LMFDB - Embedded newform 720.2.cu.c.113.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(113,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 10, 9]))

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

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

chi := DirichletCharacter("720.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.cu (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} + \cdots + 1 $ x^16 - 6x^15 + 18x^14 - 36x^13 + 34x^12 + 18x^11 - 72x^10 + 132x^9 - 93x^8 - 102x^7 + 144x^6 - 432x^5 + 502x^4 + 288x^3 + 72x^2 + 12*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			113.3
Root			$-0.347596 + 1.29724i$ of defining polynomial
Character	$\chi$	$=$	720.113
Dual form			720.2.cu.c.497.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.18953 + 1.25897i) q^{3} +(-1.59371 + 1.56847i) q^{5} +(-1.97869 - 0.530190i) q^{7} +(-0.170031 + 2.99518i) q^{9} +O(q^{10})$	\(q+(1.18953 + 1.25897i) q^{3} +(-1.59371 + 1.56847i) q^{5} +(-1.97869 - 0.530190i) q^{7} +(-0.170031 + 2.99518i) q^{9} +(0.762281 - 0.440103i) q^{11} +(-5.36743 + 1.43820i) q^{13} +(-3.87043 - 0.140687i) q^{15} +(-1.13610 - 1.13610i) q^{17} +1.52456i q^{19} +(-1.68622 - 3.12180i) q^{21} +(-0.410850 - 1.53331i) q^{23} +(0.0797919 - 4.99936i) q^{25} +(-3.97311 + 3.34879i) q^{27} +(0.796583 + 1.37972i) q^{29} +(-3.49518 + 6.05383i) q^{31} +(1.46084 + 0.436175i) q^{33} +(3.98504 - 2.25856i) q^{35} +(-4.25746 + 4.25746i) q^{37} +(-8.19538 - 5.04667i) q^{39} +(3.11546 + 1.79871i) q^{41} +(-0.497959 + 1.85841i) q^{43} +(-4.42687 - 5.04012i) q^{45} +(2.14344 - 7.99942i) q^{47} +(-2.42805 - 1.40183i) q^{49} +(0.0788937 - 2.78174i) q^{51} +(4.65601 - 4.65601i) q^{53} +(-0.524562 + 1.89701i) q^{55} +(-1.91938 + 1.81351i) q^{57} +(-3.81780 + 6.61262i) q^{59} +(6.64002 + 11.5008i) q^{61} +(1.92445 - 5.83639i) q^{63} +(6.29833 - 10.7107i) q^{65} +(0.859733 + 3.20857i) q^{67} +(1.44168 - 2.34117i) q^{69} +5.89798i q^{71} +(1.58900 + 1.58900i) q^{73} +(6.38898 - 5.84644i) q^{75} +(-1.74166 + 0.466676i) q^{77} +(6.69401 - 3.86479i) q^{79} +(-8.94218 - 1.01854i) q^{81} +(9.59770 + 2.57170i) q^{83} +(3.59254 + 0.0286674i) q^{85} +(-0.789474 + 2.64410i) q^{87} -4.62765 q^{89} +11.3830 q^{91} +(-11.7792 + 2.80088i) q^{93} +(-2.39123 - 2.42970i) q^{95} +(3.82988 + 1.02621i) q^{97} +(1.18858 + 2.35800i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{3} - 6 q^{5} + 2 q^{7}+O(q^{10}) $ 16 * q + 6 * q^3 - 6 * q^5 + 2 * q^7	$ 16 q + 6 q^{3} - 6 q^{5} + 2 q^{7} - 2 q^{13} + 6 q^{15} - 12 q^{21} - 18 q^{23} + 4 q^{25} - 18 q^{27} + 4 q^{31} - 12 q^{33} + 4 q^{37} - 24 q^{41} + 2 q^{43} - 36 q^{45} + 12 q^{47} - 36 q^{51} + 16 q^{55} - 6 q^{57} + 8 q^{61} - 36 q^{63} + 66 q^{65} - 4 q^{67} - 8 q^{73} - 42 q^{75} - 6 q^{77} - 48 q^{81} + 66 q^{83} + 22 q^{85} + 18 q^{87} + 40 q^{91} - 18 q^{93} + 36 q^{95} + 28 q^{97}+O(q^{100}) $ 16 * q + 6 * q^3 - 6 * q^5 + 2 * q^7 - 2 * q^13 + 6 * q^15 - 12 * q^21 - 18 * q^23 + 4 * q^25 - 18 * q^27 + 4 * q^31 - 12 * q^33 + 4 * q^37 - 24 * q^41 + 2 * q^43 - 36 * q^45 + 12 * q^47 - 36 * q^51 + 16 * q^55 - 6 * q^57 + 8 * q^61 - 36 * q^63 + 66 * q^65 - 4 * q^67 - 8 * q^73 - 42 * q^75 - 6 * q^77 - 48 * q^81 + 66 * q^83 + 22 * q^85 + 18 * q^87 + 40 * q^91 - 18 * q^93 + 36 * q^95 + 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$

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			0
$2$		0			0
$3$	1.18953	+	1.25897i	0.686776	+	0.726869i
$3$	1.18953	+	1.25897i	0.686776	+	0.726869i
$4$		0			0
$5$	−1.59371	+	1.56847i	−0.712727	+	0.701442i
$5$	−1.59371	+	1.56847i	−0.712727	+	0.701442i
$6$		0			0
$7$	−1.97869	−	0.530190i	−0.747876	−	0.200393i	−0.135300	−	0.990805i	$-0.543200\pi$
$7$	−1.97869	−	0.530190i	−0.747876	−	0.200393i	−0.612576	+	0.790412i	$0.709867\pi$
$8$		0			0
$9$	−0.170031	+	2.99518i	−0.0566769	+	0.998393i
$10$		0			0
$11$	0.762281	−	0.440103i	0.229836	−	0.132696i	−0.380660	−	0.924715i	$-0.624303\pi$
$11$	0.762281	−	0.440103i	0.229836	−	0.132696i	0.610497	+	0.792019i	$0.290970\pi$
$12$		0			0
$13$	−5.36743	+	1.43820i	−1.48866	+	0.398885i	−0.909283	−	0.416177i	$-0.863370\pi$
$13$	−5.36743	+	1.43820i	−1.48866	+	0.398885i	−0.579374	+	0.815062i	$0.696703\pi$
$14$		0			0
$15$	−3.87043	−	0.140687i	−0.999340	−	0.0363252i
$16$		0			0
$17$	−1.13610	−	1.13610i	−0.275544	−	0.275544i	0.555783	−	0.831327i	$-0.312418\pi$
$17$	−1.13610	−	1.13610i	−0.275544	−	0.275544i	−0.831327	+	0.555783i	$0.812418\pi$
$18$		0			0
$19$			1.52456i			0.349758i	0.984590	+	0.174879i	$0.0559535\pi$
$19$			1.52456i			0.349758i	−0.984590	+	0.174879i	$0.944047\pi$
$20$		0			0
$21$	−1.68622	−	3.12180i	−0.367964	−	0.681233i
$22$		0			0
$23$	−0.410850	−	1.53331i	−0.0856682	−	0.319718i	0.909772	−	0.415109i	$-0.136257\pi$
$23$	−0.410850	−	1.53331i	−0.0856682	−	0.319718i	−0.995440	+	0.0953909i	$0.969590\pi$
$24$		0			0
$25$	0.0797919	−	4.99936i	0.0159584	−	0.999873i
$26$		0			0
$27$	−3.97311	+	3.34879i	−0.764625	+	0.644476i
$28$		0			0
$29$	0.796583	+	1.37972i	0.147922	+	0.256208i	0.930459	−	0.366396i	$-0.119408\pi$
$29$	0.796583	+	1.37972i	0.147922	+	0.256208i	−0.782537	+	0.622603i	$0.786075\pi$
$30$		0			0
$31$	−3.49518	+	6.05383i	−0.627752	+	1.08730i	0.360249	+	0.932856i	$0.382692\pi$
$31$	−3.49518	+	6.05383i	−0.627752	+	1.08730i	−0.988002	+	0.154443i	$0.950642\pi$
$32$		0			0
$33$	1.46084	+	0.436175i	0.254299	+	0.0759284i
$34$		0			0
$35$	3.98504	−	2.25856i	0.673595	−	0.381767i
$36$		0			0
$37$	−4.25746	+	4.25746i	−0.699922	+	0.699922i	−0.964393	−	0.264472i	$-0.914802\pi$
$37$	−4.25746	+	4.25746i	−0.699922	+	0.699922i	0.264472	+	0.964393i	$0.414802\pi$
$38$		0			0
$39$	−8.19538	−	5.04667i	−1.31231	−	0.808114i
$40$		0			0
$41$	3.11546	+	1.79871i	0.486552	+	0.280911i	0.723143	−	0.690698i	$-0.242697\pi$
$41$	3.11546	+	1.79871i	0.486552	+	0.280911i	−0.236591	+	0.971609i	$0.576030\pi$
$42$		0			0
$43$	−0.497959	+	1.85841i	−0.0759380	+	0.283404i	−0.993444	−	0.114317i	$-0.963532\pi$
$43$	−0.497959	+	1.85841i	−0.0759380	+	0.283404i	0.917506	+	0.397721i	$0.130199\pi$
$44$		0			0
$45$	−4.42687	−	5.04012i	−0.659919	−	0.751337i
$46$		0			0
$47$	2.14344	−	7.99942i	0.312652	−	1.16683i	−0.613503	−	0.789693i	$-0.710240\pi$
$47$	2.14344	−	7.99942i	0.312652	−	1.16683i	0.926155	−	0.377142i	$-0.123093\pi$
$48$		0			0
$49$	−2.42805	−	1.40183i	−0.346864	−	0.200262i
$50$		0			0
$51$	0.0788937	−	2.78174i	0.0110473	−	0.389522i
$52$		0			0
$53$	4.65601	−	4.65601i	0.639552	−	0.639552i	−0.310893	−	0.950445i	$-0.600628\pi$
$53$	4.65601	−	4.65601i	0.639552	−	0.639552i	0.950445	+	0.310893i	$0.100628\pi$
$54$		0			0
$55$	−0.524562	+	1.89701i	−0.0707319	+	0.255793i
$56$		0			0
$57$	−1.91938	+	1.81351i	−0.254229	+	0.240206i
$58$		0			0
$59$	−3.81780	+	6.61262i	−0.497035	+	0.860890i	−0.999994	−	0.00342048i	$-0.998911\pi$
$59$	−3.81780	+	6.61262i	−0.497035	+	0.860890i	0.502959	+	0.864310i	$0.332245\pi$
$60$		0			0
$61$	6.64002	+	11.5008i	0.850167	+	1.47253i	0.881057	+	0.473010i	$0.156833\pi$
$61$	6.64002	+	11.5008i	0.850167	+	1.47253i	−0.0308900	+	0.999523i	$0.509834\pi$
$62$		0			0
$63$	1.92445	−	5.83639i	0.242458	−	0.735317i
$64$		0			0
$65$	6.29833	−	10.7107i	0.781211	−	1.32850i
