0412829i	$-0.0131445\pi$
$758$	6.93725	−	12.0157i	0.251972	−	0.436429i
$759$		0			0
$760$	1.67712	−	4.02334i	0.0608357	−	0.145942i
$761$	−16.5203			−0.598859			−0.299429	−	0.954118i	$-0.596796\pi$
$761$	−16.5203			−0.598859			−0.299429	+	0.954118i	$0.596796\pi$
$762$		0			0
$763$	7.46863	−	12.9360i	0.270382	−	0.468316i
$764$	8.29150	+	14.3613i	0.299976	+	0.519574i
$765$		0			0
$766$	−7.70850	−	13.3515i	−0.278519	−	0.482410i
$767$		0			0
$768$		0			0
$769$	−4.35425	−	7.54178i	−0.157018	−	0.271964i	0.776774	−	0.629780i	$-0.216855\pi$
$769$	−4.35425	−	7.54178i	−0.157018	−	0.271964i	−0.933792	+	0.357816i	$0.883521\pi$
$770$	5.67712	+	9.83307i	0.204589	+	0.354359i
$771$		0			0
$772$	6.35425			0.228694
$773$	6.96863	+	12.0700i	0.250644	+	0.434128i	0.963703	−	0.266976i	$-0.0860243\pi$
$773$	6.96863	+	12.0700i	0.250644	+	0.434128i	−0.713059	+	0.701104i	$0.752691\pi$
$774$		0			0
$775$	1.64575	+	2.85052i	0.0591171	+	0.102394i
$776$	−1.82288	+	3.15731i	−0.0654374	+	0.113341i
$777$		0			0
$778$	−19.5203			−0.699835
$779$	5.62549	−	13.4953i	0.201554	−	0.483519i
$780$		0			0
$781$	17.9261	−	31.0490i	0.641448	−	1.11102i
$782$	0.177124	−	0.306788i	0.00633395	−	0.0109707i
$783$		0			0
$784$		0			0
$785$	−9.43725	−	16.3458i	−0.336830	−	0.583407i
$786$		0			0
$787$	−50.1033			−1.78599			−0.892994	−	0.450068i	$-0.851400\pi$
$787$	−50.1033			−1.78599			−0.892994	+	0.450068i	$0.851400\pi$
$788$	1.32288	+	2.29129i	0.0471255	+	0.0816237i
$789$		0			0
$790$	−5.29150			−0.188263
$791$	0.937254			0.0333249
$792$		0			0
$793$		0			0
$794$	−12.7288	−	22.0469i	−0.451727	−	0.782414i
$795$		0			0
$796$	−9.46863	+	16.4001i	−0.335607	+	0.581288i
$797$	−41.6863			−1.47660			−0.738302	−	0.674471i	$-0.764372\pi$
$797$	−41.6863			−1.47660			−0.738302	+	0.674471i	$0.764372\pi$
$798$		0			0
$799$	3.04052			0.107566
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$		0			0
$802$	3.00000	+	5.19615i	0.105934	+	0.183483i
$803$	17.9261	−	31.0490i	0.632600	−	1.09569i
$804$		0			0
$805$	−2.64575			−0.0932505
$806$		0			0
$807$		0			0
$808$	−9.93725	−	17.2118i	−0.349591	−	0.605510i
$809$	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
$811$	−16.3229	−	28.2720i	−0.573174	−	0.992766i	−0.996237	−	0.0866660i	$-0.972379\pi$
$811$	−16.3229	−	28.2720i	−0.573174	−	0.992766i	0.423064	−	0.906100i	$-0.360955\pi$
$812$	2.17712	−	3.77089i	0.0764021	−	0.132332i
$813$		0			0
$814$	−4.91699	+	8.51648i	−0.172341	+	0.298503i
$815$	6.64575	−	11.5108i	0.232791	−	0.403205i
$816$		0			0
$817$	10.0627	−	24.1400i	0.352051	−	0.844553i
$818$	−39.5830			−1.38399
$819$		0			0
$820$	−1.67712	+	2.90486i	−0.0585677	+	0.101442i
