LMFDB - Embedded newform 780.2.r.a.73.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [780,2,Mod(73,780)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(780, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))

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

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

chi := DirichletCharacter("780.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 780 = 2^{2} \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	780.r (of order $4$, 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:	$6.22833135766$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			73.2
Character	$\chi$	$=$	780.73
Dual form			780.2.r.a.577.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{3} +(-1.89326 - 1.18977i) q^{5} +0.757795i q^{7} +1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{3} +(-1.89326 - 1.18977i) q^{5} +0.757795i q^{7} +1.00000i q^{9} +(-0.270759 + 0.270759i) q^{11} +(-3.47747 + 0.952487i) q^{13} +(0.497443 + 2.18003i) q^{15} +(3.66128 + 3.66128i) q^{17} +(-1.74382 + 1.74382i) q^{19} +(0.535842 - 0.535842i) q^{21} +(0.736531 - 0.736531i) q^{23} +(2.16889 + 4.50510i) q^{25} +(0.707107 - 0.707107i) q^{27} -6.49877i q^{29} +(7.47428 + 7.47428i) q^{31} +0.382911 q^{33} +(0.901603 - 1.43470i) q^{35} +7.43357i q^{37} +(3.13245 + 1.78543i) q^{39} +(1.24770 + 1.24770i) q^{41} +(-8.28487 + 8.28487i) q^{43} +(1.18977 - 1.89326i) q^{45} +3.33626i q^{47} +6.42575 q^{49} -5.17783i q^{51} +(-3.05887 - 3.05887i) q^{53} +(0.834760 - 0.190477i) q^{55} +2.46613 q^{57} +(10.0059 + 10.0059i) q^{59} -5.75265 q^{61} -0.757795 q^{63} +(7.71700 + 2.33408i) q^{65} +6.02788 q^{67} -1.04161 q^{69} +(-2.44408 - 2.44408i) q^{71} -12.1731 q^{73} +(1.65195 - 4.71922i) q^{75} +(-0.205180 - 0.205180i) q^{77} +1.12800i q^{79} -1.00000 q^{81} +11.6530i q^{83} +(-2.57568 - 11.2878i) q^{85} +(-4.59532 + 4.59532i) q^{87} +(-7.93269 - 7.93269i) q^{89} +(-0.721790 - 2.63520i) q^{91} -10.5702i q^{93} +(5.37625 - 1.22676i) q^{95} +0.531121 q^{97} +(-0.270759 - 0.270759i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q+O(q^{10}) $ 28 * q	$ 28 q + 8 q^{11} - 4 q^{13} - 4 q^{15} - 4 q^{17} - 16 q^{19} + 8 q^{21} - 8 q^{23} + 12 q^{25} - 8 q^{33} + 8 q^{39} + 12 q^{41} + 16 q^{43} + 4 q^{45} - 36 q^{49} + 36 q^{53} + 40 q^{55} + 16 q^{59} + 8 q^{61} - 40 q^{65} + 48 q^{67} - 8 q^{69} + 8 q^{71} + 48 q^{73} - 48 q^{77} - 28 q^{81} - 4 q^{85} - 24 q^{87} - 36 q^{89} - 24 q^{91} + 72 q^{95} - 72 q^{97} + 8 q^{99}+O(q^{100}) $ 28 * q + 8 * q^11 - 4 * q^13 - 4 * q^15 - 4 * q^17 - 16 * q^19 + 8 * q^21 - 8 * q^23 + 12 * q^25 - 8 * q^33 + 8 * q^39 + 12 * q^41 + 16 * q^43 + 4 * q^45 - 36 * q^49 + 36 * q^53 + 40 * q^55 + 16 * q^59 + 8 * q^61 - 40 * q^65 + 48 * q^67 - 8 * q^69 + 8 * q^71 + 48 * q^73 - 48 * q^77 - 28 * q^81 - 4 * q^85 - 24 * q^87 - 36 * q^89 - 24 * q^91 + 72 * q^95 - 72 * q^97 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/780\mathbb{Z}\right)^\times$.

$n$	$157$	$301$	$391$	$521$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$		0			0
$5$	−1.89326	−	1.18977i	−0.846693	−	0.532082i
$5$	−1.89326	−	1.18977i	−0.846693	−	0.532082i
$6$		0			0
$7$			0.757795i			0.286419i	0.989692	+	0.143210i	$0.0457423\pi$
$7$			0.757795i			0.286419i	−0.989692	+	0.143210i	$0.954258\pi$
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$	−0.270759	+	0.270759i	−0.0816370	+	0.0816370i	−0.746746	−	0.665109i	$-0.768385\pi$
$11$	−0.270759	+	0.270759i	−0.0816370	+	0.0816370i	0.665109	+	0.746746i	$0.268385\pi$
$12$		0			0
$13$	−3.47747	+	0.952487i	−0.964475	+	0.264172i
$13$	−3.47747	+	0.952487i	−0.964475	+	0.264172i
$14$		0			0
$15$	0.497443	+	2.18003i	0.128439	+	0.562882i
$16$		0			0
$17$	3.66128	+	3.66128i	0.887990	+	0.887990i	0.994330	−	0.106340i	$-0.0339132\pi$
$17$	3.66128	+	3.66128i	0.887990	+	0.887990i	−0.106340	+	0.994330i	$0.533913\pi$
$18$		0			0
$19$	−1.74382	+	1.74382i	−0.400059	+	0.400059i	−0.878254	−	0.478195i	$-0.841291\pi$
$19$	−1.74382	+	1.74382i	−0.400059	+	0.400059i	0.478195	+	0.878254i	$0.341291\pi$
$20$		0			0
$21$	0.535842	−	0.535842i	0.116930	−	0.116930i
$22$		0			0
$23$	0.736531	−	0.736531i	0.153577	−	0.153577i	−0.626136	−	0.779714i	$-0.715365\pi$
$23$	0.736531	−	0.736531i	0.153577	−	0.153577i	0.779714	+	0.626136i	$0.215365\pi$
$24$		0			0
$25$	2.16889	+	4.50510i	0.433777	+	0.901020i
$26$		0			0
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$		0			0
$29$		−	6.49877i		−	1.20679i	−0.797442	−	0.603395i	$-0.793814\pi$
$29$		−	6.49877i		−	1.20679i	0.797442	−	0.603395i	$-0.206186\pi$
$30$		0			0
$31$	7.47428	+	7.47428i	1.34242	+	1.34242i	0.893644	+	0.448777i	$0.148140\pi$
$31$	7.47428	+	7.47428i	1.34242	+	1.34242i	0.448777	+	0.893644i	$0.351860\pi$
$32$		0			0
$33$	0.382911			0.0666563
$34$		0			0
$35$	0.901603	−	1.43470i	0.152399	−	0.242509i
$36$		0			0
$37$			7.43357i			1.22207i	0.791603	+	0.611036i	$0.209247\pi$
$37$			7.43357i			1.22207i	−0.791603	+	0.611036i	$0.790753\pi$
$38$		0			0
$39$	3.13245	+	1.78543i	0.501593	+	0.285898i
$40$		0			0
$41$	1.24770	+	1.24770i	0.194857	+	0.194857i	0.797791	−	0.602934i	$-0.206002\pi$
$41$	1.24770	+	1.24770i	0.194857	+	0.194857i	−0.602934	+	0.797791i	$0.706002\pi$
$42$		0			0
$43$	−8.28487	+	8.28487i	−1.26343	+	1.26343i	−0.314012	+	0.949419i	$0.601673\pi$
$43$	−8.28487	+	8.28487i	−1.26343	+	1.26343i	−0.949419	+	0.314012i	$0.898327\pi$
$44$		0			0
$45$	1.18977	−	1.89326i	0.177361	−	0.282231i
$46$		0			0
$47$			3.33626i			0.486643i	0.969946	+	0.243322i	$0.0782370\pi$
$47$			3.33626i			0.486643i	−0.969946	+	0.243322i	$0.921763\pi$
$48$		0			0
$49$	6.42575			0.917964
$50$		0			0
$51$		−	5.17783i		−	0.725041i
$52$		0			0
$53$	−3.05887	−	3.05887i	−0.420168	−	0.420168i	0.465093	−	0.885262i	$-0.346021\pi$
$53$	−3.05887	−	3.05887i	−0.420168	−	0.420168i	−0.885262	+	0.465093i	$0.846021\pi$
$54$		0			0
$55$	0.834760	−	0.190477i	0.112559	−	0.0256839i
$56$		0			0
$57$	2.46613			0.326647
$58$		0			0
$59$	10.0059	+	10.0059i	1.30266	+	1.30266i	0.926594	+	0.376064i	$0.122723\pi$
$59$	10.0059	+	10.0059i	1.30266	+	1.30266i	0.376064	+	0.926594i	$0.377277\pi$
$60$		0			0
$61$	−5.75265			−0.736551			−0.368276	−	0.929717i	$-0.620052\pi$
$61$	−5.75265			−0.736551			−0.368276	+	0.929717i	$0.620052\pi$
$62$		0			0
$63$	−0.757795			−0.0954732
$64$		0			0
$65$	7.71700	+	2.33408i	0.957176	+	0.289507i
$66$		0			0
$67$	6.02788			0.736422			0.368211	−	0.929742i	$-0.379970\pi$
$67$	6.02788			0.736422			0.368211	+	0.929742i	$0.379970\pi$