$66$		0			0
$67$	0.859733	+	3.20857i	0.105033	+	0.391989i	0.998349	−	0.0574406i	$-0.0182940\pi$
$67$	0.859733	+	3.20857i	0.105033	+	0.391989i	−0.893316	+	0.449429i	$0.851627\pi$
$68$		0			0
$69$	1.44168	−	2.34117i	0.173558	−	0.281844i
$70$		0			0
$71$			5.89798i			0.699961i	0.936757	+	0.349980i	$0.113812\pi$
$71$			5.89798i			0.699961i	−0.936757	+	0.349980i	$0.886188\pi$
$72$		0			0
$73$	1.58900	+	1.58900i	0.185979	+	0.185979i	0.793955	−	0.607976i	$-0.208018\pi$
$73$	1.58900	+	1.58900i	0.185979	+	0.185979i	−0.607976	+	0.793955i	$0.708018\pi$
$74$		0			0
$75$	6.38898	−	5.84644i	0.737736	−	0.675089i
$76$		0			0
$77$	−1.74166	+	0.466676i	−0.198480	+	0.0531827i
$78$		0			0
$79$	6.69401	−	3.86479i	0.753135	−	0.434823i	−0.0736905	−	0.997281i	$-0.523478\pi$
$79$	6.69401	−	3.86479i	0.753135	−	0.434823i	0.826826	+	0.562458i	$0.190144\pi$
$80$		0			0
$81$	−8.94218	−	1.01854i	−0.993575	−	0.113172i
$82$		0			0
$83$	9.59770	+	2.57170i	1.05348	+	0.282280i	0.743691	−	0.668523i	$-0.233073\pi$
$83$	9.59770	+	2.57170i	1.05348	+	0.282280i	0.309794	+	0.950804i	$0.399740\pi$
$84$		0			0
$85$	3.59254	+	0.0286674i	0.389666	+	0.00310942i
$86$		0			0
$87$	−0.789474	+	2.64410i	−0.0846405	+	0.283477i
$88$		0			0
$89$	−4.62765			−0.490530			−0.245265	−	0.969456i	$-0.578875\pi$
$89$	−4.62765			−0.490530			−0.245265	+	0.969456i	$0.578875\pi$
$90$		0			0
$91$	11.3830			1.19327
$92$		0			0
$93$	−11.7792	+	2.80088i	−1.22145	+	0.290437i
$94$		0			0
$95$	−2.39123	−	2.42970i	−0.245335	−	0.249282i
$96$		0			0
$97$	3.82988	+	1.02621i	0.388865	+	0.104196i	0.447954	−	0.894057i	$-0.352153\pi$
$97$	3.82988	+	1.02621i	0.388865	+	0.104196i	−0.0590888	+	0.998253i	$0.518820\pi$
$98$		0			0
$99$	1.18858	+	2.35800i	0.119456	+	0.236988i
$100$		0			0
$101$	−2.23195	+	1.28862i	−0.222087	+	0.128222i	−0.606916	−	0.794766i	$-0.707594\pi$
$101$	−2.23195	+	1.28862i	−0.222087	+	0.128222i	0.384829	+	0.922988i	$0.374260\pi$
$102$		0			0
$103$	−12.6183	+	3.38106i	−1.24332	+	0.333146i	−0.819752	−	0.572719i	$-0.805889\pi$
$103$	−12.6183	+	3.38106i	−1.24332	+	0.333146i	−0.423566	+	0.905865i	$0.639222\pi$
$104$		0			0
$105$	7.58380	+	2.33044i	0.740103	+	0.227427i
$106$		0			0
$107$	−9.23034	−	9.23034i	−0.892331	−	0.892331i	0.102411	−	0.994742i	$-0.467344\pi$
$107$	−9.23034	−	9.23034i	−0.892331	−	0.892331i	−0.994742	+	0.102411i	$0.967344\pi$
$108$		0			0
$109$			8.05480i			0.771510i	0.922601	+	0.385755i	$0.126059\pi$
$109$			8.05480i			0.771510i	−0.922601	+	0.385755i	$0.873941\pi$
$110$		0			0
$111$	−10.4244	−	0.295649i	−0.989441	−	0.0280618i
$112$		0			0
$113$	3.10662	+	11.5941i	0.292246	+	1.09068i	0.943380	+	0.331714i	$0.107627\pi$
$113$	3.10662	+	11.5941i	0.292246	+	1.09068i	−0.651134	+	0.758963i	$0.725706\pi$
$114$		0			0
$115$	3.05973	+	1.79924i	0.285322	+	0.167780i
$116$		0			0
$117$	−3.39503	−	16.3209i	−0.313871	−	1.50887i
$118$		0			0
$119$	1.64564	+	2.85034i	0.150856	+	0.261290i
$120$		0			0
$121$	−5.11262	+	8.85532i	−0.464784	+	0.805029i
$122$		0			0
$123$	1.44140	+	6.06190i	0.129967	+	0.546583i
$124$		0			0
$125$	7.71420	+	8.09266i	0.689979	+	0.723830i
$126$		0			0
$127$	−1.90230	+	1.90230i	−0.168802	+	0.168802i	−0.786452	−	0.617651i	$-0.788085\pi$
$127$	−1.90230	+	1.90230i	−0.168802	+	0.168802i	0.617651	+	0.786452i	$0.288085\pi$
$128$		0			0
$129$	−2.93202	+	1.58372i	−0.258150	+	0.139438i
$130$		0			0
$131$	18.5109	+	10.6873i	1.61731	+	0.933754i	0.987613	+	0.156912i	$0.0501541\pi$
$131$	18.5109	+	10.6873i	1.61731	+	0.933754i	0.629696	+	0.776841i	$0.283179\pi$
$132$		0			0
$133$	0.808307	−	3.01664i	0.0700891	−	0.261576i
$134$		0			0
$135$	1.07947	−	11.5687i	0.0929063	−	0.995675i
$136$		0			0
$137$	1.77541	−	6.62594i	0.151684	−	0.566092i	−0.847683	−	0.530504i	$-0.822003\pi$
$137$	1.77541	−	6.62594i	0.151684	−	0.566092i	0.999367	−	0.0355883i	$-0.0113305\pi$
$138$		0			0
$139$	1.24863	+	0.720896i	0.105907	+	0.0611456i	0.552018	−	0.833832i	$-0.313858\pi$
$139$	1.24863	+	0.720896i	0.105907	+	0.0611456i	−0.446111	+	0.894978i	$0.647191\pi$
$140$		0			0
$141$	12.6207	−	6.81703i	1.06286	−	0.574097i
$142$		0			0
$143$	−3.45853	+	3.45853i	−0.289217	+	0.289217i
$144$		0			0
$145$	−3.43357	−	0.949452i	−0.285143	−	0.0788477i
$146$		0			0
$147$	−1.12337	−	4.72437i	−0.0926536	−	0.389659i
$148$		0			0
$149$	8.28457	−	14.3493i	0.678699	−	1.17554i	−0.296674	−	0.954979i	$-0.595878\pi$
$149$	8.28457	−	14.3493i	0.678699	−	1.17554i	0.975373	−	0.220562i	$-0.0707891\pi$
$150$		0			0
$151$	−0.00283730	−	0.00491435i	−0.000230896	−	0.000399924i	0.865910	−	0.500200i	$-0.166740\pi$
$151$	−0.00283730	−	0.00491435i	−0.000230896	−	0.000399924i	−0.866141	+	0.499800i	$0.833407\pi$
$152$		0			0
$153$	3.59599	−	3.20964i	0.290718	−	0.259484i
$154$		0			0
$155$	−3.92497	−	15.1301i	−0.315261	−	1.21528i
$156$		0			0
$157$	2.18944	+	8.17112i	0.174737	+	0.652126i	0.996596	+	0.0824362i	$0.0262701\pi$
$157$	2.18944	+	8.17112i	0.174737	+	0.652126i	−0.821860	+	0.569690i	$0.807063\pi$
$158$		0			0
$159$	11.4003	+	0.323326i	0.904099	+	0.0256414i
$160$		0			0
$161$			3.25179i			0.256277i
$162$		0			0
$163$	−4.19302	−	4.19302i	−0.328422	−	0.328422i	0.523564	−	0.851986i	$-0.324602\pi$
$163$	−4.19302	−	4.19302i	−0.328422	−	0.328422i	−0.851986	+	0.523564i	$0.824602\pi$
$164$		0			0
$165$	−3.01227	+	1.59614i	−0.234505	+	0.124260i
$166$		0			0
$167$	5.76334	−	1.54428i	0.445980	−	0.119500i	−0.0288375	−	0.999584i	$-0.509181\pi$
$167$	5.76334	−	1.54428i	0.445980	−	0.119500i	0.474818	+	0.880084i	$0.342514\pi$
$168$		0			0
$169$	15.4826	−	8.93886i	1.19097	−	0.687605i
$170$		0			0
$171$	−4.56633	−	0.259222i	−0.349196	−	0.0198232i
$172$		0			0
$173$	13.1994	+	3.53677i	1.00353	+	0.268896i	0.722925	−	0.690927i	$-0.242797\pi$
$173$	13.1994	+	3.53677i	1.00353	+	0.268896i	0.280608	+	0.959822i	$0.409464\pi$
$174$		0			0
$175$	−2.80849	+	9.84991i	−0.212302	+	0.744583i
$176$		0			0
$177$	−12.8665	+	3.05941i	−0.967106	+	0.229959i
$178$		0			0
$179$	17.2370			1.28836			0.644178	−	0.764875i	$-0.277199\pi$
$179$	17.2370			1.28836			0.644178	+	0.764875i	$0.277199\pi$
$180$		0			0
$181$	14.7708			1.09790			0.548952	−	0.835854i	$-0.315027\pi$
$181$	14.7708			1.09790			0.548952	+	0.835854i	$0.315027\pi$
$182$		0			0
$183$	−6.58076	+	22.0402i	−0.486464	+	1.62926i
$184$		0			0
$185$	0.107429	−	13.4628i	0.00789837	−	0.989807i
$186$		0			0
$187$	−1.36603	−	0.366025i	−0.0998937	−	0.0267664i
$188$		0			0
$189$	9.63706	−	4.51974i	0.700993	−	0.328763i
$190$		0			0
$191$	−4.56792	+	2.63729i	−0.330523	+	0.190827i	−0.656073	−	0.754697i	$-0.727784\pi$
$191$	−4.56792	+	2.63729i	−0.330523	+	0.190827i	0.325550	+	0.945525i	$0.394450\pi$
$192$		0			0
$193$	−8.98952	+	2.40873i	−0.647080	+	0.173384i	−0.567408	−	0.823437i	$-0.692054\pi$
$193$	−8.98952	+	2.40873i	−0.647080	+	0.173384i	−0.0796715	+	0.996821i	$0.525387\pi$
$194$		0			0
$195$	20.9766	−	4.81132i	1.50216	−	0.344545i
$196$		0			0
$197$	−9.49539	−	9.49539i	−0.676519	−	0.676519i	0.282692	−	0.959211i	$-0.408773\pi$
$197$	−9.49539	−	9.49539i	−0.676519	−	0.676519i	−0.959211	+	0.282692i	$0.908773\pi$
$198$		0			0
$199$		−	17.6342i		−	1.25005i	−0.780604	−	0.625026i	$-0.785088\pi$