$821$	0.291503	+	0.504897i	0.0101735	+	0.0176210i	0.871067	−	0.491164i	$-0.163428\pi$
$821$	0.291503	+	0.504897i	0.0101735	+	0.0176210i	−0.860894	+	0.508785i	$0.830095\pi$
$822$		0			0
$823$	−2.38562	−	4.13202i	−0.0831575	−	0.144033i	0.821447	−	0.570285i	$-0.193167\pi$
$823$	−2.38562	−	4.13202i	−0.0831575	−	0.144033i	−0.904605	+	0.426252i	$0.859834\pi$
$824$	−13.9373			−0.485527
$825$		0			0
$826$	−7.00000	−	12.1244i	−0.243561	−	0.421860i
$827$	23.4686	+	40.6489i	0.816084	+	1.41350i	0.908547	+	0.417783i	$0.137193\pi$
$827$	23.4686	+	40.6489i	0.816084	+	1.41350i	−0.0924627	+	0.995716i	$0.529474\pi$
$828$		0			0
$829$	0.457513			0.0158901			0.00794504	−	0.999968i	$-0.497471\pi$
$829$	0.457513			0.0158901			0.00794504	+	0.999968i	$0.497471\pi$
$830$	−2.29150	−	3.96900i	−0.0795392	−	0.137766i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	3.58301			0.123995
$836$	−11.3542	−	14.8662i	−0.392695	−	0.514158i
$837$		0			0
$838$	−2.08301	+	3.60787i	−0.0719562	+	0.124632i
$839$	−7.93725	+	13.7477i	−0.274024	+	0.474624i	−0.969889	−	0.243549i	$-0.921688\pi$
$839$	−7.93725	+	13.7477i	−0.274024	+	0.474624i	0.695864	+	0.718173i	$0.255022\pi$
$840$		0			0
$841$	13.1458	−	22.7691i	0.453302	−	0.785142i
$842$	1.53137	+	2.65242i	0.0527746	+	0.0914083i
$843$		0			0
$844$	18.5203			0.637494
$845$	6.50000	+	11.2583i	0.223607	+	0.387298i
$846$		0			0
$847$	19.6235			0.674272
$848$	−0.645751			−0.0221752
$849$		0			0
$850$	−0.177124	+	0.306788i	−0.00607531	+	0.0105228i
$851$	−1.14575	−	1.98450i	−0.0392758	−	0.0680278i
$852$		0			0
$853$	18.2915	−	31.6818i	0.626289	−	1.08476i	−0.362001	−	0.932178i	$-0.617906\pi$
$853$	18.2915	−	31.6818i	0.626289	−	1.08476i	0.988290	−	0.152587i	$-0.0487604\pi$
$854$	−23.6458			−0.809141
$855$		0			0
$856$	−9.64575			−0.329685
$857$	−6.00000	+	10.3923i	−0.204956	+	0.354994i	−0.950119	−	0.311888i	$-0.899038\pi$
$857$	−6.00000	+	10.3923i	−0.204956	+	0.354994i	0.745163	+	0.666883i	$0.232372\pi$
$858$		0			0
$859$	−12.2601	−	21.2352i	−0.418310	−	0.724535i	0.577459	−	0.816419i	$-0.304044\pi$
$859$	−12.2601	−	21.2352i	−0.418310	−	0.724535i	−0.995770	+	0.0918848i	$0.970711\pi$
$860$	−3.00000	+	5.19615i	−0.102299	+	0.177187i
$861$		0			0
$862$	−33.6458			−1.14598
$863$	−41.5830			−1.41550			−0.707751	−	0.706462i	$-0.750290\pi$
$863$	−41.5830			−1.41550			−0.707751	+	0.706462i	$0.750290\pi$
$864$		0			0
$865$	−3.96863	−	6.87386i	−0.134937	−	0.233718i
$866$	−10.9373			−0.371663
$867$		0			0
$868$	4.35425	+	7.54178i	0.147793	+	0.255985i
$869$	−11.3542	+	19.6661i	−0.385167	+	0.667128i
$870$		0			0
$871$		0			0
$872$	2.82288	−	4.88936i	0.0955946	−	0.165575i
$873$		0			0
$874$	4.32288	−	0.559237i	0.146223	−	0.0189165i