$68$		0			0
$69$	−1.04161			−0.125395
$70$		0			0
$71$	−2.44408	−	2.44408i	−0.290059	−	0.290059i	0.547044	−	0.837104i	$-0.315753\pi$
$71$	−2.44408	−	2.44408i	−0.290059	−	0.290059i	−0.837104	+	0.547044i	$0.815753\pi$
$72$		0			0
$73$	−12.1731			−1.42476			−0.712378	−	0.701796i	$-0.752382\pi$
$73$	−12.1731			−1.42476			−0.712378	+	0.701796i	$0.752382\pi$
$74$		0			0
$75$	1.65195	−	4.71922i	0.190751	−	0.544929i
$76$		0			0
$77$	−0.205180	−	0.205180i	−0.0233824	−	0.0233824i
$78$		0			0
$79$			1.12800i			0.126910i	0.997985	+	0.0634549i	$0.0202119\pi$
$79$			1.12800i			0.126910i	−0.997985	+	0.0634549i	$0.979788\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$			11.6530i			1.27909i	0.768755	+	0.639544i	$0.220877\pi$
$83$			11.6530i			1.27909i	−0.768755	+	0.639544i	$0.779123\pi$
$84$		0			0
$85$	−2.57568	−	11.2878i	−0.279371	−	1.22434i
$86$		0			0
$87$	−4.59532	+	4.59532i	−0.492670	+	0.492670i
$88$		0			0
$89$	−7.93269	−	7.93269i	−0.840864	−	0.840864i	0.148108	−	0.988971i	$-0.452682\pi$
$89$	−7.93269	−	7.93269i	−0.840864	−	0.840864i	−0.988971	+	0.148108i	$0.952682\pi$
$90$		0			0
$91$	−0.721790	−	2.63520i	−0.0756641	−	0.276245i
$92$		0			0
$93$		−	10.5702i		−	1.09608i
$94$		0			0
$95$	5.37625	−	1.22676i	0.551591	−	0.125863i
$96$		0			0
$97$	0.531121			0.0539272			0.0269636	−	0.999636i	$-0.491416\pi$
$97$	0.531121			0.0539272			0.0269636	+	0.999636i	$0.491416\pi$
$98$		0			0
$99$	−0.270759	−	0.270759i	−0.0272123	−	0.0272123i
$100$		0			0
$101$		−	13.9542i		−	1.38849i	−0.719738	−	0.694246i	$-0.755738\pi$
$101$		−	13.9542i		−	1.38849i	0.719738	−	0.694246i	$-0.244262\pi$
$102$		0			0
$103$	2.23628	−	2.23628i	0.220347	−	0.220347i	−0.588298	−	0.808644i	$-0.700202\pi$
$103$	2.23628	−	2.23628i	0.220347	−	0.220347i	0.808644	+	0.588298i	$0.200202\pi$
$104$		0			0
$105$	−1.65202	+	0.376960i	−0.161220	+	0.0367875i
$106$		0			0
$107$	−8.91181	+	8.91181i	−0.861537	+	0.861537i	−0.991517	−	0.129979i	$-0.958509\pi$
$107$	−8.91181	+	8.91181i	−0.861537	+	0.861537i	0.129979	+	0.991517i	$0.458509\pi$
$108$		0			0
$109$	−10.7279	+	10.7279i	−1.02755	+	1.02755i	−0.0279379	+	0.999610i	$0.508894\pi$
$109$	−10.7279	+	10.7279i	−1.02755	+	1.02755i	−0.999610	+	0.0279379i	$0.991106\pi$
$110$		0			0
$111$	5.25633	−	5.25633i	0.498909	−	0.498909i
$112$		0			0
$113$	−7.95438	−	7.95438i	−0.748285	−	0.748285i	0.225872	−	0.974157i	$-0.427477\pi$
$113$	−7.95438	−	7.95438i	−0.748285	−	0.748285i	−0.974157	+	0.225872i	$0.927477\pi$
$114$		0			0
$115$	−2.27075	+	0.518143i	−0.211749	+	0.0483171i
$116$		0			0
$117$	−0.952487	−	3.47747i	−0.0880575	−	0.321492i
$118$		0			0
$119$	−2.77450	+	2.77450i	−0.254338	+	0.254338i
$120$		0			0
$121$			10.8534i			0.986671i
$122$		0			0
$123$		−	1.76451i		−	0.159100i
$124$		0			0
$125$	1.25377	−	11.1098i	0.112140	−	0.993692i
$126$		0			0
$127$	−1.38653	−	1.38653i	−0.123034	−	0.123034i	0.642909	−	0.765943i	$-0.277727\pi$
$127$	−1.38653	−	1.38653i	−0.123034	−	0.123034i	−0.765943	+	0.642909i	$0.777727\pi$
$128$		0			0
$129$	11.7166			1.03159
$130$		0			0
$131$	15.8472			1.38458			0.692288	−	0.721621i	$-0.256603\pi$
$131$	15.8472			1.38458			0.692288	+	0.721621i	$0.256603\pi$
$132$		0			0
$133$	−1.32145	−	1.32145i	−0.114585	−	0.114585i
$134$		0			0
$135$	−2.18003	+	0.497443i	−0.187627	+	0.0428131i
$136$		0			0
$137$		−	3.53259i		−	0.301810i	−0.988548	−	0.150905i	$-0.951781\pi$
$137$		−	3.53259i		−	0.301810i	0.988548	−	0.150905i	$-0.0482187\pi$
$138$		0			0
$139$			2.88651i			0.244830i	0.992479	+	0.122415i	$0.0390639\pi$
$139$			2.88651i			0.244830i	−0.992479	+	0.122415i	$0.960936\pi$
$140$		0			0
$141$	2.35909	−	2.35909i	0.198671	−	0.198671i
$142$		0			0
$143$	0.683661	−	1.19945i	0.0571706	−	0.100303i
$144$		0			0
$145$	−7.73205	+	12.3039i	−0.642112	+	1.02178i
$146$		0			0
$147$	−4.54369	−	4.54369i	−0.374757	−	0.374757i
$148$		0			0
$149$	2.15283	−	2.15283i	0.176367	−	0.176367i	−0.613403	−	0.789770i	$-0.710200\pi$
$149$	2.15283	−	2.15283i	0.176367	−	0.176367i	0.789770	+	0.613403i	$0.210200\pi$
$150$		0			0
$151$	9.64281	−	9.64281i	0.784721	−	0.784721i	−0.195903	−	0.980623i	$-0.562764\pi$
$151$	9.64281	−	9.64281i	0.784721	−	0.784721i	0.980623	+	0.195903i	$0.0627637\pi$
$152$		0			0
$153$	−3.66128	+	3.66128i	−0.295997	+	0.295997i
$154$		0			0
$155$	−5.25809	−	23.0435i	−0.422340	−	1.85090i
$156$		0			0
$157$	1.57572	−	1.57572i	0.125756	−	0.125756i	−0.641428	−	0.767183i	$-0.721658\pi$
$157$	1.57572	−	1.57572i	0.125756	−	0.125756i	0.767183	+	0.641428i	$0.221658\pi$
$158$		0			0
$159$			4.32590i			0.343066i
$160$		0			0
$161$	0.558140	+	0.558140i	0.0439876	+	0.0439876i
$162$		0			0
$163$	−7.86382			−0.615942			−0.307971	−	0.951396i	$-0.599650\pi$
$163$	−7.86382			−0.615942			−0.307971	+	0.951396i	$0.599650\pi$
$164$		0			0
$165$	−0.724952	−	0.455577i	−0.0564374	−	0.0354666i
$166$		0			0
$167$			15.6642i			1.21213i	0.795414	+	0.606067i	$0.207253\pi$
$167$			15.6642i			1.21213i	−0.795414	+	0.606067i	$0.792747\pi$
$168$		0			0
$169$	11.1855	−	6.62448i	0.860426	−	0.509576i
$170$		0			0
$171$	−1.74382	−	1.74382i	−0.133353	−	0.133353i
$172$		0			0
$173$	1.09322	−	1.09322i	0.0831158	−	0.0831158i	−0.664327	−	0.747442i	$-0.731282\pi$
$173$	1.09322	−	1.09322i	0.0831158	−	0.0831158i	0.747442	+	0.664327i	$0.231282\pi$
$174$		0			0
$175$	−3.41394	+	1.64357i	−0.258070	+	0.124242i
$176$		0			0
$177$		−	14.1505i		−	1.06362i
$178$		0			0
$179$	−10.0735			−0.752930			−0.376465	−	0.926431i	$-0.622861\pi$
$179$	−10.0735			−0.752930			−0.376465	+	0.926431i	$0.622861\pi$
$180$		0			0
$181$		−	16.3381i		−	1.21440i	−0.794548	−	0.607201i	$-0.792292\pi$
$181$		−	16.3381i		−	1.21440i	0.794548	−	0.607201i	$-0.207708\pi$
$182$		0			0
$183$	4.06774	+	4.06774i	0.300696	+	0.300696i
$184$		0			0
$185$	8.84426	−	14.0737i	0.650243	−	1.03472i
$186$		0			0
$187$	−1.98265			−0.144986
$188$		0			0
$189$	0.535842	+	0.535842i	0.0389768	+	0.0389768i
$190$		0			0
$191$	−8.92940			−0.646109			−0.323054	−	0.946380i	$-0.604710\pi$
$191$	−8.92940			−0.646109			−0.323054	+	0.946380i	$0.604710\pi$
$192$		0			0
$193$	−23.4718			−1.68954			−0.844768	−	0.535133i	$-0.820261\pi$
$193$	−23.4718			−1.68954			−0.844768	+	0.535133i	$0.820261\pi$
$194$		0			0
$195$	−3.80630	−	7.10719i	−0.272575	−	0.508956i
$196$		0			0
$197$	−9.54068			−0.679745			−0.339873	−	0.940471i	$-0.610384\pi$
$197$	−9.54068			−0.679745			−0.339873	+	0.940471i	$0.610384\pi$
$198$		0			0
$199$	4.91305			0.348277			0.174139	−	0.984721i	$-0.444286\pi$