$199$		−	17.6342i		−	1.25005i	0.780604	−	0.625026i	$-0.214912\pi$
$200$		0			0
$201$	−3.01682	+	4.89907i	−0.212790	+	0.345554i
$202$		0			0
$203$	−0.844680	−	3.15239i	−0.0592849	−	0.221254i
$204$		0			0
$205$	−7.78634	+	2.01989i	−0.543822	+	0.141075i
$206$		0			0
$207$	4.66240	−	0.969859i	0.324060	−	0.0674098i
$208$		0			0
$209$	0.670964	+	1.16214i	0.0464116	+	0.0803872i
$210$		0			0
$211$	−0.0616050	+	0.106703i	−0.00424106	+	0.00734574i	−0.868138	−	0.496323i	$-0.834683\pi$
$211$	−0.0616050	+	0.106703i	−0.00424106	+	0.00734574i	0.863897	+	0.503668i	$0.168017\pi$
$212$		0			0
$213$	−7.42540	+	7.01583i	−0.508780	+	0.480716i
$214$		0			0
$215$	−2.12126	−	3.74279i	−0.144669	−	0.255256i
$216$		0			0
$217$	10.1256	−	10.1256i	0.687368	−	0.687368i
$218$		0			0
$219$	−0.110345	+	3.89068i	−0.00745640	+	0.262908i
$220$		0			0
$221$	7.73186	+	4.46399i	0.520101	+	0.300281i
$222$		0			0
$223$	−0.648014	+	2.41842i	−0.0433942	+	0.161949i	−0.984223	−	0.176933i	$-0.943382\pi$
$223$	−0.648014	+	2.41842i	−0.0433942	+	0.161949i	0.940829	+	0.338883i	$0.110049\pi$
$224$		0			0
$225$	14.9604	+	1.08904i	0.997361	+	0.0726024i
$226$		0			0
$227$	−3.94671	+	14.7293i	−0.261952	+	0.977619i	0.702137	+	0.712042i	$0.252229\pi$
$227$	−3.94671	+	14.7293i	−0.261952	+	0.977619i	−0.964090	+	0.265577i	$0.914437\pi$
$228$		0			0
$229$	−19.1083	−	11.0322i	−1.26271	−	0.729029i	−0.289116	−	0.957294i	$-0.593361\pi$
$229$	−19.1083	−	11.0322i	−1.26271	−	0.729029i	−0.973599	+	0.228265i	$0.926695\pi$
$230$		0			0
$231$	−2.65929	−	1.63758i	−0.174969	−	0.107745i
$232$		0			0
$233$	−4.22173	+	4.22173i	−0.276575	+	0.276575i	−0.831740	−	0.555165i	$-0.812655\pi$
$233$	−4.22173	+	4.22173i	−0.276575	+	0.276575i	0.555165	+	0.831740i	$0.312655\pi$
$234$		0			0
$235$	9.13085	+	16.1106i	0.595631	+	1.05094i
$236$		0			0
$237$	12.8284	+	3.83030i	0.833294	+	0.248805i
$238$		0			0
$239$	6.79199	−	11.7641i	0.439338	−	0.760955i	−0.558301	−	0.829639i	$-0.688547\pi$
$239$	6.79199	−	11.7641i	0.439338	−	0.760955i	0.997639	+	0.0686835i	$0.0218799\pi$
$240$		0			0
$241$	−2.56728	−	4.44666i	−0.165373	−	0.286434i	0.771415	−	0.636333i	$-0.219549\pi$
$241$	−2.56728	−	4.44666i	−0.165373	−	0.286434i	−0.936788	+	0.349898i	$0.886216\pi$
$242$		0			0
$243$	−9.35468	−	12.4696i	−0.600103	−	0.799923i
$244$		0			0
$245$	6.06832	−	1.57421i	0.387691	−	0.100573i
$246$		0			0
$247$	−2.19262	−	8.18298i	−0.139513	−	0.520670i
$248$		0			0
$249$	8.17907	+	15.1424i	0.518327	+	0.959609i
$250$		0			0
$251$		−	2.60221i		−	0.164250i	−0.996622	−	0.0821251i	$-0.973829\pi$
$251$		−	2.60221i		−	0.164250i	0.996622	−	0.0821251i	$-0.0261707\pi$
$252$		0			0
$253$	−0.987999	−	0.987999i	−0.0621150	−	0.0621150i
$254$		0			0
$255$	4.23735	+	4.55702i	0.265353	+	0.285371i
$256$		0			0
$257$	−10.1958	+	2.73197i	−0.635999	+	0.170415i	−0.562390	−	0.826872i	$-0.690118\pi$
$257$	−10.1958	+	2.73197i	−0.635999	+	0.170415i	−0.0736085	+	0.997287i	$0.523452\pi$
$258$		0			0
$259$	10.6815	−	6.16695i	0.663714	−	0.383196i
$260$		0			0
$261$	−4.26796	+	2.15131i	−0.264180	+	0.133163i
$262$		0			0
$263$	8.12541	+	2.17720i	0.501034	+	0.134252i	0.500480	−	0.865748i	$-0.333157\pi$
$263$	8.12541	+	2.17720i	0.501034	+	0.134252i	0.000554412		1.00000i	$0.499824\pi$
$264$		0			0
$265$	−0.117486	+	14.7231i	−0.00721711	+	0.904434i
$266$		0			0
$267$	−5.50473	−	5.82609i	−0.336884	−	0.356551i
$268$		0			0
$269$	26.7708			1.63225			0.816123	−	0.577878i	$-0.196119\pi$
$269$	26.7708			1.63225			0.816123	+	0.577878i	$0.196119\pi$
$270$		0			0
$271$	18.5850			1.12896			0.564480	−	0.825447i	$-0.309077\pi$
$271$	18.5850			1.12896			0.564480	+	0.825447i	$0.309077\pi$
$272$		0			0
$273$	13.5405	+	14.3309i	0.819506	+	0.867347i
$274$		0			0
$275$	−2.13941	−	3.84604i	−0.129011	−	0.231925i
$276$		0			0
$277$	−26.3206	−	7.05259i	−1.58145	−	0.423749i	−0.642078	−	0.766640i	$-0.721927\pi$
$277$	−26.3206	−	7.05259i	−1.58145	−	0.423749i	−0.939375	+	0.342891i	$0.888594\pi$
$278$		0			0
$279$	−17.5380	−	11.4980i	−1.04997	−	0.688368i
$280$		0			0
$281$	−22.7050	+	13.1087i	−1.35447	+	0.782002i	−0.988872	−	0.148772i	$-0.952468\pi$
$281$	−22.7050	+	13.1087i	−1.35447	+	0.782002i	−0.365595	+	0.930774i	$0.619135\pi$
$282$		0			0
$283$	−3.44050	+	0.921880i	−0.204517	+	0.0548001i	−0.359623	−	0.933098i	$-0.617095\pi$
$283$	−3.44050	+	0.921880i	−0.204517	+	0.0548001i	0.155106	+	0.987898i	$0.450428\pi$
$284$		0			0
$285$	0.214486	−	5.90070i	0.0127050	−	0.349528i
$286$		0			0
$287$	−5.21088	−	5.21088i	−0.307589	−	0.307589i
$288$		0			0
$289$		−	14.4186i		−	0.848151i
$290$		0			0
$291$	3.26378	+	6.04243i	0.191326	+	0.354213i
$292$		0			0
$293$	0.771199	+	2.87816i	0.0450539	+	0.168144i	0.984787	−	0.173765i	$-0.0555933\pi$
$293$	0.771199	+	2.87816i	0.0450539	+	0.168144i	−0.939733	+	0.341909i	$0.888927\pi$
$294$		0			0
$295$	−4.28726	−	16.5267i	−0.249614	−	0.962220i
$296$		0			0
$297$	−1.55481	+	4.30130i	−0.0902192	+	0.249587i
$298$		0			0
$299$	4.41042	+	7.63907i	0.255061	+	0.441779i
$300$		0			0
$301$	1.97062	−	3.41321i	0.113584	−	0.196734i
$302$		0			0
$303$	−4.27731	−	1.27712i	−0.245725	−	0.0733684i
$304$		0			0
$305$	−28.6210	−	7.91428i	−1.63883	−	0.453170i
$306$		0			0
$307$	−21.8017	+	21.8017i	−1.24429	+	1.24429i	−0.286081	+	0.958205i	$0.592353\pi$
$307$	−21.8017	+	21.8017i	−1.24429	+	1.24429i	−0.958205	+	0.286081i	$0.907647\pi$
$308$		0			0
$309$	−19.2665	−	11.8642i	−1.09603	−	0.674933i
$310$		0			0
$311$	−29.3878	−	16.9671i	−1.66643	−	0.962114i	−0.969539	−	0.244939i	$-0.921232\pi$
$311$	−29.3878	−	16.9671i	−1.66643	−	0.962114i	−0.696892	−	0.717176i	$-0.745435\pi$
$312$		0			0
$313$	6.00279	−	22.4027i	0.339298	−	1.26628i	−0.559836	−	0.828603i	$-0.689136\pi$
$313$	6.00279	−	22.4027i	0.339298	−	1.26628i	0.899134	−	0.437673i	$-0.144197\pi$
$314$		0			0
$315$	6.08721	+	12.3199i	0.342976	+	0.694150i
$316$		0			0
$317$	−1.03536	+	3.86401i	−0.0581515	+	0.217024i	−0.988887	−	0.148669i	$-0.952501\pi$
$317$	−1.03536	+	3.86401i	−0.0581515	+	0.217024i	0.930736	+	0.365693i	$0.119168\pi$
$318$		0			0
$319$	1.21444	+	0.701157i	0.0679956	+	0.0392573i
$320$		0			0
$321$	0.640980	−	22.6005i	0.0357760	−	1.26144i
$322$		0			0
$323$	1.73205	−	1.73205i	0.0963739	−	0.0963739i
$324$		0			0
$325$	6.76180	+	26.9485i	0.375077	+	1.49483i
$326$		0			0
$327$	−10.1408	+	9.58143i	−0.560786	+	0.529854i
$328$		0			0
$329$	−8.48242	+	14.6920i	−0.467651	+	0.809995i
$330$		0			0
$331$	2.98175	+	5.16454i	0.163892	+	0.283869i	0.936261	−	0.351305i	$-0.114262\pi$
$331$	2.98175	+	5.16454i	0.163892	+	0.283869i	−0.772369	+	0.635174i	$0.780929\pi$
$332$		0			0
$333$	−12.0279	−	13.4757i	−0.659127	−	0.738466i
$334$		0			0
$335$	−6.40271	−	3.76504i	−0.349817	−	0.205706i
$336$		0			0
$337$	−2.56397	−	9.56887i	−0.139668	−	0.521250i	−0.999935	−	0.0114051i	$-0.996370\pi$
$337$	−2.56397	−	9.56887i	−0.139668	−	0.521250i	0.860267	−	0.509845i	$-0.170297\pi$
$338$		0			0
$339$	−10.9012	+	17.7026i	−0.592072	+	0.961476i
$340$		0			0
$341$			6.15295i			0.333201i
$342$		0			0
$343$	14.2007	+	14.2007i	0.766764	+	0.766764i
$344$		0			0
$345$	1.37445	+	5.99238i	0.0739978	+	0.322619i
$346$		0			0
$347$	10.2471	−	2.74569i	0.550091	−	0.147396i	0.0269407	−	0.999637i	$-0.491423\pi$