$875$	2.64575			0.0894427
$876$		0			0
$877$	16.8542	−	29.1924i	0.569128	−	0.985758i	−0.427525	−	0.904004i	$-0.640614\pi$
$877$	16.8542	−	29.1924i	0.569128	−	0.985758i	0.996653	−	0.0817543i	$-0.0260523\pi$
$878$	9.46863	+	16.4001i	0.319551	+	0.553478i
$879$		0			0
$880$	2.14575	+	3.71655i	0.0723333	+	0.125285i
$881$	40.6458			1.36939			0.684695	−	0.728830i	$-0.259935\pi$
$881$	40.6458			1.36939			0.684695	+	0.728830i	$0.259935\pi$
$882$		0			0
$883$	−6.05163	−	10.4817i	−0.203654	−	0.352738i	0.746049	−	0.665891i	$-0.231948\pi$
$883$	−6.05163	−	10.4817i	−0.203654	−	0.352738i	−0.949703	+	0.313152i	$0.898615\pi$
$884$		0			0
$885$		0			0
$886$	40.9373			1.37531
$887$	23.2288	+	40.2334i	0.779945	+	1.35090i	0.931973	+	0.362529i	$0.118086\pi$
$887$	23.2288	+	40.2334i	0.779945	+	1.35090i	−0.152027	+	0.988376i	$0.548580\pi$
$888$		0			0
$889$	−20.1458	−	34.8935i	−0.675667	−	1.17029i
$890$	−6.61438	+	11.4564i	−0.221714	+	0.384021i
$891$		0			0
$892$	1.35425			0.0453436
$893$	22.7085	+	29.7324i	0.759911	+	0.994957i
$894$		0			0
$895$	−8.79150	+	15.2273i	−0.293868	+	0.508993i
$896$	−1.32288	+	2.29129i	−0.0441942	+	0.0765466i
$897$		0			0
$898$	−11.3229	+	19.6118i	−0.377849	+	0.654454i
$899$	−2.70850	−	4.69126i	−0.0903334	−	0.156462i
$900$		0			0
$901$	−0.228757			−0.00762099
$902$	7.19738	+	12.4662i	0.239647	+	0.415080i
$903$		0			0
$904$	0.354249			0.0117821
$905$	−19.6458			−0.653047
$906$		0			0
$907$	−2.29150	+	3.96900i	−0.0760881	+	0.131788i	−0.901559	−	0.432656i	$-0.857576\pi$
$907$	−2.29150	+	3.96900i	−0.0760881	+	0.131788i	0.825471	+	0.564445i	$0.190910\pi$
$908$	−12.4059	−	21.4876i	−0.411704	−	0.713092i
$909$		0			0
$910$		0			0
$911$	−2.70850			−0.0897365			−0.0448683	−	0.998993i	$-0.514287\pi$
$911$	−2.70850			−0.0897365			−0.0448683	+	0.998993i	$0.514287\pi$
$912$		0			0
$913$	−19.6680			−0.650915
$914$	−14.1144	+	24.4468i	−0.466862	+	0.808629i
$915$		0			0
$916$	−12.6458	−	21.9031i	−0.417827	−	0.723698i
$917$	−24.1974	+	41.9111i	−0.799068	+	1.38403i
$918$		0			0
$919$	−16.2288			−0.535337			−0.267669	−	0.963511i	$-0.586253\pi$
$919$	−16.2288			−0.535337			−0.267669	+	0.963511i	$0.586253\pi$
$920$	−1.00000			−0.0329690
$921$		0			0
$922$	3.58301	+	6.20595i	0.118000	+	0.204382i
$923$		0			0
$924$		0			0
$925$	1.14575	+	1.98450i	0.0376721	+	0.0652499i
$926$	−17.3229	+	30.0041i	−0.569265	+	0.985996i
$927$		0			0
$928$	0.822876	−	1.42526i	0.0270122	−	0.0467865i
$929$	−8.03137	+	13.9107i	−0.263501	+	0.456397i	−0.967170	−	0.254131i	$-0.918210\pi$
$929$	−8.03137	+	13.9107i	−0.263501	+	0.456397i	0.703669	+	0.710528i	$0.251544\pi$
$930$		0			0
$931$		0			0
$932$	0.583005			0.0190970
$933$		0			0