$199$	4.91305			0.348277			0.174139	+	0.984721i	$0.444286\pi$
$200$		0			0
$201$	−4.26235	−	4.26235i	−0.300643	−	0.300643i
$202$		0			0
$203$	4.92473			0.345648
$204$		0			0
$205$	−0.877743	−	3.84669i	−0.0613042	−	0.268664i
$206$		0			0
$207$	0.736531	+	0.736531i	0.0511925	+	0.0511925i
$208$		0			0
$209$		−	0.944309i		−	0.0653192i
$210$		0			0
$211$	−3.51354			−0.241882			−0.120941	−	0.992660i	$-0.538591\pi$
$211$	−3.51354			−0.241882			−0.120941	+	0.992660i	$0.538591\pi$
$212$		0			0
$213$			3.45645i			0.236832i
$214$		0			0
$215$	25.5425	−	5.82833i	1.74199	−	0.397489i
$216$		0			0
$217$	−5.66397	+	5.66397i	−0.384495	+	0.384495i
$218$		0			0
$219$	8.60769	+	8.60769i	0.581654	+	0.581654i
$220$		0			0
$221$	−16.2193	−	9.24464i	−1.09103	−	0.621862i
$222$		0			0
$223$			14.2401i			0.953587i	0.879015	+	0.476793i	$0.158201\pi$
$223$			14.2401i			0.953587i	−0.879015	+	0.476793i	$0.841799\pi$
$224$		0			0
$225$	−4.50510	+	2.16889i	−0.300340	+	0.144592i
$226$		0			0
$227$	−16.1626			−1.07275			−0.536373	−	0.843981i	$-0.680206\pi$
$227$	−16.1626			−1.07275			−0.536373	+	0.843981i	$0.680206\pi$
$228$		0			0
$229$	14.5065	+	14.5065i	0.958616	+	0.958616i	0.999177	−	0.0405615i	$-0.0129147\pi$
$229$	14.5065	+	14.5065i	0.958616	+	0.958616i	−0.0405615	+	0.999177i	$0.512915\pi$
$230$		0			0
$231$			0.290168i			0.0190917i
$232$		0			0
$233$	15.2880	−	15.2880i	1.00155	−	1.00155i	0.00155214	−	0.999999i	$-0.499506\pi$
$233$	15.2880	−	15.2880i	1.00155	−	1.00155i	0.999999	−	0.00155214i	$-0.000494061\pi$
$234$		0			0
$235$	3.96938	−	6.31641i	0.258934	−	0.412037i
$236$		0			0
$237$	0.797616	−	0.797616i	0.0518107	−	0.0518107i
$238$		0			0
$239$	4.11471	−	4.11471i	0.266159	−	0.266159i	−0.561392	−	0.827550i	$-0.689734\pi$
$239$	4.11471	−	4.11471i	0.266159	−	0.266159i	0.827550	+	0.561392i	$0.189734\pi$
$240$		0			0
$241$	5.06246	−	5.06246i	0.326101	−	0.326101i	−0.525000	−	0.851102i	$-0.675935\pi$
$241$	5.06246	−	5.06246i	0.326101	−	0.326101i	0.851102	+	0.525000i	$0.175935\pi$
$242$		0			0
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$		0			0
$245$	−12.1656	−	7.64517i	−0.777233	−	0.488432i
$246$		0			0
$247$	4.40310	−	7.72502i	0.280162	−	0.491532i
$248$		0			0
$249$	8.23995	−	8.23995i	0.522185	−	0.522185i
$250$		0			0
$251$			18.9512i			1.19619i	0.801425	+	0.598095i	$0.204075\pi$
$251$			18.9512i			1.19619i	−0.801425	+	0.598095i	$0.795925\pi$
$252$		0			0
$253$			0.398845i			0.0250752i
$254$		0			0
$255$	−6.16043	+	9.80299i	−0.385781	+	0.613887i
$256$		0			0
$257$	14.9677	+	14.9677i	0.933661	+	0.933661i	0.997932	−	0.0642714i	$-0.0204723\pi$
$257$	14.9677	+	14.9677i	0.933661	+	0.933661i	−0.0642714	+	0.997932i	$0.520472\pi$
$258$		0			0
$259$	−5.63312			−0.350025
$260$		0			0
$261$	6.49877			0.402264
$262$		0			0
$263$	−21.0413	−	21.0413i	−1.29746	−	1.29746i	−0.930063	−	0.367399i	$-0.880248\pi$
$263$	−21.0413	−	21.0413i	−1.29746	−	1.29746i	−0.367399	−	0.930063i	$-0.619752\pi$
$264$		0			0
$265$	2.15189	+	9.43060i	0.132189	+	0.579317i
$266$		0			0
$267$			11.2185i			0.686562i
$268$		0			0
$269$			4.14375i			0.252649i	0.991989	+	0.126324i	$0.0403180\pi$
$269$			4.14375i			0.252649i	−0.991989	+	0.126324i	$0.959682\pi$
$270$		0			0
$271$	−0.743557	+	0.743557i	−0.0451679	+	0.0451679i	−0.729330	−	0.684162i	$-0.760168\pi$
$271$	−0.743557	+	0.743557i	−0.0451679	+	0.0451679i	0.684162	+	0.729330i	$0.260168\pi$
$272$		0			0
$273$	−1.35299	+	2.37375i	−0.0818866	+	0.143666i
$274$		0			0
$275$	−1.80704	−	0.632551i	−0.108969	−	0.0381443i
$276$		0			0
$277$	−0.945717	−	0.945717i	−0.0568226	−	0.0568226i	0.678124	−	0.734947i	$-0.262793\pi$
$277$	−0.945717	−	0.945717i	−0.0568226	−	0.0568226i	−0.734947	+	0.678124i	$0.762793\pi$
$278$		0			0
$279$	−7.47428	+	7.47428i	−0.447474	+	0.447474i
$280$		0			0
$281$	−3.23133	+	3.23133i	−0.192765	+	0.192765i	−0.796890	−	0.604125i	$-0.793523\pi$
$281$	−3.23133	+	3.23133i	−0.192765	+	0.192765i	0.604125	+	0.796890i	$0.293523\pi$
$282$		0			0
$283$	14.8304	−	14.8304i	0.881575	−	0.881575i	−0.112120	−	0.993695i	$-0.535764\pi$
$283$	14.8304	−	14.8304i	0.881575	−	0.881575i	0.993695	+	0.112120i	$0.0357640\pi$
$284$		0			0
$285$	−4.66903	−	2.93413i	−0.276569	−	0.173803i
$286$		0			0
$287$	−0.945497	+	0.945497i	−0.0558109	+	0.0558109i
$288$		0			0
$289$			9.80989i			0.577052i
$290$		0			0
$291$	−0.375559	−	0.375559i	−0.0220157	−	0.0220157i
$292$		0			0
$293$	7.32262			0.427792			0.213896	−	0.976856i	$-0.431385\pi$
$293$	7.32262			0.427792			0.213896	+	0.976856i	$0.431385\pi$
$294$		0			0
$295$	−7.03906	−	30.8485i	−0.409830	−	1.79607i
$296$		0			0
$297$			0.382911i			0.0222188i
$298$		0			0
$299$	−1.85973	+	3.26280i	−0.107551	+	0.188693i
$300$		0			0
$301$	−6.27823	−	6.27823i	−0.361871	−	0.361871i
$302$		0			0
$303$	−9.86709	+	9.86709i	−0.566849	+	0.566849i
$304$		0			0
$305$	10.8913	+	6.84434i	0.623632	+	0.391906i
$306$		0			0
$307$		−	4.48969i		−	0.256240i	−0.991759	−	0.128120i	$-0.959106\pi$
$307$		−	4.48969i		−	0.256240i	0.991759	−	0.128120i	$-0.0408943\pi$
$308$		0			0
$309$	−3.16257			−0.179912
$310$		0			0
$311$			11.5154i			0.652980i	0.945201	+	0.326490i	$0.105866\pi$
$311$			11.5154i			0.652980i	−0.945201	+	0.326490i	$0.894134\pi$
$312$		0			0
$313$	19.4823	+	19.4823i	1.10121	+	1.10121i	0.994265	+	0.106941i	$0.0341056\pi$
$313$	19.4823	+	19.4823i	1.10121	+	1.10121i	0.106941	+	0.994265i	$0.465894\pi$
$314$		0			0
$315$	1.43470	+	0.901603i	0.0808364	+	0.0507995i
$316$		0			0
$317$	27.6161			1.55107			0.775537	−	0.631302i	$-0.217479\pi$
$317$	27.6161			1.55107			0.775537	+	0.631302i	$0.217479\pi$
$318$		0			0
$319$	1.75960	+	1.75960i	0.0985188	+	0.0985188i
$320$		0			0
$321$	12.6032			0.703442
$322$		0			0
$323$	−12.7692			−0.710497
$324$		0			0
$325$	−11.8333	−	13.6005i	−0.656392	−	0.754420i
$326$		0			0
$327$	15.1716			0.838989
$328$		0			0
$329$	−2.52820			−0.139384
$330$		0			0
$331$	15.1912	+	15.1912i	0.834982	+	0.834982i	0.988193	−	0.153211i	$-0.0489615\pi$
$331$	15.1912	+	15.1912i	0.834982	+	0.834982i	−0.153211	+	0.988193i	$0.548962\pi$
$332$		0			0
$333$	−7.43357			−0.407357
$334$		0			0
$335$	−11.4124	−	7.17179i	−0.623523	−	0.391837i
$336$		0			0
$337$	6.41447	+	6.41447i	0.349418	+	0.349418i	0.859893	−	0.510475i	$-0.170530\pi$
$337$	6.41447	+	6.41447i	0.349418	+	0.349418i	−0.510475	+	0.859893i	$0.670530\pi$
$338$		0			0
$339$			11.2492i			0.610972i
$340$		0			0
$341$	−4.04746			−0.219182
$342$		0			0
$343$			10.1740i			0.549342i
$344$		0			0