$347$	10.2471	−	2.74569i	0.550091	−	0.147396i	0.523150	+	0.852241i	$0.324757\pi$
$348$		0			0
$349$	−8.08831	+	4.66979i	−0.432957	+	0.249968i	−0.700606	−	0.713549i	$-0.747087\pi$
$349$	−8.08831	+	4.66979i	−0.432957	+	0.249968i	0.267648	+	0.963517i	$0.413753\pi$
$350$		0			0
$351$	16.5091	−	23.6885i	0.881193	−	1.26440i
$352$		0			0
$353$	−18.5470	−	4.96965i	−0.987156	−	0.264508i	−0.271100	−	0.962551i	$-0.587388\pi$
$353$	−18.5470	−	4.96965i	−0.987156	−	0.264508i	−0.716055	+	0.698043i	$0.754054\pi$
$354$		0			0
$355$	−9.25081	−	9.39963i	−0.490982	−	0.498881i
$356$		0			0
$357$	−1.63096	+	5.46239i	−0.0863194	+	0.289100i
$358$		0			0
$359$	−12.5944			−0.664705			−0.332352	−	0.943155i	$-0.607842\pi$
$359$	−12.5944			−0.664705			−0.332352	+	0.943155i	$0.607842\pi$
$360$		0			0
$361$	16.6757			0.877669
$362$		0			0
$363$	−17.2302	+	4.09702i	−0.904353	+	0.215038i
$364$		0			0
$365$	−5.02471	−	0.0400957i	−0.263005	−	0.00209870i
$366$		0			0
$367$	−27.3263	−	7.32206i	−1.42642	−	0.382209i	−0.538665	−	0.842520i	$-0.681071\pi$
$367$	−27.3263	−	7.32206i	−1.42642	−	0.382209i	−0.887757	+	0.460312i	$0.847738\pi$
$368$		0			0
$369$	−5.91718	+	9.02551i	−0.308036	+	0.469849i
$370$		0			0
$371$	−11.6814	+	6.74425i	−0.606467	+	0.350144i
$372$		0			0
$373$	−2.25734	+	0.604851i	−0.116880	+	0.0313180i	−0.316785	−	0.948497i	$-0.602603\pi$
$373$	−2.25734	+	0.604851i	−0.116880	+	0.0313180i	0.199905	+	0.979815i	$0.435937\pi$
$374$		0			0
$375$	−1.01217	+	19.3384i	−0.0522684	+	0.998633i
$376$		0			0
$377$	−6.25992	−	6.25992i	−0.322402	−	0.322402i
$378$		0			0
$379$			18.4618i			0.948320i	0.880439	+	0.474160i	$0.157248\pi$
$379$			18.4618i			0.948320i	−0.880439	+	0.474160i	$0.842752\pi$
$380$		0			0
$381$	−4.65779	−	0.132101i	−0.238626	−	0.00676772i
$382$		0			0
$383$	6.26481	+	23.3806i	0.320117	+	1.19469i	0.919131	+	0.393953i	$0.128893\pi$
$383$	6.26481	+	23.3806i	0.320117	+	1.19469i	−0.599014	+	0.800739i	$0.704441\pi$
$384$		0			0
$385$	2.04372	−	3.47549i	0.104158	−	0.177127i
$386$		0			0
$387$	−5.48159	−	1.80746i	−0.278645	−	0.0918784i
$388$		0			0
$389$	13.5444	+	23.4596i	0.686729	+	1.18945i	0.972890	+	0.231268i	$0.0742876\pi$
$389$	13.5444	+	23.4596i	0.686729	+	1.18945i	−0.286161	+	0.958182i	$0.592379\pi$
$390$		0			0
$391$	−1.27523	+	2.20876i	−0.0644911	+	0.111702i
$392$		0			0
$393$	8.56432	+	36.0177i	0.432013	+	1.81685i
$394$		0			0
$395$	−4.60647	+	16.6587i	−0.231776	+	0.838190i
$396$		0			0
$397$	−18.2252	+	18.2252i	−0.914698	+	0.914698i	−0.996637	−	0.0819389i	$-0.973889\pi$
$397$	−18.2252	+	18.2252i	−0.914698	+	0.914698i	0.0819389	+	0.996637i	$0.473889\pi$
$398$		0			0
$399$	4.75938	−	2.57075i	0.238267	−	0.128699i
$400$		0			0
$401$	−11.1294	−	6.42558i	−0.555777	−	0.320878i	0.195672	−	0.980669i	$-0.437311\pi$
$401$	−11.1294	−	6.42558i	−0.555777	−	0.320878i	−0.751449	+	0.659791i	$0.770645\pi$
$402$		0			0
$403$	10.0535	−	37.5202i	0.500801	−	1.86902i
$404$		0			0
$405$	15.8488	−	12.4023i	0.787531	−	0.616275i
$406$		0			0
$407$	−1.37166	+	5.11910i	−0.0679906	+	0.253744i
$408$		0			0
$409$	22.2450	+	12.8431i	1.09994	+	0.635053i	0.936206	−	0.351451i	$-0.114312\pi$
$409$	22.2450	+	12.8431i	1.09994	+	0.635053i	0.163737	+	0.986504i	$0.447645\pi$
$410$		0			0
$411$	10.4538	−	5.64656i	0.515648	−	0.278524i
$412$		0			0
$413$	11.0602	−	11.0602i	0.544237	−	0.544237i
$414$		0			0
$415$	−19.3295	+	10.9552i	−0.948850	+	0.537770i
$416$		0			0
$417$	0.577694	+	2.42952i	0.0282898	+	0.118974i
$418$		0			0
$419$	−6.13243	+	10.6217i	−0.299589	+	0.518903i	−0.976042	−	0.217583i	$-0.930183\pi$
$419$	−6.13243	+	10.6217i	−0.299589	+	0.518903i	0.676453	+	0.736486i	$0.263516\pi$
$420$		0			0
$421$	−7.24056	−	12.5410i	−0.352883	−	0.611212i	0.633870	−	0.773439i	$-0.281465\pi$
$421$	−7.24056	−	12.5410i	−0.352883	−	0.611212i	−0.986753	+	0.162228i	$0.948132\pi$
$422$		0			0
$423$	23.5952	+	7.78012i	1.14724	+	0.378283i
$424$		0			0
$425$	−5.77042	+	5.58911i	−0.279906	+	0.271112i
$426$		0			0
$427$	−7.04094	−	26.2771i	−0.340735	−	1.27164i
$428$		0			0
$429$	−8.46824	−	0.240170i	−0.408850	−	0.0115955i
$430$		0			0
$431$			35.9660i			1.73242i	0.499678	+	0.866211i	$0.333452\pi$
$431$			35.9660i			1.73242i	−0.499678	+	0.866211i	$0.666548\pi$
$432$		0			0
$433$	−0.331545	−	0.331545i	−0.0159331	−	0.0159331i	0.699095	−	0.715028i	$-0.253586\pi$
$433$	−0.331545	−	0.331545i	−0.0159331	−	0.0159331i	−0.715028	+	0.699095i	$0.753586\pi$
$434$		0			0
$435$	−2.88901	−	5.45218i	−0.138517	−	0.261412i
$436$		0			0
$437$	2.33763	−	0.626366i	0.111824	−	0.0299632i
$438$		0			0
$439$	1.28953	−	0.744511i	0.0615459	−	0.0355336i	−0.468911	−	0.883245i	$-0.655354\pi$
$439$	1.28953	−	0.744511i	0.0615459	−	0.0355336i	0.530457	+	0.847712i	$0.322020\pi$
$440$		0			0
$441$	4.61158	−	7.03407i	0.219599	−	0.334956i
$442$		0			0
$443$	−30.9468	−	8.29218i	−1.47033	−	0.393973i	−0.567285	−	0.823522i	$-0.692006\pi$
$443$	−30.9468	−	8.29218i	−1.47033	−	0.393973i	−0.903044	+	0.429548i	$0.858673\pi$
$444$		0			0
$445$	7.37510	−	7.25833i	0.349613	−	0.344078i
$446$		0			0
$447$	27.9202	−	6.63888i	1.32058	−	0.314008i
$448$		0			0
$449$	−21.8283			−1.03014			−0.515071	−	0.857147i	$-0.672234\pi$
$449$	−21.8283			−1.03014			−0.515071	+	0.857147i	$0.672234\pi$
$450$		0			0
$451$	3.16647			0.149103
$452$		0			0
$453$	0.00281198	−	0.00941786i	0.000132118	−	0.000442490i
$454$		0			0
$455$	−18.1412	+	17.8540i	−0.850472	+	0.837006i
$456$		0			0
$457$	0.880339	+	0.235886i	0.0411805	+	0.0110343i	0.279351	−	0.960189i	$-0.409881\pi$
$457$	0.880339	+	0.235886i	0.0411805	+	0.0110343i	−0.238170	+	0.971223i	$0.576548\pi$
$458$		0			0
$459$	8.31839	+	0.709282i	0.388269	+	0.0331065i
$460$		0			0
$461$	−18.7320	+	10.8149i	−0.872434	+	0.503700i	−0.868156	−	0.496291i	$-0.834695\pi$
$461$	−18.7320	+	10.8149i	−0.872434	+	0.503700i	−0.00427761	+	0.999991i	$0.501362\pi$
$462$		0			0
$463$	18.1245	−	4.85644i	0.842316	−	0.225698i	0.188236	−	0.982124i	$-0.439723\pi$
$463$	18.1245	−	4.85644i	0.842316	−	0.225698i	0.654079	+	0.756426i	$0.273056\pi$
$464$		0			0
$465$	14.3795	−	22.9392i	0.666834	−	1.06378i
$466$		0			0
$467$	−16.8295	−	16.8295i	−0.778777	−	0.778777i	0.200846	−	0.979623i	$-0.435631\pi$
$467$	−16.8295	−	16.8295i	−0.778777	−	0.778777i	−0.979623	+	0.200846i	$0.935631\pi$
$468$		0			0
$469$		−	6.80460i		−	0.314207i
$470$		0			0
$471$	−7.68281	+	12.4763i	−0.354005	+	0.574875i
$472$		0			0
$473$	0.438306	+	1.63578i	0.0201533	+	0.0752133i
$474$		0			0
$475$	7.62184	+	0.121648i	0.349714	+	0.00558158i
$476$		0			0
$477$	13.1539	+	14.7372i	0.602276	+	0.674772i
$478$		0			0
$479$	8.91724	+	15.4451i	0.407439	+	0.705705i	0.994602	−	0.103764i	$-0.0330886\pi$
$479$	8.91724	+	15.4451i	0.407439	+	0.705705i	−0.587163	+	0.809469i	$0.699755\pi$
$480$		0			0
$481$	16.7285	−	28.9747i	0.762756	−	1.32113i
$482$		0			0
$483$	−4.09392	+	3.86810i	−0.186280	+	0.176005i
$484$		0			0
$485$	−7.71328	+	4.37158i	−0.350242	+	0.198503i
$486$		0			0
$487$	21.8232	−	21.8232i	0.988904	−	0.988904i	−0.0110354	−	0.999939i	$-0.503513\pi$
$487$	21.8232	−	21.8232i	0.988904	−	0.988904i	0.999939	+	0.0110354i	$0.00351274\pi$
$488$		0			0
