LMFDB - Embedded newform 980.2.v.c.117.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [980,2,Mod(117,980)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(980, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 10]))

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

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

chi := DirichletCharacter("980.117");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.v (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:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			117.11
Character	$\chi$	$=$	980.117
Dual form			980.2.v.c.913.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.595923 - 2.22401i) q^{3} +(1.87454 - 1.21905i) q^{5} +(-1.99304 - 1.15068i) q^{9} +O(q^{10})$	\(q+(0.595923 - 2.22401i) q^{3} +(1.87454 - 1.21905i) q^{5} +(-1.99304 - 1.15068i) q^{9} +(2.17591 + 3.76879i) q^{11} +(-4.14432 - 4.14432i) q^{13} +(-1.59411 - 4.89547i) q^{15} +(3.92538 + 1.05180i) q^{17} +(3.14006 - 5.43874i) q^{19} +(-0.874967 - 3.26542i) q^{23} +(2.02782 - 4.57033i) q^{25} +(1.13744 - 1.13744i) q^{27} -1.36777i q^{29} +(-3.03006 + 1.74941i) q^{31} +(9.67851 - 2.59335i) q^{33} +(-7.46792 + 2.00102i) q^{37} +(-11.6867 + 6.74733i) q^{39} +8.83302i q^{41} +(0.887363 - 0.887363i) q^{43} +(-5.13878 + 0.272617i) q^{45} +(-0.519600 - 1.93917i) q^{47} +(4.67845 - 8.10332i) q^{51} +(-5.44564 - 1.45916i) q^{53} +(8.67318 + 4.41220i) q^{55} +(-10.2246 - 10.2246i) q^{57} +(6.20889 + 10.7541i) q^{59} +(-6.77681 - 3.91259i) q^{61} +(-12.8208 - 2.71656i) q^{65} +(-1.76575 + 6.58987i) q^{67} -7.78376 q^{69} +13.8022 q^{71} +(-1.96447 + 7.33150i) q^{73} +(-8.95606 - 7.23347i) q^{75} +(6.67590 + 3.85434i) q^{79} +(-5.30391 - 9.18664i) q^{81} +(-6.24881 - 6.24881i) q^{83} +(8.64051 - 2.81360i) q^{85} +(-3.04194 - 0.815086i) q^{87} +(-4.58662 + 7.94426i) q^{89} +(2.08502 + 7.78142i) q^{93} +(-0.743936 - 14.0231i) q^{95} +(10.6092 - 10.6092i) q^{97} -10.0151i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 16 q^{11} + 48 q^{23} - 32 q^{25} + 32 q^{37} + 32 q^{43} - 48 q^{51} + 24 q^{53} - 64 q^{65} + 32 q^{67} - 8 q^{81} - 128 q^{85} + 96 q^{93} - 64 q^{95}+O(q^{100}) $ 48 * q - 16 * q^11 + 48 * q^23 - 32 * q^25 + 32 * q^37 + 32 * q^43 - 48 * q^51 + 24 * q^53 - 64 * q^65 + 32 * q^67 - 8 * q^81 - 128 * q^85 + 96 * q^93 - 64 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$	$1$

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
$3$	0.595923	−	2.22401i	0.344056	−	1.28404i	−0.549655	−	0.835392i	$-0.685241\pi$
$3$	0.595923	−	2.22401i	0.344056	−	1.28404i	0.893711	−	0.448643i	$-0.148093\pi$
$4$		0			0
$5$	1.87454	−	1.21905i	0.838321	−	0.545177i
$5$	1.87454	−	1.21905i	0.838321	−	0.545177i
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−1.99304	−	1.15068i	−0.664347	−	0.383561i
$10$		0			0
$11$	2.17591	+	3.76879i	0.656061	+	1.13633i	0.981627	+	0.190812i	$0.0611121\pi$
$11$	2.17591	+	3.76879i	0.656061	+	1.13633i	−0.325565	+	0.945520i	$0.605555\pi$
$12$		0			0
$13$	−4.14432	−	4.14432i	−1.14943	−	1.14943i	−0.986665	−	0.162762i	$-0.947960\pi$