$345$	1.97205	+	1.23928i	0.106171	+	0.0667207i
$346$		0			0
$347$	5.68497	−	5.68497i	0.305185	−	0.305185i	−0.537853	−	0.843038i	$-0.680765\pi$
$347$	5.68497	−	5.68497i	0.305185	−	0.305185i	0.843038	+	0.537853i	$0.180765\pi$
$348$		0			0
$349$	11.4358	+	11.4358i	0.612144	+	0.612144i	0.943504	−	0.331360i	$-0.107508\pi$
$349$	11.4358	+	11.4358i	0.612144	+	0.612144i	−0.331360	+	0.943504i	$0.607508\pi$
$350$		0			0
$351$	−1.78543	+	3.13245i	−0.0952992	+	0.167198i
$352$		0			0
$353$			31.3965i			1.67107i	0.549440	+	0.835533i	$0.314841\pi$
$353$			31.3965i			1.67107i	−0.549440	+	0.835533i	$0.685159\pi$
$354$		0			0
$355$	1.71939	+	7.53519i	0.0912558	+	0.399926i
$356$		0			0
$357$	3.92373			0.207666
$358$		0			0
$359$	6.01997	+	6.01997i	0.317722	+	0.317722i	0.847892	−	0.530170i	$-0.177872\pi$
$359$	6.01997	+	6.01997i	0.317722	+	0.317722i	−0.530170	+	0.847892i	$0.677872\pi$
$360$		0			0
$361$			12.9182i			0.679906i
$362$		0			0
$363$	7.67450	−	7.67450i	0.402807	−	0.402807i
$364$		0			0
$365$	23.0469	+	14.4832i	1.20633	+	0.758087i
$366$		0			0
$367$	−8.54622	+	8.54622i	−0.446109	+	0.446109i	−0.894059	−	0.447950i	$-0.852154\pi$
$367$	−8.54622	+	8.54622i	−0.446109	+	0.446109i	0.447950	+	0.894059i	$0.352154\pi$
$368$		0			0
$369$	−1.24770	+	1.24770i	−0.0649525	+	0.0649525i
$370$		0			0
$371$	2.31800	−	2.31800i	0.120344	−	0.120344i
$372$		0			0
$373$	−16.3180	−	16.3180i	−0.844916	−	0.844916i	0.144577	−	0.989494i	$-0.453818\pi$
$373$	−16.3180	−	16.3180i	−0.844916	−	0.844916i	−0.989494	+	0.144577i	$0.953818\pi$
$374$		0			0
$375$	−8.74238	+	6.96928i	−0.451454	+	0.359892i
$376$		0			0
$377$	6.18999	+	22.5992i	0.318801	+	1.16392i
$378$		0			0
$379$	4.35008	−	4.35008i	0.223449	−	0.223449i	−0.586500	−	0.809949i	$-0.699495\pi$
$379$	4.35008	−	4.35008i	0.223449	−	0.223449i	0.809949	+	0.586500i	$0.199495\pi$
$380$		0			0
$381$			1.96084i			0.100457i
$382$		0			0
$383$			14.2761i			0.729472i	0.931111	+	0.364736i	$0.118841\pi$
$383$			14.2761i			0.729472i	−0.931111	+	0.364736i	$0.881159\pi$
$384$		0			0
$385$	0.144342	+	0.632577i	0.00735636	+	0.0322391i
$386$		0			0
$387$	−8.28487	−	8.28487i	−0.421144	−	0.421144i
$388$		0			0
$389$	−12.1264			−0.614834			−0.307417	−	0.951575i	$-0.599465\pi$
$389$	−12.1264			−0.614834			−0.307417	+	0.951575i	$0.599465\pi$
$390$		0			0
$391$	5.39329			0.272750
$392$		0			0
$393$	−11.2057	−	11.2057i	−0.565251	−	0.565251i
$394$		0			0
$395$	1.34206	−	2.13560i	0.0675264	−	0.107454i
$396$		0			0
$397$		−	12.7532i		−	0.640064i	−0.947407	−	0.320032i	$-0.896306\pi$
$397$		−	12.7532i		−	0.640064i	0.947407	−	0.320032i	$-0.103694\pi$
$398$		0			0
$399$			1.86882i			0.0935580i
$400$		0			0
$401$	−26.7530	+	26.7530i	−1.33598	+	1.33598i	−0.436068	+	0.899913i	$0.643629\pi$
$401$	−26.7530	+	26.7530i	−1.33598	+	1.33598i	−0.899913	+	0.436068i	$0.856371\pi$
$402$		0			0
$403$	−33.1107	−	18.8724i	−1.64936	−	0.940101i
$404$		0			0
$405$	1.89326	+	1.18977i	0.0940770	+	0.0591202i
$406$		0			0
$407$	−2.01271	−	2.01271i	−0.0997663	−	0.0997663i
$408$		0			0
$409$	9.38156	−	9.38156i	0.463888	−	0.463888i	−0.436039	−	0.899928i	$-0.643619\pi$
$409$	9.38156	−	9.38156i	0.463888	−	0.463888i	0.899928	+	0.436039i	$0.143619\pi$
$410$		0			0
$411$	−2.49792	+	2.49792i	−0.123213	+	0.123213i
$412$		0			0
$413$	−7.58242	+	7.58242i	−0.373106	+	0.373106i
$414$		0			0
$415$	13.8645	−	22.0623i	0.680580	−	1.08299i
$416$		0			0
$417$	2.04107	−	2.04107i	0.0999516	−	0.0999516i
$418$		0			0
$419$		−	25.9668i		−	1.26856i	−0.773103	−	0.634281i	$-0.781296\pi$
$419$		−	25.9668i		−	1.26856i	0.773103	−	0.634281i	$-0.218704\pi$
$420$		0			0
$421$	−0.191380	−	0.191380i	−0.00932731	−	0.00932731i	0.702428	−	0.711755i	$-0.252099\pi$
$421$	−0.191380	−	0.191380i	−0.00932731	−	0.00932731i	−0.711755	+	0.702428i	$0.752099\pi$
$422$		0			0
$423$	−3.33626			−0.162214
$424$		0			0
$425$	−8.55352	+	24.4353i	−0.414907	+	1.18529i
$426$		0			0
$427$		−	4.35933i		−	0.210963i
$428$		0			0
$429$	−1.33156	+	0.364718i	−0.0642884	+	0.0176088i
$430$		0			0
$431$	9.41122	+	9.41122i	0.453322	+	0.453322i	0.896456	−	0.443133i	$-0.146133\pi$
$431$	9.41122	+	9.41122i	0.453322	+	0.453322i	−0.443133	+	0.896456i	$0.646133\pi$
$432$		0			0
$433$	16.3212	−	16.3212i	0.784348	−	0.784348i	−0.196214	−	0.980561i	$-0.562865\pi$
$433$	16.3212	−	16.3212i	0.784348	−	0.784348i	0.980561	+	0.196214i	$0.0628646\pi$
$434$		0			0
$435$	14.1675	−	3.23277i	0.679281	−	0.154999i
$436$		0			0
$437$			2.56875i			0.122880i
$438$		0			0
$439$	26.4013			1.26007			0.630033	−	0.776569i	$-0.283041\pi$
$439$	26.4013			1.26007			0.630033	+	0.776569i	$0.283041\pi$
$440$		0			0
$441$			6.42575i			0.305988i
$442$		0			0
$443$	27.0539	+	27.0539i	1.28537	+	1.28537i	0.937567	+	0.347803i	$0.113072\pi$
$443$	27.0539	+	27.0539i	1.28537	+	1.28537i	0.347803	+	0.937567i	$0.386928\pi$
$444$		0			0
$445$	5.58058	+	24.4568i	0.264545	+	1.15936i
$446$		0			0
$447$	−3.04456			−0.144003
$448$		0			0
$449$	−13.2725	−	13.2725i	−0.626366	−	0.626366i	0.320786	−	0.947152i	$-0.396053\pi$
$449$	−13.2725	−	13.2725i	−0.626366	−	0.626366i	−0.947152	+	0.320786i	$0.896053\pi$
$450$		0			0
$451$	−0.675650			−0.0318151
$452$		0			0
$453$	−13.6370			−0.640722
$454$		0			0
$455$	−1.76875	+	5.84790i	−0.0829205	+	0.274154i
$456$		0			0
$457$	−12.3265			−0.576612			−0.288306	−	0.957538i	$-0.593092\pi$
$457$	−12.3265			−0.576612			−0.288306	+	0.957538i	$0.593092\pi$
$458$		0			0
$459$	5.17783			0.241680
$460$		0			0
$461$	0.617390	+	0.617390i	0.0287547	+	0.0287547i	0.721338	−	0.692583i	$-0.243527\pi$
$461$	0.617390	+	0.617390i	0.0287547	+	0.0287547i	−0.692583	+	0.721338i	$0.743527\pi$
$462$		0			0
$463$	7.81640			0.363259			0.181629	−	0.983367i	$-0.441863\pi$
$463$	7.81640			0.363259			0.181629	+	0.983367i	$0.441863\pi$
$464$		0			0
$465$	−12.5762	+	20.0122i	−0.583206	+	0.928045i
$466$		0			0
$467$	2.39523	+	2.39523i	0.110838	+	0.110838i	0.760351	−	0.649513i	$-0.225027\pi$
$467$	2.39523	+	2.39523i	0.110838	+	0.110838i	−0.649513	+	0.760351i	$0.725027\pi$
$468$		0			0
$469$			4.56789i			0.210926i
$470$		0			0
$471$	−2.22840			−0.102679
$472$		0			0
$473$		−	4.48641i		−	0.206285i
$474$		0			0
$475$	−11.6382	−	4.07393i	−0.533998	−	0.186925i
$476$		0			0
$477$	3.05887	−	3.05887i	0.140056	−	0.140056i
$478$		0			0
$479$	−27.0674	−	27.0674i	−1.23674	−	1.23674i	−0.961325	−	0.275417i	$-0.911184\pi$
$479$	−27.0674	−	27.0674i	−1.23674	−	1.23674i	−0.275417	−	0.961325i	$-0.588816\pi$
$480$		0			0
$481$	−7.08039	−	25.8500i	−0.322838	−	1.17866i