$489$	0.291174	−	10.2666i	0.0131674	−	0.464273i
$490$		0			0
$491$	−35.1670	−	20.3037i	−1.58707	−	0.916292i	−0.993787	−	0.111295i	$-0.964500\pi$
$491$	−35.1670	−	20.3037i	−1.58707	−	0.916292i	−0.593278	−	0.804998i	$-0.702166\pi$
$492$		0			0
$493$	0.662503	−	2.47249i	0.0298376	−	0.111356i
$494$		0			0
$495$	−5.59269	−	1.89371i	−0.251373	−	0.0851157i
$496$		0			0
$497$	3.12705	−	11.6703i	0.140267	−	0.523484i
$498$		0			0
$499$	−37.3397	−	21.5581i	−1.67156	−	0.965073i	−0.966768	−	0.255655i	$-0.917709\pi$
$499$	−37.3397	−	21.5581i	−1.67156	−	0.965073i	−0.704788	−	0.709418i	$-0.748958\pi$
$500$		0			0
$501$	8.79988	+	5.41892i	0.393150	+	0.242100i
$502$		0			0
$503$	28.0936	−	28.0936i	1.25263	−	1.25263i	0.298093	−	0.954537i	$-0.403649\pi$
$503$	28.0936	−	28.0936i	1.25263	−	1.25263i	0.954537	−	0.298093i	$-0.0963506\pi$
$504$		0			0
$505$	1.53591	−	5.55443i	0.0683471	−	0.247169i
$506$		0			0
$507$	29.6708	+	8.85909i	1.31773	+	0.393446i
$508$		0			0
$509$	7.39188	−	12.8031i	0.327639	−	0.567488i	−0.654404	−	0.756145i	$-0.727080\pi$
$509$	7.39188	−	12.8031i	0.327639	−	0.567488i	0.982043	+	0.188658i	$0.0604136\pi$
$510$		0			0
$511$	−2.30168	−	3.98663i	−0.101820	−	0.176358i
$512$		0			0
$513$	−5.10544	−	6.05725i	−0.225411	−	0.267434i
$514$		0			0
$515$	14.8067	−	25.1799i	0.652463	−	1.10956i
$516$		0			0
$517$	−1.88667	−	7.04114i	−0.0829755	−	0.309669i
$518$		0			0
$519$	11.2484	+	20.8248i	0.493750	+	0.914108i
$520$		0			0
$521$			28.4812i			1.24778i	0.781511	+	0.623892i	$0.214449\pi$
$521$			28.4812i			1.24778i	−0.781511	+	0.623892i	$0.785551\pi$
$522$		0			0
$523$	−15.4076	−	15.4076i	−0.673726	−	0.673726i	0.284847	−	0.958573i	$-0.408057\pi$
$523$	−15.4076	−	15.4076i	−0.673726	−	0.673726i	−0.958573	+	0.284847i	$0.908057\pi$
$524$		0			0
$525$	−15.7416	+	8.18095i	−0.687019	+	0.357046i
$526$		0			0
$527$	10.8486	−	2.90687i	0.472572	−	0.126625i
$528$		0			0
$529$	17.7363	−	10.2401i	0.771145	−	0.445221i
$530$		0			0
$531$	−19.1568	−	12.5593i	−0.831335	−	0.545028i
$532$		0			0
$533$	−19.3089	−	5.17380i	−0.836361	−	0.224102i
$534$		0			0
$535$	29.1880	+	0.232911i	1.26191	+	0.0100696i
$536$		0			0
$537$	20.5040	+	21.7010i	0.884813	+	0.936466i
$538$		0			0
$539$	−2.46780			−0.106296
$540$		0			0
$541$	−1.11754			−0.0480466			−0.0240233	−	0.999711i	$-0.507648\pi$
$541$	−1.11754			−0.0480466			−0.0240233	+	0.999711i	$0.507648\pi$
$542$		0			0
$543$	17.5703	+	18.5960i	0.754015	+	0.798033i
$544$		0			0
$545$	−12.6337	−	12.8370i	−0.541169	−	0.549875i
$546$		0			0
$547$	31.1213	+	8.33894i	1.33065	+	0.356547i	0.852958	−	0.521979i	$-0.174806\pi$
$547$	31.1213	+	8.33894i	1.33065	+	0.356547i	0.477694	+	0.878526i	$0.341473\pi$
$548$		0			0
$549$	−35.5761	+	17.9325i	−1.51835	+	0.765342i
$550$		0			0
$551$	−2.10347	+	1.21444i	−0.0896109	+	0.0517369i
$552$		0			0
$553$	−15.2945	+	4.09814i	−0.650387	+	0.174271i
$554$		0			0
$555$	17.0772	−	15.8792i	0.724885	−	0.674035i
$556$		0			0
$557$	30.4033	+	30.4033i	1.28823	+	1.28823i	0.935862	+	0.352366i	$0.114623\pi$
$557$	30.4033	+	30.4033i	1.28823	+	1.28823i	0.352366	+	0.935862i	$0.385377\pi$
$558$		0			0
$559$		−	10.6910i		−	0.452182i
$560$		0			0
$561$	−1.16411	−	2.15519i	−0.0491489	−	0.0909922i
$562$		0			0
$563$	−0.300692	−	1.12220i	−0.0126727	−	0.0472950i	0.959300	−	0.282389i	$-0.0911269\pi$
$563$	−0.300692	−	1.12220i	−0.0126727	−	0.0472950i	−0.971973	+	0.235094i	$0.924460\pi$
$564$		0			0
$565$	−23.1360	−	13.6049i	−0.973338	−	0.572361i
$566$		0			0
$567$	17.1538	+	6.75644i	0.720393	+	0.283744i
$568$		0			0
$569$	−0.145367	−	0.251784i	−0.00609412	−	0.0105553i	0.862962	−	0.505268i	$-0.168606\pi$
$569$	−0.145367	−	0.251784i	−0.00609412	−	0.0105553i	−0.869056	+	0.494713i	$0.835273\pi$
$570$		0			0
$571$	13.0283	−	22.5656i	0.545215	−	0.944341i	−0.453378	−	0.891318i	$-0.649781\pi$
$571$	13.0283	−	22.5656i	0.545215	−	0.944341i	0.998593	−	0.0530223i	$-0.0168854\pi$
$572$		0			0
$573$	−8.75395	−	2.61375i	−0.365702	−	0.109191i
$574$		0			0
$575$	−7.69838	+	1.93164i	−0.321044	+	0.0805551i
$576$		0			0
$577$	−2.52834	+	2.52834i	−0.105256	+	0.105256i	−0.757774	−	0.652517i	$-0.773713\pi$
$577$	−2.52834	+	2.52834i	−0.105256	+	0.105256i	0.652517	+	0.757774i	$0.273713\pi$
$578$		0			0
$579$	−13.7258	−	8.45230i	−0.570427	−	0.351266i
$580$		0			0
$581$	−17.6274	−	10.1772i	−0.731309	−	0.422222i
$582$		0			0
$583$	1.50006	−	5.59831i	0.0621262	−	0.231858i
$584$		0			0
$585$	31.0096	+	20.6858i	1.28209	+	0.855251i
$586$		0			0
$587$	−10.7212	+	40.0121i	−0.442511	+	1.65147i	0.279914	+	0.960025i	$0.409694\pi$
$587$	−10.7212	+	40.0121i	−0.442511	+	1.65147i	−0.722425	+	0.691449i	$0.756973\pi$
$588$		0			0
$589$	−9.22943	−	5.32861i	−0.380292	−	0.219562i
$590$		0			0
$591$	0.659386	−	23.2495i	0.0271235	−	0.956358i
$592$		0			0
$593$	26.6583	−	26.6583i	1.09473	−	1.09473i	0.0997087	−	0.995017i	$-0.468209\pi$
$593$	26.6583	−	26.6583i	1.09473	−	1.09473i	0.995017	−	0.0997087i	$-0.0317911\pi$
$594$		0			0
$595$	−7.09335	−	1.96145i	−0.290799	−	0.0804117i
$596$		0			0
$597$	22.2009	−	20.9764i	0.908624	−	0.858506i
$598$		0			0
$599$	13.2427	−	22.9370i	0.541080	−	0.937178i	−0.457762	−	0.889075i	$-0.651349\pi$
$599$	13.2427	−	22.9370i	0.541080	−	0.937178i	0.998842	−	0.0481037i	$-0.0153178\pi$
$600$		0			0
$601$	4.26710	+	7.39084i	0.174059	+	0.301479i	0.939835	−	0.341628i	$-0.110978\pi$
$601$	4.26710	+	7.39084i	0.174059	+	0.301479i	−0.765776	+	0.643107i	$0.777645\pi$
$602$		0			0
$603$	−9.75641	+	2.02950i	−0.397312	+	0.0826475i
$604$		0			0
$605$	−5.74131	−	22.1318i	−0.233417	−	0.899784i
$606$		0			0
$607$	11.9000	+	44.4113i	0.483005	+	1.80260i	0.588881	+	0.808220i	$0.299569\pi$
$607$	11.9000	+	44.4113i	0.483005	+	1.80260i	−0.105876	+	0.994379i	$0.533765\pi$
$608$		0			0
$609$	2.96400	−	4.81329i	0.120107	−	0.195045i
$610$		0			0
$611$			46.0190i			1.86173i
$612$		0			0
$613$	17.3219	+	17.3219i	0.699625	+	0.699625i	0.964330	−	0.264705i	$-0.0852744\pi$
$613$	17.3219	+	17.3219i	0.699625	+	0.699625i	−0.264705	+	0.964330i	$0.585274\pi$
$614$		0			0
$615$	−11.8051	−	7.40008i	−0.476027	−	0.298400i
$616$		0			0
$617$	36.3708	−	9.74553i	1.46423	−	0.392340i	0.563284	−	0.826263i	$-0.309538\pi$
$617$	36.3708	−	9.74553i	1.46423	−	0.392340i	0.900950	+	0.433923i	$0.142871\pi$
$618$		0			0
$619$	−8.57434	+	4.95040i	−0.344632	+	0.198973i	−0.662318	−	0.749223i	$-0.730427\pi$
$619$	−8.57434	+	4.95040i	−0.344632	+	0.198973i	0.317687	+	0.948196i	$0.397094\pi$
$620$		0			0
$621$	6.76710	+	4.71617i	0.271554	+	0.189253i
$622$		0			0
$623$	9.15670	+	2.45353i	0.366855	+	0.0982986i
$624$		0			0
$625$	−24.9873	−	0.797817i	−0.999491	−	0.0319127i
$626$		0			0
$627$	−0.664976	+	2.22713i	−0.0265566	+	0.0889431i
$628$		0			0
$629$	9.67378			0.385719
$630$		0			0
$631$	22.0279			0.876918			0.438459	−	0.898751i	$-0.355524\pi$
$631$	22.0279			0.876918			0.438459	+	0.898751i	$0.355524\pi$
$632$		0			0
$633$	−0.207617	+	0.0493675i	−0.00825205	+	0.00196218i
$634$		0			0
$635$	0.0480011	−	6.01540i	0.00190487	−	0.238714i
$636$		0			0
$637$	15.0485	+	4.03223i	0.596242	+	0.159763i
$638$		0			0
$639$	−17.6655	−	1.00284i	−0.698836	−	0.0396716i
$640$		0			0