$13$	−4.14432	−	4.14432i	−1.14943	−	1.14943i	−0.162762	−	0.986665i	$-0.552040\pi$
$14$		0			0
$15$	−1.59411	−	4.89547i	−0.411597	−	1.26401i
$16$		0			0
$17$	3.92538	+	1.05180i	0.952046	+	0.255100i	0.701230	−	0.712935i	$-0.252635\pi$
$17$	3.92538	+	1.05180i	0.952046	+	0.255100i	0.250816	+	0.968035i	$0.419301\pi$
$18$		0			0
$19$	3.14006	−	5.43874i	0.720379	−	1.24773i	−0.240469	−	0.970657i	$-0.577301\pi$
$19$	3.14006	−	5.43874i	0.720379	−	1.24773i	0.960848	−	0.277076i	$-0.0893654\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.874967	−	3.26542i	−0.182443	−	0.680887i	−0.995163	−	0.0982332i	$-0.968681\pi$
$23$	−0.874967	−	3.26542i	−0.182443	−	0.680887i	0.812720	−	0.582654i	$-0.197986\pi$
$24$		0			0
$25$	2.02782	−	4.57033i	0.405564	−	0.914066i
$26$		0			0
$27$	1.13744	−	1.13744i	0.218901	−	0.218901i
$28$		0			0
$29$		−	1.36777i		−	0.253989i	−0.991903	−	0.126994i	$-0.959467\pi$
$29$		−	1.36777i		−	0.253989i	0.991903	−	0.126994i	$-0.0405330\pi$
$30$		0			0
$31$	−3.03006	+	1.74941i	−0.544215	+	0.314203i	−0.746786	−	0.665065i	$-0.768404\pi$
$31$	−3.03006	+	1.74941i	−0.544215	+	0.314203i	0.202570	+	0.979268i	$0.435071\pi$
$32$		0			0
$33$	9.67851	−	2.59335i	1.68481	−	0.451444i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−7.46792	+	2.00102i	−1.22772	+	0.328966i	−0.813691	−	0.581298i	$-0.802545\pi$
$37$	−7.46792	+	2.00102i	−1.22772	+	0.328966i	−0.414028	+	0.910264i	$0.635878\pi$
$38$		0			0
$39$	−11.6867	+	6.74733i	−1.87137	+	1.08044i
$40$		0			0
$41$			8.83302i			1.37949i	0.724054	+	0.689743i	$0.242276\pi$
$41$			8.83302i			1.37949i	−0.724054	+	0.689743i	$0.757724\pi$
$42$		0			0
$43$	0.887363	−	0.887363i	0.135322	−	0.135322i	−0.636201	−	0.771523i	$-0.719495\pi$
$43$	0.887363	−	0.887363i	0.135322	−	0.135322i	0.771523	+	0.636201i	$0.219495\pi$
$44$		0			0
$45$	−5.13878	+	0.272617i	−0.766044	+	0.0406394i
$46$		0			0
$47$	−0.519600	−	1.93917i	−0.0757914	−	0.282857i	0.917620	−	0.397458i	$-0.130108\pi$
$47$	−0.519600	−	1.93917i	−0.0757914	−	0.282857i	−0.993412	+	0.114601i	$0.963441\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	4.67845	−	8.10332i	0.655114	−	1.13469i
$52$		0			0
$53$	−5.44564	−	1.45916i	−0.748017	−	0.200430i	−0.135378	−	0.990794i	$-0.543225\pi$
$53$	−5.44564	−	1.45916i	−0.748017	−	0.200430i	−0.612638	+	0.790363i	$0.709892\pi$
$54$		0			0
$55$	8.67318	+	4.41220i	1.16949	+	0.594941i
$56$		0			0
$57$	−10.2246	−	10.2246i	−1.35428	−	1.35428i
$58$		0			0
$59$	6.20889	+	10.7541i	0.808328	+	1.40007i	0.914021	+	0.405667i	$0.132961\pi$
$59$	6.20889	+	10.7541i	0.808328	+	1.40007i	−0.105693	+	0.994399i	$0.533706\pi$
$60$		0			0
$61$	−6.77681	−	3.91259i	−0.867681	−	0.500956i	−0.00110425	−	0.999999i	$-0.500351\pi$
$61$	−6.77681	−	3.91259i	−0.867681	−	0.500956i	−0.866577	+	0.499043i	$0.833685\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−12.8208	−	2.71656i	−1.59023	−	0.336948i
$66$		0			0
$67$	−1.76575	+	6.58987i	−0.215721	+	0.805080i	0.770191	+	0.637813i	$0.220161\pi$
$67$	−1.76575	+	6.58987i	−0.215721	+	0.805080i	−0.985912	+	0.167267i	$0.946506\pi$
$68$		0			0
$69$	−7.78376			−0.937054
$70$		0			0
$71$	13.8022			1.63802			0.819011	−	0.573778i	$-0.194523\pi$