$482$		0			0
$483$		−	0.789329i		−	0.0359157i
$484$		0			0
$485$	−1.00555	−	0.631912i	−0.0456597	−	0.0286937i
$486$		0			0
$487$	−25.0001			−1.13286			−0.566432	−	0.824109i	$-0.691676\pi$
$487$	−25.0001			−1.13286			−0.566432	+	0.824109i	$0.691676\pi$
$488$		0			0
$489$	5.56056	+	5.56056i	0.251457	+	0.251457i
$490$		0			0
$491$			37.1645i			1.67721i	0.544740	+	0.838605i	$0.316629\pi$
$491$			37.1645i			1.67721i	−0.544740	+	0.838605i	$0.683371\pi$
$492$		0			0
$493$	23.7938	−	23.7938i	1.07162	−	1.07162i
$494$		0			0
$495$	0.190477	+	0.834760i	0.00856129	+	0.0375197i
$496$		0			0
$497$	1.85211	−	1.85211i	0.0830786	−	0.0830786i
$498$		0			0
$499$	−2.79744	+	2.79744i	−0.125231	+	0.125231i	−0.766944	−	0.641714i	$-0.778224\pi$
$499$	−2.79744	+	2.79744i	−0.125231	+	0.125231i	0.641714	+	0.766944i	$0.278224\pi$
$500$		0			0
$501$	11.0763	−	11.0763i	0.494851	−	0.494851i
$502$		0			0
$503$	5.79985	+	5.79985i	0.258603	+	0.258603i	0.824486	−	0.565883i	$-0.191465\pi$
$503$	5.79985	+	5.79985i	0.258603	+	0.258603i	−0.565883	+	0.824486i	$0.691465\pi$
$504$		0			0
$505$	−16.6023	+	26.4189i	−0.738792	+	1.17563i
$506$		0			0
$507$	−12.5936	−	3.22515i	−0.559301	−	0.143234i
$508$		0			0
$509$	11.4644	−	11.4644i	0.508152	−	0.508152i	−0.405807	−	0.913959i	$-0.633009\pi$
$509$	11.4644	−	11.4644i	0.508152	−	0.508152i	0.913959	+	0.405807i	$0.133009\pi$
$510$		0			0
$511$		−	9.22472i		−	0.408078i
$512$		0			0
$513$			2.46613i			0.108882i
$514$		0			0
$515$	−6.89452	+	1.57320i	−0.303809	+	0.0693235i
$516$		0			0
$517$	−0.903323	−	0.903323i	−0.0397281	−	0.0397281i
$518$		0			0
$519$	−1.54604			−0.0678637
$520$		0			0
$521$	−10.4850			−0.459356			−0.229678	−	0.973267i	$-0.573767\pi$
$521$	−10.4850			−0.459356			−0.229678	+	0.973267i	$0.573767\pi$
$522$		0			0
$523$	14.4821	+	14.4821i	0.633258	+	0.633258i	0.948884	−	0.315625i	$-0.102214\pi$
$523$	14.4821	+	14.4821i	0.633258	+	0.633258i	−0.315625	+	0.948884i	$0.602214\pi$
$524$		0			0
$525$	3.57620	+	1.25184i	0.156078	+	0.0546348i
$526$		0			0
$527$			54.7308i			2.38411i
$528$		0			0
$529$			21.9150i			0.952828i
$530$		0			0
$531$	−10.0059	+	10.0059i	−0.434219	+	0.434219i
$532$		0			0
$533$	−5.52723	−	3.15041i	−0.239411	−	0.136459i
$534$		0			0
$535$	27.4754	−	6.26938i	1.18787	−	0.271049i
$536$		0			0
$537$	7.12305	+	7.12305i	0.307382	+	0.307382i
$538$		0			0
$539$	−1.73983	+	1.73983i	−0.0749398	+	0.0749398i
$540$		0			0
$541$	23.9290	−	23.9290i	1.02879	−	1.02879i	0.0292144	−	0.999573i	$-0.490699\pi$
$541$	23.9290	−	23.9290i	1.02879	−	1.02879i	0.999573	−	0.0292144i	$-0.00930057\pi$
$542$		0			0
$543$	−11.5528	+	11.5528i	−0.495777	+	0.495777i
$544$		0			0
$545$	33.0745	−	7.54699i	1.41676	−	0.323278i
$546$		0			0
$547$	19.2063	−	19.2063i	0.821202	−	0.821202i	−0.165078	−	0.986280i	$-0.552788\pi$
$547$	19.2063	−	19.2063i	0.821202	−	0.821202i	0.986280	+	0.165078i	$0.0527877\pi$
$548$		0			0
$549$		−	5.75265i		−	0.245517i
$550$		0			0
$551$	11.3327	+	11.3327i	0.482787	+	0.482787i
$552$		0			0
$553$	−0.854792			−0.0363494
$554$		0			0
$555$	−16.2054	+	3.69778i	−0.687883	+	0.156962i
$556$		0			0
$557$		−	14.3587i		−	0.608397i	−0.952609	−	0.304199i	$-0.901611\pi$
$557$		−	14.3587i		−	0.608397i	0.952609	−	0.304199i	$-0.0983886\pi$
$558$		0			0
$559$	20.9191	−	36.7016i	0.884784	−	1.55231i
$560$		0			0
$561$	1.40194	+	1.40194i	0.0591901	+	0.0591901i
$562$		0			0
$563$	18.0282	−	18.0282i	0.759797	−	0.759797i	−0.216488	−	0.976285i	$-0.569460\pi$
$563$	18.0282	−	18.0282i	0.759797	−	0.759797i	0.976285	+	0.216488i	$0.0694603\pi$
$564$		0			0
$565$	5.59583	+	24.5236i	0.235419	+	1.03172i
$566$		0			0
$567$		−	0.757795i		−	0.0318244i
$568$		0			0
$569$	−43.2664			−1.81382			−0.906911	−	0.421322i	$-0.861566\pi$
$569$	−43.2664			−1.81382			−0.906911	+	0.421322i	$0.861566\pi$
$570$		0			0
$571$		−	30.7847i		−	1.28830i	−0.764900	−	0.644149i	$-0.777211\pi$
$571$		−	30.7847i		−	1.28830i	0.764900	−	0.644149i	$-0.222789\pi$
$572$		0			0
$573$	6.31404	+	6.31404i	0.263773	+	0.263773i
$574$		0			0
$575$	4.91560	+	1.72069i	0.204995	+	0.0717579i
$576$		0			0
$577$	26.6787			1.11065			0.555324	−	0.831634i	$-0.312594\pi$
$577$	26.6787			1.11065			0.555324	+	0.831634i	$0.312594\pi$
$578$		0			0
$579$	16.5971	+	16.5971i	0.689750	+	0.689750i
$580$		0			0
$581$	−8.83062			−0.366356
$582$		0			0
$583$	1.65644			0.0686025
$584$		0			0
$585$	−2.33408	+	7.71700i	−0.0965024	+	0.319059i
$586$		0			0
$587$	−19.1418			−0.790065			−0.395033	−	0.918667i	$-0.629267\pi$
$587$	−19.1418			−0.790065			−0.395033	+	0.918667i	$0.629267\pi$
$588$		0			0
$589$	−26.0676			−1.07409
$590$		0			0
$591$	6.74628	+	6.74628i	0.277505	+	0.277505i
$592$		0			0
$593$	−6.60540			−0.271251			−0.135626	−	0.990760i	$-0.543304\pi$
$593$	−6.60540			−0.271251			−0.135626	+	0.990760i	$0.543304\pi$
$594$		0			0
$595$	8.55387	−	1.95183i	0.350674	−	0.0800174i
$596$		0			0
$597$	−3.47405	−	3.47405i	−0.142184	−	0.142184i
$598$		0			0
$599$		−	21.3441i		−	0.872095i	−0.899924	−	0.436048i	$-0.856378\pi$
$599$		−	21.3441i		−	0.872095i	0.899924	−	0.436048i	$-0.143622\pi$
$600$		0			0
$601$	−35.0766			−1.43080			−0.715402	−	0.698713i	$-0.753757\pi$
$601$	−35.0766			−1.43080			−0.715402	+	0.698713i	$0.753757\pi$
$602$		0			0
$603$			6.02788i			0.245474i
$604$		0			0
$605$	12.9130	−	20.5483i	0.524990	−	0.835407i
$606$		0			0
$607$	25.7956	−	25.7956i	1.04701	−	1.04701i	0.0481716	−	0.998839i	$-0.484661\pi$
$607$	25.7956	−	25.7956i	1.04701	−	1.04701i	0.998839	−	0.0481716i	$-0.0153394\pi$
$608$		0			0
$609$	−3.48231	−	3.48231i	−0.141110	−	0.141110i
$610$		0			0
$611$	−3.17774	−	11.6017i	−0.128558	−	0.469355i
$612$		0			0
$613$			16.2070i			0.654595i	0.944921	+	0.327297i	$0.106138\pi$
$613$			16.2070i			0.654595i	−0.944921	+	0.327297i	$0.893862\pi$
$614$		0			0
$615$	−2.09936	+	3.34068i	−0.0846544	+	0.134709i
$616$		0			0
$617$	35.0413			1.41071			0.705355	−	0.708854i	$-0.250788\pi$
$617$	35.0413			1.41071			0.705355	+	0.708854i	$0.250788\pi$
$618$		0			0
$619$	17.4176	+	17.4176i	0.700073	+	0.700073i	0.964426	−	0.264353i	$-0.0851585\pi$
$619$	17.4176	+	17.4176i	0.700073	+	0.700073i	−0.264353	+	0.964426i	$0.585159\pi$
$620$		0			0
$621$		−	1.04161i		−	0.0417985i
$622$		0			0
$623$	6.01135	−	6.01135i	0.240840	−	0.240840i
$624$		0			0
$625$	−15.5919	+	19.5421i	−0.623674	+	0.781684i
$626$		0			0
$627$	−0.667727	+	0.667727i	−0.0266665	+	0.0266665i
$628$		0			0
$629$	−27.2164	+	27.2164i	−1.08519	+	1.08519i
$630$		0			0