$934$	−10.7601	+	18.6371i	−0.352082	+	0.609824i
$935$	0.760130	+	1.31658i	0.0248589	+	0.0430569i
$936$		0			0
$937$	−10.5314	−	18.2409i	−0.344045	−	0.595903i	0.641135	−	0.767428i	$-0.278464\pi$
$937$	−10.5314	−	18.2409i	−0.344045	−	0.595903i	−0.985180	+	0.171525i	$0.945131\pi$
$938$	−11.5203			−0.376150
$939$		0			0
$940$	−4.29150	−	7.43310i	−0.139973	−	0.242441i
$941$	9.88562	+	17.1224i	0.322262	+	0.558174i	0.980954	−	0.194238i	$-0.0622234\pi$
$941$	9.88562	+	17.1224i	0.322262	+	0.558174i	−0.658692	+	0.752412i	$0.728890\pi$
$942$		0			0
$943$	−3.35425			−0.109229
$944$	−2.64575	−	4.58258i	−0.0861119	−	0.149150i
$945$		0			0
$946$	12.8745	+	22.2993i	0.418586	+	0.725013i
$947$	12.6974	−	21.9925i	0.412610	−	0.714661i	−0.582565	−	0.812784i	$-0.697951\pi$
$947$	12.6974	−	21.9925i	0.412610	−	0.714661i	0.995174	+	0.0981237i	$0.0312841\pi$
$948$		0			0
$949$		0			0
$950$	−4.32288	+	0.559237i	−0.140253	+	0.0181440i
$951$		0			0
$952$	−0.468627	+	0.811686i	−0.0151883	+	0.0263069i
$953$	6.58301	−	11.4021i	0.213244	−	0.369350i	−0.739484	−	0.673175i	$-0.764930\pi$
$953$	6.58301	−	11.4021i	0.213244	−	0.369350i	0.952728	+	0.303824i	$0.0982636\pi$
$954$		0			0
$955$	8.29150	−	14.3613i	0.268307	−	0.464721i
$956$	−12.0000	−	20.7846i	−0.388108	−	0.672222i
$957$		0			0
$958$	10.9373			0.353367
$959$	−15.8745	−	27.4955i	−0.512615	−	0.887875i
$960$		0			0
$961$	−20.1660			−0.650516
$962$		0			0
$963$		0			0
$964$	−11.2915	+	19.5575i	−0.363675	+	0.629903i
$965$	−3.17712	−	5.50294i	−0.102275	−	0.177146i
$966$		0			0
$967$	−1.06275	+	1.84073i	−0.0341756	+	0.0591939i	−0.882607	−	0.470111i	$-0.844214\pi$
$967$	−1.06275	+	1.84073i	−0.0341756	+	0.0591939i	0.848432	+	0.529305i	$0.177547\pi$
$968$	7.41699			0.238391
$969$		0			0
$970$	3.64575			0.117058
$971$	30.8745	−	53.4762i	0.990810	−	1.71613i	0.378266	−	0.925697i	$-0.376520\pi$
$971$	30.8745	−	53.4762i	0.990810	−	1.71613i	0.612544	−	0.790437i	$-0.290146\pi$
$972$		0			0
$973$	9.64575	+	16.7069i	0.309229	+	0.535600i
$974$	−7.67712	+	13.2972i	−0.245991	+	0.426069i
$975$		0			0
$976$	−8.93725			−0.286075
$977$	16.9373			0.541871			0.270935	−	0.962598i	$-0.412667\pi$
$977$	16.9373			0.541871			0.270935	+	0.962598i	$0.412667\pi$
$978$		0			0
$979$	28.3856	+	49.1653i	0.907208	+	1.57133i
$980$		0			0
$981$		0			0
$982$	−6.72876	−	11.6545i	−0.214723	−	0.371912i
$983$	−8.56275	+	14.8311i	−0.273109	+	0.473039i	−0.969656	−	0.244472i	$-0.921385\pi$
$983$	−8.56275	+	14.8311i	−0.273109	+	0.473039i	0.696547	+	0.717511i	$0.254719\pi$
$984$		0			0
$985$	1.32288	−	2.29129i	0.0421503	−	0.0730065i
$986$	0.291503	−	0.504897i	0.00928333	−	0.0160792i
$987$		0			0
$988$		0			0
$989$	−6.00000			−0.190789