$71$	13.8022			1.63802			0.819011	+	0.573778i	$0.194523\pi$
$72$		0			0
$73$	−1.96447	+	7.33150i	−0.229924	+	0.858087i	0.750448	+	0.660929i	$0.229838\pi$
$73$	−1.96447	+	7.33150i	−0.229924	+	0.858087i	−0.980372	+	0.197158i	$0.936829\pi$
$74$		0			0
$75$	−8.95606	−	7.23347i	−1.03416	−	0.835249i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	6.67590	+	3.85434i	0.751098	+	0.433647i	0.826090	−	0.563537i	$-0.190560\pi$
$79$	6.67590	+	3.85434i	0.751098	+	0.433647i	−0.0749925	+	0.997184i	$0.523893\pi$
$80$		0			0
$81$	−5.30391	−	9.18664i	−0.589323	−	1.02074i
$82$		0			0
$83$	−6.24881	−	6.24881i	−0.685896	−	0.685896i	0.275426	−	0.961322i	$-0.411181\pi$
$83$	−6.24881	−	6.24881i	−0.685896	−	0.685896i	−0.961322	+	0.275426i	$0.911181\pi$
$84$		0			0
$85$	8.64051	−	2.81360i	0.937194	−	0.305178i
$86$		0			0
$87$	−3.04194	−	0.815086i	−0.326130	−	0.0873863i
$88$		0			0
$89$	−4.58662	+	7.94426i	−0.486181	+	0.842090i	−0.999874	−	0.0158838i	$-0.994944\pi$
$89$	−4.58662	+	7.94426i	−0.486181	+	0.842090i	0.513693	+	0.857974i	$0.328277\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	2.08502	+	7.78142i	0.216207	+	0.806895i
$94$		0			0
$95$	−0.743936	−	14.0231i	−0.0763263	−	1.43873i
$96$		0			0
$97$	10.6092	−	10.6092i	1.07720	−	1.07720i	0.0804446	−	0.996759i	$-0.474366\pi$
$97$	10.6092	−	10.6092i	1.07720	−	1.07720i	0.996759	−	0.0804446i	$-0.0256340\pi$
$98$		0			0
$99$		−	10.0151i		−	1.00656i
$100$		0			0
$101$	9.16493	−	5.29138i	0.911945	−	0.526512i	0.0308886	−	0.999523i	$-0.490166\pi$
$101$	9.16493	−	5.29138i	0.911945	−	0.526512i	0.881056	+	0.473011i	$0.156833\pi$
$102$		0			0
$103$	11.7941	−	3.16023i	1.16211	−	0.311387i	0.374303	−	0.927306i	$-0.377882\pi$
$103$	11.7941	−	3.16023i	1.16211	−	0.311387i	0.787809	+	0.615920i	$0.211215\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.13239	−	1.10727i	0.399494	−	0.107044i	−0.0534777	−	0.998569i	$-0.517031\pi$
$107$	4.13239	−	1.10727i	0.399494	−	0.107044i	0.452971	+	0.891525i	$0.350364\pi$
$108$		0			0
$109$	−11.4716	+	6.62311i	−1.09878	+	0.634379i	−0.935900	−	0.352267i	$-0.885411\pi$
$109$	−11.4716	+	6.62311i	−1.09878	+	0.634379i	−0.162878	+	0.986646i	$0.552078\pi$
$110$		0			0
$111$			17.8012i			1.68962i
$112$		0			0
$113$	−11.2991	+	11.2991i	−1.06293	+	1.06293i	−0.0650499	+	0.997882i	$0.520721\pi$
$113$	−11.2991	+	11.2991i	−1.06293	+	1.06293i	−0.997882	+	0.0650499i	$0.979279\pi$
$114$		0			0
$115$	−5.62088	−	5.05454i	−0.524150	−	0.471338i
$116$		0			0
$117$	3.49100	+	13.0286i	0.322743	+	1.20449i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−3.96917	+	6.87480i	−0.360833	+	0.624981i
$122$		0			0
$123$	19.6448	+	5.26380i	1.77131	+	0.474621i
$124$		0			0
$125$	−1.77024	−	11.0393i	−0.158335	−	0.987385i
$126$		0			0
$127$	7.73609	+	7.73609i	0.686467	+	0.686467i	0.961449	−	0.274982i	$-0.0886720\pi$
$127$	7.73609	+	7.73609i	0.686467	+	0.686467i	−0.274982	+	0.961449i	$0.588672\pi$
$128$		0			0
$129$	−1.44471	−	2.50231i	−0.127199	−	0.220316i
$130$		0			0
$131$	−7.93661	−	4.58220i	−0.693424	−	0.400349i	0.111469	−	0.993768i	$-0.464444\pi$