$631$	4.06003	−	4.06003i	0.161627	−	0.161627i	−0.621660	−	0.783287i	$-0.713541\pi$
$631$	4.06003	−	4.06003i	0.161627	−	0.161627i	0.783287	+	0.621660i	$0.213541\pi$
$632$		0			0
$633$	2.48445	+	2.48445i	0.0987481	+	0.0987481i
$634$		0			0
$635$	0.975408	+	4.27470i	0.0387079	+	0.169636i
$636$		0			0
$637$	−22.3453	+	6.12044i	−0.885354	+	0.242501i
$638$		0			0
$639$	2.44408	−	2.44408i	0.0966864	−	0.0966864i
$640$		0			0
$641$			2.59375i			0.102447i	0.998687	+	0.0512235i	$0.0163121\pi$
$641$			2.59375i			0.102447i	−0.998687	+	0.0512235i	$0.983688\pi$
$642$		0			0
$643$		−	6.87827i		−	0.271253i	−0.990760	−	0.135626i	$-0.956695\pi$
$643$		−	6.87827i		−	0.271253i	0.990760	−	0.135626i	$-0.0433046\pi$
$644$		0			0
$645$	−22.1826	−	13.9400i	−0.873437	−	0.548889i
$646$		0			0
$647$	−17.2080	−	17.2080i	−0.676517	−	0.676517i	0.282693	−	0.959210i	$-0.408772\pi$
$647$	−17.2080	−	17.2080i	−0.676517	−	0.676517i	−0.959210	+	0.282693i	$0.908772\pi$
$648$		0			0
$649$	−5.41838			−0.212690
$650$		0			0
$651$	8.01007			0.313939
$652$		0			0
$653$	9.16881	+	9.16881i	0.358803	+	0.358803i	0.863372	−	0.504568i	$-0.168348\pi$
$653$	9.16881	+	9.16881i	0.358803	+	0.358803i	−0.504568	+	0.863372i	$0.668348\pi$
$654$		0			0
$655$	−30.0029	−	18.8546i	−1.17231	−	0.736708i
$656$		0			0
$657$		−	12.1731i		−	0.474919i
$658$		0			0
$659$		−	30.6177i		−	1.19269i	−0.802726	−	0.596347i	$-0.796618\pi$
$659$		−	30.6177i		−	1.19269i	0.802726	−	0.596347i	$-0.203382\pi$
$660$		0			0
$661$	5.87877	−	5.87877i	0.228658	−	0.228658i	−0.583474	−	0.812132i	$-0.698307\pi$
$661$	5.87877	−	5.87877i	0.228658	−	0.228658i	0.812132	+	0.583474i	$0.198307\pi$
$662$		0			0
$663$	4.93181	+	18.0057i	0.191536	+	0.699284i
$664$		0			0
$665$	0.929632	+	4.07409i	0.0360496	+	0.157986i
$666$		0			0
$667$	−4.78655	−	4.78655i	−0.185336	−	0.185336i
$668$		0			0
$669$	10.0693	−	10.0693i	0.389300	−	0.389300i
$670$		0			0
$671$	1.55758	−	1.55758i	0.0601298	−	0.0601298i
$672$		0			0
$673$	36.0127	−	36.0127i	1.38819	−	1.38819i	0.559066	−	0.829123i	$-0.311160\pi$
$673$	36.0127	−	36.0127i	1.38819	−	1.38819i	0.829123	−	0.559066i	$-0.188840\pi$
$674$		0			0
$675$	4.71922	+	1.65195i	0.181643	+	0.0635837i
$676$		0			0
$677$	−8.99420	+	8.99420i	−0.345675	+	0.345675i	−0.858496	−	0.512821i	$-0.828601\pi$
$677$	−8.99420	+	8.99420i	−0.345675	+	0.345675i	0.512821	+	0.858496i	$0.328601\pi$
$678$		0			0
$679$			0.402481i			0.0154458i
$680$		0			0
$681$	11.4287	+	11.4287i	0.437947	+	0.437947i
$682$		0			0
$683$	25.2488			0.966120			0.483060	−	0.875587i	$-0.339525\pi$
$683$	25.2488			0.966120			0.483060	+	0.875587i	$0.339525\pi$
$684$		0			0
$685$	−4.20298	+	6.68813i	−0.160588	+	0.255540i
$686$		0			0
$687$		−	20.5153i		−	0.782706i
$688$		0			0
$689$	13.5507	+	7.72358i	0.516239	+	0.294245i
$690$		0			0
$691$	10.5698	+	10.5698i	0.402093	+	0.402093i	0.878970	−	0.476877i	$-0.158231\pi$
$691$	10.5698	+	10.5698i	0.402093	+	0.402093i	−0.476877	+	0.878970i	$0.658231\pi$
$692$		0			0
$693$	0.205180	−	0.205180i	0.00779414	−	0.00779414i
$694$		0			0
$695$	3.43428	−	5.46492i	0.130270	−	0.207296i
$696$		0			0
$697$			9.13632i			0.346063i
$698$		0			0
$699$	−21.6205			−0.817763
$700$		0			0
$701$		−	21.6459i		−	0.817554i	−0.912634	−	0.408777i	$-0.865955\pi$
$701$		−	21.6459i		−	0.817554i	0.912634	−	0.408777i	$-0.134045\pi$
$702$		0			0
$703$	−12.9628	−	12.9628i	−0.488901	−	0.488901i
$704$		0			0
$705$	−7.27316	+	1.65960i	−0.273923	+	0.0625041i
$706$		0			0
$707$	10.5744			0.397691
$708$		0			0
$709$	−17.3793	−	17.3793i	−0.652693	−	0.652693i	0.300947	−	0.953641i	$-0.402697\pi$
$709$	−17.3793	−	17.3793i	−0.652693	−	0.652693i	−0.953641	+	0.300947i	$0.902697\pi$
$710$		0			0
$711$	−1.12800			−0.0423033
$712$		0			0
$713$	11.0101			0.412331
$714$		0			0
$715$	−2.72142	+	1.45747i	−0.101775	+	0.0545065i
$716$		0			0
$717$	−5.81908			−0.217318
$718$		0			0
$719$	−38.1899			−1.42424			−0.712122	−	0.702056i	$-0.752266\pi$
$719$	−38.1899			−1.42424			−0.712122	+	0.702056i	$0.752266\pi$
$720$		0			0
$721$	1.69464	+	1.69464i	0.0631116	+	0.0631116i
$722$		0			0
$723$	−7.15939			−0.266261
$724$		0			0
$725$	29.2776	−	14.0951i	1.08734	−	0.523479i
$726$		0			0
$727$	−31.8564	−	31.8564i	−1.18149	−	1.18149i	−0.979359	−	0.202130i	$-0.935214\pi$
$727$	−31.8564	−	31.8564i	−1.18149	−	1.18149i	−0.202130	−	0.979359i	$-0.564786\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	−60.6664			−2.24383
$732$		0			0
$733$			25.5193i			0.942576i	0.881979	+	0.471288i	$0.156211\pi$
$733$			25.5193i			0.942576i	−0.881979	+	0.471288i	$0.843789\pi$
$734$		0			0
$735$	3.19645	+	14.0084i	0.117903	+	0.516706i
$736$		0			0
$737$	−1.63210	+	1.63210i	−0.0601193	+	0.0601193i
$738$		0			0
$739$	−24.7125	−	24.7125i	−0.909065	−	0.909065i	0.0871320	−	0.996197i	$-0.472230\pi$
$739$	−24.7125	−	24.7125i	−0.909065	−	0.909065i	−0.996197	+	0.0871320i	$0.972230\pi$
$740$		0			0
$741$	−8.57588	+	2.34896i	−0.315043	+	0.0862911i
$742$		0			0
$743$		−	30.2441i		−	1.10955i	−0.832002	−	0.554773i	$-0.812805\pi$
$743$		−	30.2441i		−	1.10955i	0.832002	−	0.554773i	$-0.187195\pi$
$744$		0			0
$745$	−6.63725	+	1.51450i	−0.243170	+	0.0554869i
$746$		0			0
$747$	−11.6530			−0.426363
$748$		0			0
$749$	−6.75332	−	6.75332i	−0.246761	−	0.246761i
$750$		0			0
$751$		−	42.3577i		−	1.54565i	−0.634617	−	0.772826i	$-0.718842\pi$
$751$		−	42.3577i		−	1.54565i	0.634617	−	0.772826i	$-0.281158\pi$
$752$		0			0
$753$	13.4005	−	13.4005i	0.488342	−	0.488342i
$754$		0			0
$755$	−29.7291	+	6.78363i	−1.08195	+	0.246882i
$756$		0			0
$757$	0.302832	−	0.302832i	0.0110066	−	0.0110066i	−0.701582	−	0.712589i	$-0.747523\pi$
$757$	0.302832	−	0.302832i	0.0110066	−	0.0110066i	0.712589	+	0.701582i	$0.247523\pi$
$758$		0			0
$759$	0.282026	−	0.282026i	0.0102369	−	0.0102369i
$760$		0			0
$761$	21.8724	−	21.8724i	0.792872	−	0.792872i	−0.189088	−	0.981960i	$-0.560553\pi$
$761$	21.8724	−	21.8724i	0.792872	−	0.792872i	0.981960	+	0.189088i	$0.0605531\pi$
$762$		0			0
$763$	−8.12955	−	8.12955i	−0.294310	−	0.294310i
$764$		0			0
$765$	11.2878	−	2.57568i	0.408113	−	0.0931237i
$766$		0			0
$767$	−44.3257	−	25.2647i	−1.60051	−	0.912255i
$768$		0			0
$769$	−38.3328	+	38.3328i	−1.38231	+	1.38231i	−0.541820	+	0.840495i	$0.682265\pi$
$769$	−38.3328	+	38.3328i	−1.38231	+	1.38231i	−0.840495	+	0.541820i	$0.817735\pi$
$770$		0			0
$771$		−	21.1676i		−	0.762331i
$772$		0			0
$773$		−	12.1142i		−	0.435717i	−0.975980	−	0.217859i	$-0.930093\pi$
$773$		−	12.1142i		−	0.435717i	0.975980	−	0.217859i	$-0.0699072\pi$