$990$		0			0
$991$	3.17712	−	5.50294i	0.100925	−	0.174807i	−0.811141	−	0.584850i	$-0.801153\pi$
$991$	3.17712	−	5.50294i	0.100925	−	0.174807i	0.912066	+	0.410044i	$0.134487\pi$
$992$	1.64575	+	2.85052i	0.0522527	+	0.0905043i
$993$		0			0
$994$	−11.0516	−	19.1420i	−0.350536	−	0.607147i
$995$	18.9373			0.600351
$996$		0			0
$997$	−5.50000	−	9.52628i	−0.174187	−	0.301700i	0.765693	−	0.643206i	$-0.222396\pi$
$997$	−5.50000	−	9.52628i	−0.174187	−	0.301700i	−0.939880	+	0.341506i	$0.889063\pi$
$998$	−6.32288	−	10.9515i	−0.200147	−	0.346665i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.l.j.1531.2		4
3.2	odd	2		570.2.i.i.391.2	yes	4
19.7	even	3	inner	1710.2.l.j.1261.2		4
57.26	odd	6		570.2.i.i.121.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.i.i.121.2	✓	4	57.26	odd	6
570.2.i.i.391.2	yes	4	3.2	odd	2
1710.2.l.j.1261.2		4	19.7	even	3	inner
1710.2.l.j.1531.2		4	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +2.64575 q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +2.64575 q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{10} -4.29150 q^{11} +(-1.32288 + 2.29129i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.177124 + 0.306788i) q^{17} +(-4.32288 + 0.559237i) q^{19} +1.00000 q^{20} +(2.14575 - 3.71655i) q^{22} +(0.500000 + 0.866025i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-1.32288 - 2.29129i) q^{28} +(0.822876 + 1.42526i) q^{29} -3.29150 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.177124 - 0.306788i) q^{34} +(-1.32288 + 2.29129i) q^{35} -2.29150 q^{37} +(1.67712 - 4.02334i) q^{38} +(-0.500000 + 0.866025i) q^{40} +(-1.67712 + 2.90486i) q^{41} +(-3.00000 + 5.19615i) q^{43} +(2.14575 + 3.71655i) q^{44} -1.00000 q^{46} +(-4.29150 - 7.43310i) q^{47} +1.00000 q^{50} +(0.322876 + 0.559237i) q^{53} +(2.14575 - 3.71655i) q^{55} +2.64575 q^{56} -1.64575 q^{58} +(-2.64575 + 4.58258i) q^{59} +(4.46863 + 7.73989i) q^{61} +(1.64575 - 2.85052i) q^{62} +1.00000 q^{64} +(2.17712 + 3.77089i) q^{67} +0.354249 q^{68} +(-1.32288 - 2.29129i) q^{70} +(-4.17712 + 7.23499i) q^{71} +(-4.17712 + 7.23499i) q^{73} +(1.14575 - 1.98450i) q^{74} +(2.64575 + 3.46410i) q^{76} -11.3542 q^{77} +(2.64575 - 4.58258i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-1.67712 - 2.90486i) q^{82} +4.58301 q^{83} +(-0.177124 - 0.306788i) q^{85} +(-3.00000 - 5.19615i) q^{86} -4.29150 q^{88} +(-6.61438 - 11.4564i) q^{89} +(0.500000 - 0.866025i) q^{92} +8.58301 q^{94} +(1.67712 - 4.02334i) q^{95} +(-1.82288 + 3.15731i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} - 2 q^{5} + 4 q^{8}+O(q^{10}) \) 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

Related objects

Downloads

Learn more