$641$	21.8054	−	12.5894i	0.861263	−	0.497251i	−0.00317173	−	0.999995i	$-0.501010\pi$
$641$	21.8054	−	12.5894i	0.861263	−	0.497251i	0.864435	+	0.502744i	$0.167676\pi$
$642$		0			0
$643$	−30.0492	+	8.05166i	−1.18502	+	0.317526i	−0.796918	−	0.604088i	$-0.793538\pi$
$643$	−30.0492	+	8.05166i	−1.18502	+	0.317526i	−0.388107	+	0.921614i	$0.626871\pi$
$644$		0			0
$645$	2.18877	−	7.12277i	0.0861826	−	0.280459i
$646$		0			0
$647$	7.86580	+	7.86580i	0.309237	+	0.309237i	0.844613	−	0.535377i	$-0.179830\pi$
$647$	7.86580	+	7.86580i	0.309237	+	0.309237i	−0.535377	+	0.844613i	$0.679830\pi$
$648$		0			0
$649$			6.72090i			0.263818i
$650$		0			0
$651$	24.7925	+	0.703147i	0.971695	+	0.0275585i
$652$		0			0
$653$	0.0749391	+	0.279676i	0.00293259	+	0.0109446i	0.967377	−	0.253343i	$-0.0815300\pi$
$653$	0.0749391	+	0.279676i	0.00293259	+	0.0109446i	−0.964444	+	0.264287i	$0.914863\pi$
$654$		0			0
$655$	−46.2637	+	12.0015i	−1.80767	+	0.468937i
$656$		0			0
$657$	−5.02953	+	4.48917i	−0.196221	+	0.175139i
$658$		0			0
$659$	−13.4009	−	23.2111i	−0.522026	−	0.904175i	−0.999672	−	0.0256228i	$-0.991843\pi$
$659$	−13.4009	−	23.2111i	−0.522026	−	0.904175i	0.477646	−	0.878552i	$-0.341490\pi$
$660$		0			0
$661$	−12.6438	+	21.8997i	−0.491787	+	0.851800i	−0.999955	−	0.00945786i	$-0.996989\pi$
$661$	−12.6438	+	21.8997i	−0.491787	+	0.851800i	0.508168	+	0.861258i	$0.330323\pi$
$662$		0			0
$663$	3.57724	+	15.0443i	0.138928	+	0.584271i
$664$		0			0
$665$	3.44332	+	6.07544i	0.133526	+	0.235596i
$666$		0			0
$667$	1.78827	−	1.78827i	0.0692421	−	0.0692421i
$668$		0			0
$669$	−3.81556	+	2.06095i	−0.147518	+	0.0796811i
$670$		0			0
$671$	10.1231	+	5.84458i	0.390799	+	0.225628i
$672$		0			0
$673$	6.30290	−	23.5227i	0.242959	−	0.906735i	−0.731439	−	0.681906i	$-0.761151\pi$
$673$	6.30290	−	23.5227i	0.242959	−	0.906735i	0.974398	−	0.224829i	$-0.0721822\pi$
$674$		0			0
$675$	16.4248	+	20.1302i	0.632191	+	0.774812i
$676$		0			0
$677$	−0.240265	+	0.896681i	−0.00923414	+	0.0344623i	−0.970389	−	0.241547i	$-0.922345\pi$
$677$	−0.240265	+	0.896681i	−0.00923414	+	0.0344623i	0.961155	+	0.276009i	$0.0890120\pi$
$678$		0			0
$679$	−7.03407	−	4.06112i	−0.269943	−	0.155852i
$680$		0			0
$681$	−23.2386	+	12.5522i	−0.890503	+	0.481000i
$682$		0			0
$683$	22.2024	−	22.2024i	0.849550	−	0.849550i	−0.140526	−	0.990077i	$-0.544880\pi$
$683$	22.2024	−	22.2024i	0.849550	−	0.849550i	0.990077	+	0.140526i	$0.0448795\pi$
$684$		0			0
$685$	7.56311	+	13.3445i	0.288972	+	0.509866i
$686$		0			0
$687$	−8.84071	−	37.1801i	−0.337294	−	1.41851i
$688$		0			0
$689$	−18.2945	+	31.6871i	−0.696966	+	1.20718i
$690$		0			0
$691$	4.05877	+	7.02999i	0.154403	+	0.267433i	0.932841	−	0.360287i	$-0.117321\pi$
$691$	4.05877	+	7.02999i	0.154403	+	0.267433i	−0.778439	+	0.627721i	$0.783988\pi$
$692$		0			0
$693$	−1.10164	−	5.29593i	−0.0418479	−	0.201176i
$694$		0			0
$695$	−3.12065	+	0.809543i	−0.118373	+	0.0307077i
$696$		0			0
$697$	−1.49595	−	5.58297i	−0.0566633	−	0.211470i
$698$		0			0
$699$	−10.3369	−	0.293168i	−0.390979	−	0.0110887i
$700$		0			0
$701$		−	19.6359i		−	0.741637i	−0.928705	−	0.370819i	$-0.879077\pi$
$701$		−	19.6359i		−	0.741637i	0.928705	−	0.370819i	$-0.120923\pi$
$702$		0			0
$703$	−6.49076	−	6.49076i	−0.244804	−	0.244804i
$704$		0			0
$705$	−9.42143	+	30.6596i	−0.354832	+	1.15471i
$706$		0			0
$707$	5.09956	−	1.36642i	0.191789	−	0.0513896i
$708$		0			0
$709$	−2.68383	+	1.54951i	−0.100793	+	0.0581931i	−0.549549	−	0.835461i	$-0.685201\pi$
$709$	−2.68383	+	1.54951i	−0.100793	+	0.0581931i	0.448756	+	0.893654i	$0.351867\pi$
$710$		0			0
$711$	10.4375	+	20.7069i	0.391438	+	0.776569i
$712$		0			0
$713$	10.7184	+	2.87199i	0.401408	+	0.107557i
$714$		0			0
$715$	0.0872699	−	10.9365i	0.00326371	−	0.409002i
$716$		0			0
$717$	22.8900	−	5.44280i	0.854841	−	0.203265i
$718$		0			0
$719$	20.3126			0.757533			0.378767	−	0.925492i	$-0.376348\pi$
$719$	20.3126			0.757533			0.378767	+	0.925492i	$0.376348\pi$
$720$		0			0
$721$	26.7604			0.996608
$722$		0			0
$723$	2.54437	−	8.52158i	0.0946261	−	0.316921i
$724$		0			0
$725$	6.96129	−	3.87232i	0.258536	−	0.143814i
$726$		0			0
$727$	17.0647	+	4.57247i	0.632895	+	0.169584i	0.560983	−	0.827827i	$-0.310423\pi$
$727$	17.0647	+	4.57247i	0.632895	+	0.169584i	0.0719119	+	0.997411i	$0.477090\pi$
$728$		0			0
$729$	4.57117	−	26.6102i	0.169303	−	0.985564i
$730$		0			0
$731$	2.67706	−	1.54560i	0.0990147	−	0.0571662i
$732$		0			0
$733$	25.4785	−	6.82693i	0.941068	−	0.252158i	0.244500	−	0.969649i	$-0.421376\pi$
$733$	25.4785	−	6.82693i	0.941068	−	0.252158i	0.696568	+	0.717491i	$0.254709\pi$
$734$		0			0
$735$	9.20035	+	5.76729i	0.339360	+	0.212730i
$736$		0			0
$737$	2.06746	+	2.06746i	0.0761558	+	0.0761558i
$738$		0			0
$739$			6.41459i			0.235965i	0.993016	+	0.117982i	$0.0376426\pi$
$739$			6.41459i			0.235965i	−0.993016	+	0.117982i	$0.962357\pi$
$740$		0			0
$741$	7.69396	−	12.4944i	0.282645	−	0.458992i
$742$		0			0
$743$	4.95625	+	18.4970i	0.181827	+	0.678588i	0.995288	+	0.0969677i	$0.0309144\pi$
$743$	4.95625	+	18.4970i	0.181827	+	0.678588i	−0.813460	+	0.581620i	$0.802419\pi$
$744$		0			0
$745$	9.30331	+	35.8627i	0.340847	+	1.31391i
$746$		0			0
$747$	−9.33459	+	28.3096i	−0.341535	+	1.03579i
$748$		0			0
$749$	13.3702	+	23.1579i	0.488536	+	0.846170i
$750$		0			0
$751$	1.96958	−	3.41141i	0.0718709	−	0.124484i	−0.827850	−	0.560949i	$-0.810436\pi$
$751$	1.96958	−	3.41141i	0.0718709	−	0.124484i	0.899721	+	0.436465i	$0.143770\pi$
$752$		0			0
$753$	3.27612	−	3.09541i	0.119388	−	0.112803i
$754$		0			0
$755$	0.0122298	+	0.00338180i	0.000445090	+	0.000123076i
$756$		0			0
$757$	17.3710	−	17.3710i	0.631361	−	0.631361i	−0.317049	−	0.948409i	$-0.602692\pi$
$757$	17.3710	−	17.3710i	0.631361	−	0.631361i	0.948409	+	0.317049i	$0.102692\pi$
$758$		0			0
$759$	0.0686093	−	2.41912i	0.00249036	−	0.0878085i
$760$		0			0
$761$	7.11860	+	4.10993i	0.258049	+	0.148985i	0.623444	−	0.781868i	$-0.285733\pi$
$761$	7.11860	+	4.10993i	0.258049	+	0.148985i	−0.365395	+	0.930853i	$0.619066\pi$
$762$		0			0
$763$	4.27057	−	15.9380i	0.154605	−	0.576994i
$764$		0			0
$765$	−0.696707	+	10.7554i	−0.0251895	+	0.388863i
$766$		0			0
$767$	10.9815	−	40.9835i	0.396519	−	1.47983i
$768$		0			0
$769$	−1.91615	−	1.10629i	−0.0690983	−	0.0398939i	0.465053	−	0.885283i	$-0.346035\pi$
$769$	−1.91615	−	1.10629i	−0.0690983	−	0.0398939i	−0.534151	+	0.845389i	$0.679369\pi$
$770$		0			0
$771$	−15.5677	−	9.58654i	−0.560659	−	0.345251i
$772$		0			0
$773$	8.23173	−	8.23173i	0.296075	−	0.296075i	−0.543400	−	0.839474i	$-0.682863\pi$
$773$	8.23173	−	8.23173i	0.296075	−	0.296075i	0.839474	+	0.543400i	$0.182863\pi$
$774$		0			0
$775$	29.9864	+	17.9567i	1.07714	+	0.645024i
$776$		0			0
$777$	20.4700	+	6.11191i	0.734356	+	0.219264i
$778$		0			0
$779$	−2.74224	+	4.74970i	−0.0982511	+	0.170176i
$780$		0			0
$781$	2.59572	+	4.49591i	0.0928820	+	0.160876i
$782$		0			0
$783$	−7.78531	−	2.81419i	−0.278224	−	0.100571i
$784$		0			0
$785$	−16.3055	−	9.58827i	−0.581968	−	0.342220i
$786$		0			0
$787$	9.07119	+	33.8541i	0.323353	+	1.20677i	0.915957	+	0.401276i	$0.131433\pi$
$787$	9.07119	+	33.8541i	0.323353	+	1.20677i	−0.592604	+	0.805494i	$0.701900\pi$
$788$		0			0