$774$		0			0
$775$	−17.4615	+	49.8833i	−0.627236	+	1.79186i
$776$		0			0
$777$	3.98322	+	3.98322i	0.142897	+	0.142897i
$778$		0			0
$779$	−4.35151			−0.155909
$780$		0			0
$781$	1.32352			0.0473591
$782$		0			0
$783$	−4.59532	−	4.59532i	−0.164223	−	0.164223i
$784$		0			0
$785$	−4.85798	+	1.10850i	−0.173389	+	0.0395641i
$786$		0			0
$787$		−	17.9307i		−	0.639160i	−0.947559	−	0.319580i	$-0.896458\pi$
$787$		−	17.9307i		−	0.639160i	0.947559	−	0.319580i	$-0.103542\pi$
$788$		0			0
$789$			29.7569i			1.05937i
$790$		0			0
$791$	6.02779	−	6.02779i	0.214323	−	0.214323i
$792$		0			0
$793$	20.0046	−	5.47932i	0.710385	−	0.194576i
$794$		0			0
$795$	5.14683	−	8.19006i	0.182539	−	0.290471i
$796$		0			0
$797$	−0.445355	−	0.445355i	−0.0157753	−	0.0157753i	0.699175	−	0.714950i	$-0.253551\pi$
$797$	−0.445355	−	0.445355i	−0.0157753	−	0.0157753i	−0.714950	+	0.699175i	$0.753551\pi$
$798$		0			0
$799$	−12.2150	+	12.2150i	−0.432134	+	0.432134i
$800$		0			0
$801$	7.93269	−	7.93269i	0.280288	−	0.280288i
$802$		0			0
$803$	3.29598	−	3.29598i	0.116313	−	0.116313i
$804$		0			0
$805$	−0.392646	−	1.72076i	−0.0138390	−	0.0606489i
$806$		0			0
$807$	2.93007	−	2.93007i	0.103143	−	0.103143i
$808$		0			0
$809$		−	39.9138i		−	1.40329i	−0.712525	−	0.701647i	$-0.752448\pi$
$809$		−	39.9138i		−	1.40329i	0.712525	−	0.701647i	$-0.247552\pi$
$810$		0			0
$811$	22.2111	+	22.2111i	0.779937	+	0.779937i	0.979820	−	0.199883i	$-0.0640561\pi$
$811$	22.2111	+	22.2111i	0.779937	+	0.779937i	−0.199883	+	0.979820i	$0.564056\pi$
$812$		0			0
$813$	1.05155			0.0368794
$814$		0			0
$815$	14.8883	+	9.35615i	0.521513	+	0.327731i
$816$		0			0
$817$		−	28.8946i		−	1.01089i
$818$		0			0
$819$	2.63520	−	0.721790i	0.0920815	−	0.0252214i
$820$		0			0
$821$	−7.18756	−	7.18756i	−0.250848	−	0.250848i	0.570470	−	0.821318i	$-0.306761\pi$
$821$	−7.18756	−	7.18756i	−0.250848	−	0.250848i	−0.821318	+	0.570470i	$0.806761\pi$
$822$		0			0
$823$	8.03849	−	8.03849i	0.280204	−	0.280204i	−0.552986	−	0.833190i	$-0.686512\pi$
$823$	8.03849	−	8.03849i	0.280204	−	0.280204i	0.833190	+	0.552986i	$0.186512\pi$
$824$		0			0
$825$	0.830492	+	1.72505i	0.0289140	+	0.0600587i
$826$		0			0
$827$		−	30.0148i		−	1.04372i	−0.853032	−	0.521858i	$-0.825239\pi$
$827$		−	30.0148i		−	1.04372i	0.853032	−	0.521858i	$-0.174761\pi$
$828$		0			0
$829$	20.8805			0.725211			0.362605	−	0.931943i	$-0.381887\pi$
$829$	20.8805			0.725211			0.362605	+	0.931943i	$0.381887\pi$
$830$		0			0
$831$			1.33745i			0.0463955i
$832$		0			0
$833$	23.5264	+	23.5264i	0.815143	+	0.815143i
$834$		0			0
$835$	18.6368	−	29.6565i	0.644954	−	1.02630i
$836$		0			0
$837$	10.5702			0.365361
$838$		0			0
$839$	0.842388	+	0.842388i	0.0290825	+	0.0290825i	0.721498	−	0.692416i	$-0.243454\pi$
$839$	0.842388	+	0.842388i	0.0290825	+	0.0290825i	−0.692416	+	0.721498i	$0.743454\pi$
$840$		0			0
$841$	−13.2340			−0.456344
$842$		0			0
$843$	4.56978			0.157392
$844$		0			0
$845$	−29.0588	−	0.766344i	−0.999652	−	0.0263630i
$846$		0			0
$847$	−8.22463			−0.282602
$848$		0			0
$849$	−20.9733			−0.719803
$850$		0			0
$851$	5.47506	+	5.47506i	0.187683	+	0.187683i
$852$		0			0
$853$	34.4825			1.18066			0.590329	−	0.807163i	$-0.298998\pi$
$853$	34.4825			1.18066			0.590329	+	0.807163i	$0.298998\pi$
$854$		0			0
$855$	1.22676	+	5.37625i	0.0419543	+	0.183864i
$856$		0			0
$857$	−20.0392	−	20.0392i	−0.684525	−	0.684525i	0.276491	−	0.961016i	$-0.410828\pi$
$857$	−20.0392	−	20.0392i	−0.684525	−	0.684525i	−0.961016	+	0.276491i	$0.910828\pi$
$858$		0			0
$859$		−	7.07842i		−	0.241513i	−0.992682	−	0.120756i	$-0.961468\pi$
$859$		−	7.07842i		−	0.241513i	0.992682	−	0.120756i	$-0.0385320\pi$
$860$		0			0
$861$	1.33714			0.0455694
$862$		0			0
$863$			5.93173i			0.201918i	0.994891	+	0.100959i	$0.0321912\pi$
$863$			5.93173i			0.201918i	−0.994891	+	0.100959i	$0.967809\pi$
$864$		0			0
$865$	−3.37043	+	0.769069i	−0.114598	+	0.0261491i
$866$		0			0
$867$	6.93664	−	6.93664i	0.235581	−	0.235581i
$868$		0			0
$869$	−0.305416	−	0.305416i	−0.0103605	−	0.0103605i
$870$		0			0
$871$	−20.9617	+	5.74147i	−0.710261	+	0.194542i
$872$		0			0
$873$			0.531121i			0.0179757i
$874$		0			0
$875$	8.41896	+	0.950098i	0.284613	+	0.0321192i
$876$		0			0
$877$	−30.9204			−1.04411			−0.522054	−	0.852913i	$-0.674834\pi$
$877$	−30.9204			−1.04411			−0.522054	+	0.852913i	$0.674834\pi$
$878$		0			0
$879$	−5.17787	−	5.17787i	−0.174645	−	0.174645i
$880$		0			0
$881$			23.1994i			0.781606i	0.920474	+	0.390803i	$0.127803\pi$
$881$			23.1994i			0.781606i	−0.920474	+	0.390803i	$0.872197\pi$
$882$		0			0
$883$	−17.6405	+	17.6405i	−0.593651	+	0.593651i	−0.938616	−	0.344965i	$-0.887891\pi$
$883$	−17.6405	+	17.6405i	−0.593651	+	0.593651i	0.344965	+	0.938616i	$0.387891\pi$
$884$		0			0
$885$	−16.8358	+	26.7906i	−0.565931	+	0.900556i
$886$		0			0
$887$	−20.7775	+	20.7775i	−0.697641	+	0.697641i	−0.963901	−	0.266260i	$-0.914212\pi$
$887$	−20.7775	+	20.7775i	−0.697641	+	0.697641i	0.266260	+	0.963901i	$0.414212\pi$
$888$		0			0
$889$	1.05070	−	1.05070i	0.0352394	−	0.0352394i
$890$		0			0
$891$	0.270759	−	0.270759i	0.00907078	−	0.00907078i
$892$		0			0
$893$	−5.81782	−	5.81782i	−0.194686	−	0.194686i
$894$		0			0
$895$	19.0718	+	11.9852i	0.637501	+	0.400621i
$896$		0			0
$897$	3.62217	−	0.992123i	0.120941	−	0.0331260i
$898$		0			0
$899$	48.5736	−	48.5736i	1.62002	−	1.62002i
$900$		0			0
$901$		−	22.3987i		−	0.746210i
$902$		0			0
$903$			8.87876i			0.295467i
$904$		0			0
$905$	−19.4386	+	30.9323i	−0.646161	+	1.02823i
$906$		0			0
$907$	29.6450	+	29.6450i	0.984347	+	0.984347i	0.999879	−	0.0155322i	$-0.00494424\pi$
$907$	29.6450	+	29.6450i	0.984347	+	0.984347i	−0.0155322	+	0.999879i	$0.504944\pi$
$908$		0			0
$909$	13.9542			0.462831
$910$		0			0
$911$	19.1481			0.634404			0.317202	−	0.948358i	$-0.397257\pi$
$911$	19.1481			0.634404			0.317202	+	0.948358i	$0.397257\pi$
$912$		0			0
$913$	−3.15517	−	3.15517i	−0.104421	−	0.104421i
$914$		0			0
$915$	−2.86162	−	12.5410i	−0.0946021	−	0.414592i
$916$		0			0
$917$			12.0089i			0.396570i
$918$		0			0
$919$		−	44.8859i		−	1.48065i	−0.672249	−	0.740325i	$-0.734672\pi$
$919$		−	44.8859i		−	1.48065i	0.672249	−	0.740325i	$-0.265328\pi$
$920$		0			0
$921$	−3.17469	+	3.17469i	−0.104610	+	0.104610i
$922$		0			0
$923$	10.8272	+	6.17126i	0.356381	+	0.203129i
$924$		0			0
$925$	−33.4890	+	16.1226i	−1.10111	+	0.530107i
$926$		0			0
$927$	2.23628	+	2.23628i	0.0734489	+	0.0734489i
$928$		0			0