$789$	6.92440	+	12.8195i	0.246515	+	0.456387i
$790$		0			0
$791$		−	24.5882i		−	0.874256i
$792$		0			0
$793$	−52.1803	−	52.1803i	−1.85298	−	1.85298i
$794$		0			0
$795$	−18.6758	+	17.3657i	−0.662362	+	0.615898i
$796$		0			0
$797$	−25.2788	+	6.77343i	−0.895421	+	0.239927i	−0.677049	−	0.735938i	$-0.736741\pi$
$797$	−25.2788	+	6.77343i	−0.895421	+	0.239927i	−0.218372	+	0.975866i	$0.570075\pi$
$798$		0			0
$799$	−11.5233	+	6.65297i	−0.407664	+	0.235365i
$800$		0			0
$801$	0.786842	−	13.8606i	0.0278017	−	0.489741i
$802$		0			0
$803$	1.91059	+	0.511942i	0.0674233	+	0.0180660i
$804$		0			0
$805$	−5.10034	−	5.18239i	−0.179763	−	0.182655i
$806$		0			0
$807$	31.8447	+	33.7038i	1.12099	+	1.18643i
$808$		0			0
$809$	−40.3389			−1.41824			−0.709120	−	0.705088i	$-0.750908\pi$
$809$	−40.3389			−1.41824			−0.709120	+	0.705088i	$0.750908\pi$
$810$		0			0
$811$	4.50040			0.158030			0.0790152	−	0.996873i	$-0.474822\pi$
$811$	4.50040			0.158030			0.0790152	+	0.996873i	$0.474822\pi$
$812$		0			0
$813$	22.1075	+	23.3981i	0.775343	+	0.820606i
$814$		0			0
$815$	13.2591	+	0.105803i	0.464445	+	0.00370613i
$816$		0			0
$817$	−2.83326	−	0.759168i	−0.0991231	−	0.0265599i
$818$		0			0
$819$	−1.93546	+	34.0942i	−0.0676306	+	1.19135i
$820$		0			0
$821$	13.3109	−	7.68503i	0.464552	−	0.268209i	−0.249404	−	0.968399i	$-0.580235\pi$
$821$	13.3109	−	7.68503i	0.464552	−	0.268209i	0.713956	+	0.700190i	$0.246901\pi$
$822$		0			0
$823$	14.0723	−	3.77065i	0.490528	−	0.131437i	−0.00507263	−	0.999987i	$-0.501615\pi$
$823$	14.0723	−	3.77065i	0.490528	−	0.131437i	0.495601	+	0.868551i	$0.334948\pi$
$824$		0			0
$825$	2.29716	−	7.26844i	0.0799769	−	0.253055i
$826$		0			0
$827$	−3.31824	−	3.31824i	−0.115387	−	0.115387i	0.647056	−	0.762443i	$-0.276000\pi$
$827$	−3.31824	−	3.31824i	−0.115387	−	0.115387i	−0.762443	+	0.647056i	$0.776000\pi$
$828$		0			0
$829$		−	33.9539i		−	1.17927i	−0.807671	−	0.589633i	$-0.799272\pi$
$829$		−	33.9539i		−	1.17927i	0.807671	−	0.589633i	$-0.200728\pi$
$830$		0			0
$831$	−22.4302	−	41.5263i	−0.778094	−	1.44053i
$832$		0			0
$833$	1.16588	+	4.35112i	0.0403953	+	0.150757i
$834$		0			0
$835$	−6.76290	+	11.5008i	−0.234040	+	0.398000i
$836$		0			0
$837$	−6.38629	−	35.7571i	−0.220743	−	1.23595i
$838$		0			0
$839$	5.71824	+	9.90428i	0.197416	+	0.341934i	0.947690	−	0.319193i	$-0.103412\pi$
$839$	5.71824	+	9.90428i	0.197416	+	0.341934i	−0.750274	+	0.661127i	$0.770079\pi$
$840$		0			0
$841$	13.2309	−	22.9166i	0.456238	−	0.790228i
$842$		0			0
$843$	−43.5119	−	12.9918i	−1.49863	−	0.447460i
$844$		0			0
$845$	−10.6543	+	38.5299i	−0.366519	+	1.32547i
$846$		0			0
$847$	14.8113	−	14.8113i	0.508923	−	0.508923i
$848$		0			0
$849$	−5.25321	−	3.23490i	−0.180290	−	0.111021i
$850$		0			0
$851$	8.27720	+	4.77884i	0.283739	+	0.163817i
$852$		0			0
$853$	−6.18947	+	23.0994i	−0.211923	+	0.790909i	0.775304	+	0.631589i	$0.217597\pi$
$853$	−6.18947	+	23.0994i	−0.211923	+	0.790909i	−0.987227	+	0.159320i	$0.949070\pi$
$854$		0			0
$855$	7.68397	−	6.74904i	0.262786	−	0.230812i
$856$		0			0
$857$	−3.88189	+	14.4874i	−0.132603	+	0.494881i	−0.999996	−	0.00274224i	$-0.999127\pi$
$857$	−3.88189	+	14.4874i	−0.132603	+	0.494881i	0.867393	+	0.497623i	$0.165794\pi$
$858$		0			0
$859$	37.5983	+	21.7074i	1.28284	+	0.740646i	0.977366	−	0.211555i	$-0.0678529\pi$
$859$	37.5983	+	21.7074i	1.28284	+	0.740646i	0.305471	+	0.952201i	$0.401186\pi$
$860$		0			0
$861$	0.361857	−	12.7589i	0.0123321	−	0.434821i
$862$		0			0
$863$	−2.78648	+	2.78648i	−0.0948527	+	0.0948527i	−0.752941	−	0.658088i	$-0.771365\pi$
$863$	−2.78648	+	2.78648i	−0.0948527	+	0.0948527i	0.658088	+	0.752941i	$0.271365\pi$
$864$		0			0
$865$	−26.5833	+	15.0663i	−0.903859	+	0.512271i
$866$		0			0
$867$	18.1526	−	17.1513i	0.616495	−	0.582490i
$868$		0			0
$869$	3.40181	−	5.89211i	0.115399	−	0.199876i
$870$		0			0
$871$	−9.22911	−	15.9853i	−0.312717	−	0.541641i
$872$		0			0
$873$	−3.72489	+	11.2967i	−0.126068	+	0.382335i
$874$		0			0
$875$	−10.9734	−	20.1029i	−0.370968	−	0.679602i
$876$		0			0
$877$	11.1359	+	41.5598i	0.376033	+	1.40338i	0.851829	+	0.523820i	$0.175493\pi$
$877$	11.1359	+	41.5598i	0.376033	+	1.40338i	−0.475796	+	0.879556i	$0.657840\pi$
$878$		0			0
$879$	−2.70616	+	4.39458i	−0.0912764	+	0.148225i
$880$		0			0
$881$			47.0487i			1.58511i	0.609801	+	0.792555i	$0.291249\pi$
$881$			47.0487i			1.58511i	−0.609801	+	0.792555i	$0.708751\pi$
$882$		0			0
$883$	−21.0669	−	21.0669i	−0.708957	−	0.708957i	0.257359	−	0.966316i	$-0.417148\pi$
$883$	−21.0669	−	21.0669i	−0.708957	−	0.708957i	−0.966316	+	0.257359i	$0.917148\pi$
$884$		0			0
$885$	15.7068	−	25.0565i	0.527979	−	0.842267i
$886$		0			0
$887$	−3.50739	+	0.939801i	−0.117766	+	0.0315554i	−0.317221	−	0.948352i	$-0.602750\pi$
$887$	−3.50739	+	0.939801i	−0.117766	+	0.0315554i	0.199454	+	0.979907i	$0.436083\pi$
$888$		0			0
$889$	4.77265	−	2.75549i	0.160069	−	0.0924161i
$890$		0			0
$891$	−7.26472	+	3.15906i	−0.243377	+	0.105833i
$892$		0			0
$893$	12.1956	+	3.26780i	0.408110	+	0.109353i
$894$		0			0
$895$	−27.4708	+	27.0358i	−0.918246	+	0.903707i
$896$		0			0
$897$	−4.37106	+	14.6395i	−0.145945	+	0.488799i
$898$		0			0
$899$	−11.1368			−0.371433
$900$		0			0
$901$	−10.5794			−0.352450
$902$		0			0
$903$	6.64125	−	1.57916i	0.221007	−	0.0525512i
$904$		0			0
$905$	−23.5403	+	23.1676i	−0.782506	+	0.770116i
$906$		0			0
$907$	−10.1363	−	2.71600i	−0.336569	−	0.0901833i	0.0865764	−	0.996245i	$-0.472407\pi$
$907$	−10.1363	−	2.71600i	−0.336569	−	0.0901833i	−0.423145	+	0.906062i	$0.639074\pi$
$908$		0			0
$909$	−3.48014	−	6.90419i	−0.115429	−	0.228998i
$910$		0			0
$911$	−6.77512	+	3.91162i	−0.224470	+	0.129598i	−0.608018	−	0.793923i	$-0.708035\pi$
$911$	−6.77512	+	3.91162i	−0.224470	+	0.129598i	0.383548	+	0.923521i	$0.374702\pi$
$912$		0			0
$913$	8.44796	−	2.26362i	0.279587	−	0.0749150i
$914$		0			0
$915$	−24.0817	−	45.4474i	−0.796116	−	1.50244i
$916$		0			0
$917$	−30.9612	−	30.9612i	−1.02243	−	1.02243i
$918$		0			0
$919$		−	4.61000i		−	0.152070i	−0.997105	−	0.0760349i	$-0.975774\pi$
$919$		−	4.61000i		−	0.152070i	0.997105	−	0.0760349i	$-0.0242260\pi$
$920$		0			0
$921$	−53.3815	−	1.51397i	−1.75898	−	0.0498869i
$922$		0			0
$923$	−8.48246	−	31.6570i	−0.279204	−	1.04200i
$924$		0			0
$925$	20.9449	+	21.6243i	0.688663	+	0.711002i
$926$		0			0
$927$	−7.98139	−	38.3689i	−0.262143	−	1.26020i
$928$		0			0
$929$	−15.7062	−	27.2039i	−0.515302	−	0.892530i	−0.999842	−	0.0177609i	$-0.994346\pi$
$929$	−15.7062	−	27.2039i	−0.515302	−	0.892530i	0.484540	−	0.874769i	$-0.338987\pi$
$930$		0			0
$931$	2.13718	−	3.70170i	0.0700433	−	0.121318i
$932$		0			0
$933$	−13.5966	−	57.1814i	−0.445134	−	1.87203i
$934$		0			0
$935$	2.75114	−	1.55924i	0.0899720	−	0.0509925i
$936$		0			0
$937$	−21.3617	+	21.3617i	−0.697856	+	0.697856i	−0.963948	−	0.266092i	$-0.914268\pi$
$937$	−21.3617	+	21.3617i	−0.697856	+	0.697856i	0.266092	+	0.963948i	$0.414268\pi$
$938$		0			0
$939$	35.3449	−	19.0914i	1.15344	−	0.623023i
$940$		0			0
$941$	−5.77035	−	3.33151i	−0.188108	−	0.108604i	0.402989	−	0.915205i	$-0.367971\pi$
$941$	−5.77035	−	3.33151i	−0.188108	−	0.108604i	−0.591096	+	0.806601i	$0.701305\pi$
$942$		0			0
$943$	1.47800	−	5.51597i	0.0481303	−	0.179625i
$944$		0			0
$945$	−8.26955	+	22.3186i	−0.269009	+	0.726024i
$946$		0			0
$947$	−0.867814	+	3.23873i	−0.0282002	+	0.105245i	−0.978591	−	0.205812i	$-0.934016\pi$
$947$	−0.867814	+	3.23873i	−0.0282002	+	0.105245i	0.950391	+	0.311057i	$0.100683\pi$
$948$		0			0
$949$	−10.8142	−	6.24356i	−0.351043	−	0.202675i
$950$		0			0
$951$	−6.09628	+	3.29287i	−0.197685	+	0.106779i
$952$		0			0
$953$	30.7161	−	30.7161i	0.994992	−	0.994992i	−0.00499525	−	0.999988i	$-0.501590\pi$
$953$	30.7161	−	30.7161i	0.994992	−	0.994992i	0.999988	+	0.00499525i	$0.00159004\pi$
$954$		0			0
$955$	3.14340	−	11.3677i	0.101718	−	0.367850i
$956$		0			0
$957$	0.561875	+	2.36300i	0.0181629	+	0.0763848i
$958$		0			0
$959$	−7.02601	+	12.1694i	−0.226882	+	0.392970i
$960$		0			0
$961$	−8.93253	−	15.4716i	−0.288146	−	0.499084i
$962$		0			0
$963$	29.2160	−	26.0771i	0.941471	−	0.840322i
$964$		0			0
$965$	10.5486	−	17.9386i	0.339572	−	0.577465i
$966$		0			0
$967$	1.48419	+	5.53906i	0.0477282	+	0.178124i	0.985675	−	0.168654i	$-0.0539422\pi$
$967$	1.48419	+	5.53906i	0.0477282	+	0.178124i	−0.937947	+	0.346779i	$0.887276\pi$
$968$		0			0
$969$	4.24094	+	0.120278i	0.136238	+	0.00386389i
$970$		0			0
$971$		−	14.2248i		−	0.456496i	−0.973603	−	0.228248i	$-0.926700\pi$
$971$		−	14.2248i		−	0.456496i	0.973603	−	0.228248i	$-0.0732998\pi$
$972$		0			0
$973$	−2.08844	−	2.08844i	−0.0669524	−	0.0669524i
$974$		0			0
$975$	−25.8841	+	40.5690i	−0.828954	+	1.29925i
$976$		0			0
$977$	30.1529	−	8.07944i	0.964676	−	0.258484i	0.258097	−	0.966119i	$-0.416904\pi$
$977$	30.1529	−	8.07944i	0.964676	−	0.258484i	0.706578	+	0.707635i	$0.250238\pi$
$978$		0			0
$979$	−3.52757	+	2.03664i	−0.112742	+	0.0650913i
$980$		0			0
$981$	−24.1256	−	1.36956i	−0.770270	−	0.0437268i
$982$		0			0
$983$	−9.94750	−	2.66543i	−0.317276	−	0.0850139i	0.0966666	−	0.995317i	$-0.469182\pi$
$983$	−9.94750	−	2.66543i	−0.317276	−	0.0850139i	−0.413943	+	0.910303i	$0.635849\pi$
$984$		0			0
$985$	30.0261	+	0.239599i	0.956712	+	0.00763427i
$986$		0			0
$987$	−28.5869	+	6.79742i	−0.909932	+	0.216364i
$988$		0			0
$989$	3.05411			0.0971150
$990$		0			0
$991$	−37.9180			−1.20450			−0.602252	−	0.798306i	$-0.705730\pi$
$991$	−37.9180			−1.20450			−0.602252	+	0.798306i	$0.705730\pi$
$992$		0			0
$993$	−2.95514	+	9.89733i	−0.0937785	+	0.314082i
$994$		0			0
$995$	27.6587	+	28.1036i	0.876839	+	0.890945i
$996$		0			0
$997$	30.1153	+	8.06937i	0.953761	+	0.255559i	0.701957	−	0.712219i	$-0.252310\pi$
$997$	30.1153	+	8.06937i	0.953761	+	0.255559i	0.251804	+	0.967778i	$0.418976\pi$
$998$		0			0
$999$	2.65799	−	31.1727i	0.0840952	−	0.986260i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.cu.c.113.3		16
4.3	odd	2		45.2.l.a.23.4	yes	16
5.2	odd	4	inner	720.2.cu.c.257.4		16
9.2	odd	6	inner	720.2.cu.c.353.4		16
12.11	even	2		135.2.m.a.98.1		16
20.3	even	4		225.2.p.b.32.1		16
20.7	even	4		45.2.l.a.32.4	yes	16
20.19	odd	2		225.2.p.b.68.1		16
36.7	odd	6		135.2.m.a.8.1		16
36.11	even	6		45.2.l.a.38.4	yes	16
36.23	even	6		405.2.f.a.323.3		16
36.31	odd	6		405.2.f.a.323.6		16
45.2	even	12	inner	720.2.cu.c.497.3		16
60.23	odd	4		675.2.q.a.557.4		16
60.47	odd	4		135.2.m.a.17.1		16
60.59	even	2		675.2.q.a.368.4		16
180.7	even	12		135.2.m.a.62.1		16
180.43	even	12		675.2.q.a.332.4		16
180.47	odd	12		45.2.l.a.2.4	✓	16
180.67	even	12		405.2.f.a.242.3		16
180.79	odd	6		675.2.q.a.143.4		16
180.83	odd	12		225.2.p.b.182.1		16
180.119	even	6		225.2.p.b.218.1		16
180.167	odd	12		405.2.f.a.242.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.l.a.2.4	✓	16	180.47	odd	12
45.2.l.a.23.4	yes	16	4.3	odd	2
45.2.l.a.32.4	yes	16	20.7	even	4
45.2.l.a.38.4	yes	16	36.11	even	6
135.2.m.a.8.1		16	36.7	odd	6
135.2.m.a.17.1		16	60.47	odd	4
135.2.m.a.62.1		16	180.7	even	12
135.2.m.a.98.1		16	12.11	even	2
225.2.p.b.32.1		16	20.3	even	4
225.2.p.b.68.1		16	20.19	odd	2
225.2.p.b.182.1		16	180.83	odd	12
225.2.p.b.218.1		16	180.119	even	6
405.2.f.a.242.3		16	180.67	even	12
405.2.f.a.242.6		16	180.167	odd	12
405.2.f.a.323.3		16	36.23	even	6
405.2.f.a.323.6		16	36.31	odd	6
675.2.q.a.143.4		16	180.79	odd	6
675.2.q.a.332.4		16	180.43	even	12
675.2.q.a.368.4		16	60.59	even	2
675.2.q.a.557.4		16	60.23	odd	4
720.2.cu.c.113.3		16	1.1	even	1	trivial
720.2.cu.c.257.4		16	5.2	odd	4	inner
720.2.cu.c.353.4		16	9.2	odd	6	inner
720.2.cu.c.497.3		16	45.2	even	12	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:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.cu (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.18953 + 1.25897i) q^{3} +(-1.59371 + 1.56847i) q^{5} +(-1.97869 - 0.530190i) q^{7} +(-0.170031 + 2.99518i) q^{9} +O(q^{10})\)	\(q+(1.18953 + 1.25897i) q^{3} +(-1.59371 + 1.56847i) q^{5} +(-1.97869 - 0.530190i) q^{7} +(-0.170031 + 2.99518i) q^{9} +(0.762281 - 0.440103i) q^{11} +(-5.36743 + 1.43820i) q^{13} +(-3.87043 - 0.140687i) q^{15} +(-1.13610 - 1.13610i) q^{17} +1.52456i q^{19} +(-1.68622 - 3.12180i) q^{21} +(-0.410850 - 1.53331i) q^{23} +(0.0797919 - 4.99936i) q^{25} +(-3.97311 + 3.34879i) q^{27} +(0.796583 + 1.37972i) q^{29} +(-3.49518 + 6.05383i) q^{31} +(1.46084 + 0.436175i) q^{33} +(3.98504 - 2.25856i) q^{35} +(-4.25746 + 4.25746i) q^{37} +(-8.19538 - 5.04667i) q^{39} +(3.11546 + 1.79871i) q^{41} +(-0.497959 + 1.85841i) q^{43} +(-4.42687 - 5.04012i) q^{45} +(2.14344 - 7.99942i) q^{47} +(-2.42805 - 1.40183i) q^{49} +(0.0788937 - 2.78174i) q^{51} +(4.65601 - 4.65601i) q^{53} +(-0.524562 + 1.89701i) q^{55} +(-1.91938 + 1.81351i) q^{57} +(-3.81780 + 6.61262i) q^{59} +(6.64002 + 11.5008i) q^{61} +(1.92445 - 5.83639i) q^{63} +(6.29833 - 10.7107i) q^{65} +(0.859733 + 3.20857i) q^{67} +(1.44168 - 2.34117i) q^{69} +5.89798i q^{71} +(1.58900 + 1.58900i) q^{73} +(6.38898 - 5.84644i) q^{75} +(-1.74166 + 0.466676i) q^{77} +(6.69401 - 3.86479i) q^{79} +(-8.94218 - 1.01854i) q^{81} +(9.59770 + 2.57170i) q^{83} +(3.59254 + 0.0286674i) q^{85} +(-0.789474 + 2.64410i) q^{87} -4.62765 q^{89} +11.3830 q^{91} +(-11.7792 + 2.80088i) q^{93} +(-2.39123 - 2.42970i) q^{95} +(3.82988 + 1.02621i) q^{97} +(1.18858 + 2.35800i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{3} - 6 q^{5} + 2 q^{7}+O(q^{10}) \) 16 * q + 6 * q^3 - 6 * q^5 + 2 * q^7	\( 16 q + 6 q^{3} - 6 q^{5} + 2 q^{7} - 2 q^{13} + 6 q^{15} - 12 q^{21} - 18 q^{23} + 4 q^{25} - 18 q^{27} + 4 q^{31} - 12 q^{33} + 4 q^{37} - 24 q^{41} + 2 q^{43} - 36 q^{45} + 12 q^{47} - 36 q^{51} + 16 q^{55} - 6 q^{57} + 8 q^{61} - 36 q^{63} + 66 q^{65} - 4 q^{67} - 8 q^{73} - 42 q^{75} - 6 q^{77} - 48 q^{81} + 66 q^{83} + 22 q^{85} + 18 q^{87} + 40 q^{91} - 18 q^{93} + 36 q^{95} + 28 q^{97}+O(q^{100}) \) 16 * q + 6 * q^3 - 6 * q^5 + 2 * q^7 - 2 * q^13 + 6 * q^15 - 12 * q^21 - 18 * q^23 + 4 * q^25 - 18 * q^27 + 4 * q^31 - 12 * q^33 + 4 * q^37 - 24 * q^41 + 2 * q^43 - 36 * q^45 + 12 * q^47 - 36 * q^51 + 16 * q^55 - 6 * q^57 + 8 * q^61 - 36 * q^63 + 66 * q^65 - 4 * q^67 - 8 * q^73 - 42 * q^75 - 6 * q^77 - 48 * q^81 + 66 * q^83 + 22 * q^85 + 18 * q^87 + 40 * q^91 - 18 * q^93 + 36 * q^95 + 28 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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