$929$	−22.2379	+	22.2379i	−0.729602	+	0.729602i	−0.970540	−	0.240939i	$-0.922545\pi$
$929$	−22.2379	+	22.2379i	−0.729602	+	0.729602i	0.240939	+	0.970540i	$0.422545\pi$
$930$		0			0
$931$	−11.2053	+	11.2053i	−0.367240	+	0.367240i
$932$		0			0
$933$	8.14264	−	8.14264i	0.266578	−	0.266578i
$934$		0			0
$935$	3.75368	+	2.35890i	0.122758	+	0.0771443i
$936$		0			0
$937$	30.9956	−	30.9956i	1.01258	−	1.01258i	0.0126632	−	0.999920i	$-0.495969\pi$
$937$	30.9956	−	30.9956i	1.01258	−	1.01258i	0.999920	−	0.0126632i	$-0.00403094\pi$
$938$		0			0
$939$		−	27.5522i		−	0.899131i
$940$		0			0
$941$	4.08407	+	4.08407i	0.133137	+	0.133137i	0.770535	−	0.637398i	$-0.219989\pi$
$941$	4.08407	+	4.08407i	0.133137	+	0.133137i	−0.637398	+	0.770535i	$0.719989\pi$
$942$		0			0
$943$	1.83793			0.0598514
$944$		0			0
$945$	−0.376960	−	1.65202i	−0.0122625	−	0.0537402i
$946$		0			0
$947$			46.8028i			1.52089i	0.649405	+	0.760443i	$0.275018\pi$
$947$			46.8028i			1.52089i	−0.649405	+	0.760443i	$0.724982\pi$
$948$		0			0
$949$	42.3316	−	11.5947i	1.37414	−	0.376381i
$950$		0			0
$951$	−19.5275	−	19.5275i	−0.633224	−	0.633224i
$952$		0			0
$953$	3.93071	−	3.93071i	0.127328	−	0.127328i	−0.640571	−	0.767899i	$-0.721302\pi$
$953$	3.93071	−	3.93071i	0.127328	−	0.127328i	0.767899	+	0.640571i	$0.221302\pi$
$954$		0			0
$955$	16.9057	+	10.6239i	0.547056	+	0.343783i
$956$		0			0
$957$		−	2.48845i		−	0.0804402i
$958$		0			0
$959$	2.67698			0.0864442
$960$		0			0
$961$			80.7298i			2.60419i
$962$		0			0
$963$	−8.91181	−	8.91181i	−0.287179	−	0.287179i
$964$		0			0
$965$	44.4382	+	27.9260i	1.43052	+	0.898971i
$966$		0			0
$967$	2.85829			0.0919163			0.0459582	−	0.998943i	$-0.485366\pi$
$967$	2.85829			0.0919163			0.0459582	+	0.998943i	$0.485366\pi$
$968$		0			0
$969$	9.02918	+	9.02918i	0.290059	+	0.290059i
$970$		0			0
$971$	35.2635			1.13166			0.565830	−	0.824522i	$-0.308556\pi$
$971$	35.2635			1.13166			0.565830	+	0.824522i	$0.308556\pi$
$972$		0			0
$973$	−2.18738			−0.0701242
$974$		0			0
$975$	−1.24961	+	17.9844i	−0.0400195	+	0.575962i
$976$		0			0
$977$	40.6669			1.30105			0.650525	−	0.759485i	$-0.274549\pi$
$977$	40.6669			1.30105			0.650525	+	0.759485i	$0.274549\pi$
$978$		0			0
$979$	4.29570			0.137291
$980$		0			0
$981$	−10.7279	−	10.7279i	−0.342516	−	0.342516i
$982$		0			0
$983$	−36.6917			−1.17028			−0.585142	−	0.810931i	$-0.698961\pi$
$983$	−36.6917			−1.17028			−0.585142	+	0.810931i	$0.698961\pi$
$984$		0			0
$985$	18.0630	+	11.3512i	0.575535	+	0.361680i
$986$		0			0
$987$	1.78771	+	1.78771i	0.0569033	+	0.0569033i
$988$		0			0
$989$			12.2041i			0.388069i
$990$		0			0
$991$	18.8693			0.599402			0.299701	−	0.954033i	$-0.403113\pi$
$991$	18.8693			0.599402			0.299701	+	0.954033i	$0.403113\pi$
$992$		0			0
$993$		−	21.4836i		−	0.681760i
$994$		0			0
$995$	−9.30170	−	5.84541i	−0.294884	−	0.185312i
$996$		0			0
$997$	7.20270	−	7.20270i	0.228112	−	0.228112i	−0.583792	−	0.811904i	$-0.698432\pi$
$997$	7.20270	−	7.20270i	0.228112	−	0.228112i	0.811904	+	0.583792i	$0.198432\pi$
$998$		0			0
$999$	5.25633	+	5.25633i	0.166303	+	0.166303i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	780.2.r.a.73.2	✓	28
3.2	odd	2		2340.2.u.i.73.12		28
5.2	odd	4		780.2.bm.a.697.4	yes	28
5.3	odd	4		3900.2.bm.b.2257.9		28
5.4	even	2		3900.2.r.b.3193.9		28
13.5	odd	4		780.2.bm.a.733.4	yes	28
15.2	even	4		2340.2.bp.i.1477.8		28
39.5	even	4		2340.2.bp.i.1513.8		28
65.18	even	4		3900.2.r.b.1357.9		28
65.44	odd	4		3900.2.bm.b.2293.9		28
65.57	even	4	inner	780.2.r.a.577.2	yes	28
195.122	odd	4		2340.2.u.i.577.12		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
780.2.r.a.73.2	✓	28	1.1	even	1	trivial
780.2.r.a.577.2	yes	28	65.57	even	4	inner
780.2.bm.a.697.4	yes	28	5.2	odd	4
780.2.bm.a.733.4	yes	28	13.5	odd	4
2340.2.u.i.73.12		28	3.2	odd	2
2340.2.u.i.577.12		28	195.122	odd	4
2340.2.bp.i.1477.8		28	15.2	even	4
2340.2.bp.i.1513.8		28	39.5	even	4
3900.2.r.b.1357.9		28	65.18	even	4
3900.2.r.b.3193.9		28	5.4	even	2
3900.2.bm.b.2257.9		28	5.3	odd	4
3900.2.bm.b.2293.9		28	65.44	odd	4

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:	\( N \)	\(=\)	\( 780 = 2^{2} \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	780.r (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{3} +(-1.89326 - 1.18977i) q^{5} +0.757795i q^{7} +1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{3} +(-1.89326 - 1.18977i) q^{5} +0.757795i q^{7} +1.00000i q^{9} +(-0.270759 + 0.270759i) q^{11} +(-3.47747 + 0.952487i) q^{13} +(0.497443 + 2.18003i) q^{15} +(3.66128 + 3.66128i) q^{17} +(-1.74382 + 1.74382i) q^{19} +(0.535842 - 0.535842i) q^{21} +(0.736531 - 0.736531i) q^{23} +(2.16889 + 4.50510i) q^{25} +(0.707107 - 0.707107i) q^{27} -6.49877i q^{29} +(7.47428 + 7.47428i) q^{31} +0.382911 q^{33} +(0.901603 - 1.43470i) q^{35} +7.43357i q^{37} +(3.13245 + 1.78543i) q^{39} +(1.24770 + 1.24770i) q^{41} +(-8.28487 + 8.28487i) q^{43} +(1.18977 - 1.89326i) q^{45} +3.33626i q^{47} +6.42575 q^{49} -5.17783i q^{51} +(-3.05887 - 3.05887i) q^{53} +(0.834760 - 0.190477i) q^{55} +2.46613 q^{57} +(10.0059 + 10.0059i) q^{59} -5.75265 q^{61} -0.757795 q^{63} +(7.71700 + 2.33408i) q^{65} +6.02788 q^{67} -1.04161 q^{69} +(-2.44408 - 2.44408i) q^{71} -12.1731 q^{73} +(1.65195 - 4.71922i) q^{75} +(-0.205180 - 0.205180i) q^{77} +1.12800i q^{79} -1.00000 q^{81} +11.6530i q^{83} +(-2.57568 - 11.2878i) q^{85} +(-4.59532 + 4.59532i) q^{87} +(-7.93269 - 7.93269i) q^{89} +(-0.721790 - 2.63520i) q^{91} -10.5702i q^{93} +(5.37625 - 1.22676i) q^{95} +0.531121 q^{97} +(-0.270759 - 0.270759i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q+O(q^{10}) \) 28 * q	\( 28 q + 8 q^{11} - 4 q^{13} - 4 q^{15} - 4 q^{17} - 16 q^{19} + 8 q^{21} - 8 q^{23} + 12 q^{25} - 8 q^{33} + 8 q^{39} + 12 q^{41} + 16 q^{43} + 4 q^{45} - 36 q^{49} + 36 q^{53} + 40 q^{55} + 16 q^{59} + 8 q^{61} - 40 q^{65} + 48 q^{67} - 8 q^{69} + 8 q^{71} + 48 q^{73} - 48 q^{77} - 28 q^{81} - 4 q^{85} - 24 q^{87} - 36 q^{89} - 24 q^{91} + 72 q^{95} - 72 q^{97} + 8 q^{99}+O(q^{100}) \) 28 * q + 8 * q^11 - 4 * q^13 - 4 * q^15 - 4 * q^17 - 16 * q^19 + 8 * q^21 - 8 * q^23 + 12 * q^25 - 8 * q^33 + 8 * q^39 + 12 * q^41 + 16 * q^43 + 4 * q^45 - 36 * q^49 + 36 * q^53 + 40 * q^55 + 16 * q^59 + 8 * q^61 - 40 * q^65 + 48 * q^67 - 8 * q^69 + 8 * q^71 + 48 * q^73 - 48 * q^77 - 28 * q^81 - 4 * q^85 - 24 * q^87 - 36 * q^89 - 24 * q^91 + 72 * q^95 - 72 * q^97 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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