$131$	−7.93661	−	4.58220i	−0.693424	−	0.400349i	−0.804894	+	0.593419i	$0.797778\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	0.745583	−	3.51879i	0.0641696	−	0.302849i
$136$		0			0
$137$	−0.622060	+	2.32156i	−0.0531461	+	0.198344i	−0.987394	−	0.158279i	$-0.949405\pi$
$137$	−0.622060	+	2.32156i	−0.0531461	+	0.198344i	0.934248	+	0.356623i	$0.116072\pi$
$138$		0			0
$139$	3.28295			0.278456			0.139228	−	0.990260i	$-0.455538\pi$
$139$	3.28295			0.278456			0.139228	+	0.990260i	$0.455538\pi$
$140$		0			0
$141$	−4.62239			−0.389276
$142$		0			0
$143$	6.60139	−	24.6367i	0.552036	−	2.06023i
$144$		0			0
$145$	−1.66738	−	2.56394i	−0.138469	−	0.212924i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−3.03618	−	1.75294i	−0.248734	−	0.143606i	0.370451	−	0.928852i	$-0.379203\pi$
$149$	−3.03618	−	1.75294i	−0.248734	−	0.143606i	−0.619184	+	0.785246i	$0.712537\pi$
$150$		0			0
$151$	11.0130	+	19.0752i	0.896229	+	1.55231i	0.832276	+	0.554362i	$0.187038\pi$
$151$	11.0130	+	19.0752i	0.896229	+	1.55231i	0.0639533	+	0.997953i	$0.479629\pi$
$152$		0			0
$153$	−6.61316	−	6.61316i	−0.534642	−	0.534642i
$154$		0			0
$155$	−3.54736	+	6.97315i	−0.284931	+	0.560097i
$156$		0			0
$157$	6.14467	+	1.64646i	0.490398	+	0.131402i	0.495540	−	0.868585i	$-0.334970\pi$
$157$	6.14467	+	1.64646i	0.490398	+	0.131402i	−0.00514217	+	0.999987i	$0.501637\pi$
$158$		0			0
$159$	−6.49037	+	11.2416i	−0.514720	+	0.891521i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−1.07061	−	3.99559i	−0.0838570	−	0.312959i	0.911238	−	0.411880i	$-0.135128\pi$
$163$	−1.07061	−	3.99559i	−0.0838570	−	0.312959i	−0.995095	+	0.0989210i	$0.968461\pi$
$164$		0			0
$165$	14.9814	−	16.6600i	1.16630	−	1.29698i
$166$		0			0
$167$	−4.72566	+	4.72566i	−0.365683	+	0.365683i	−0.865900	−	0.500217i	$-0.833253\pi$
$167$	−4.72566	+	4.72566i	−0.365683	+	0.365683i	0.500217	+	0.865900i	$0.333253\pi$
$168$		0			0
$169$			21.3508i			1.64237i
$170$		0			0
$171$	−12.5165	+	7.22642i	−0.957163	+	0.552618i
$172$		0			0
$173$	10.2785	−	2.75412i	0.781462	−	0.209392i	0.154033	−	0.988066i	$-0.450774\pi$
$173$	10.2785	−	2.75412i	0.781462	−	0.209392i	0.627429	+	0.778674i	$0.284107\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	27.6173	−	7.40004i	2.07584	−	0.556221i
$178$		0			0
$179$	14.7160	−	8.49628i	1.09992	−	0.635042i	0.163723	−	0.986506i	$-0.447650\pi$
$179$	14.7160	−	8.49628i	1.09992	−	0.635042i	0.936201	+	0.351465i	$0.114316\pi$
$180$		0			0
$181$		−	12.8696i		−	0.956587i	−0.878200	−	0.478293i	$-0.841256\pi$
$181$		−	12.8696i		−	0.956587i	0.878200	−	0.478293i	$-0.158744\pi$
$182$		0			0
$183$	−12.7401	+	12.7401i	−0.941776	+	0.941776i
$184$		0			0
$185$	−11.5596	+	12.8548i	−0.849877	+	0.945103i
$186$		0			0
$187$	4.57726	+	17.0826i	0.334722	+	1.24920i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−0.377637	+	0.654086i	−0.0273248	+	0.0473280i	−0.879364	−	0.476149i	$-0.842032\pi$
$191$	−0.377637	+	0.654086i	−0.0273248	+	0.0473280i	0.852040	+	0.523477i	$0.175366\pi$
$192$		0			0
$193$	26.3179	+	7.05186i	1.89440	+	0.507604i	0.997915	+	0.0645348i	$0.0205564\pi$
$193$	26.3179	+	7.05186i	1.89440	+	0.507604i	0.896488	+	0.443069i	$0.146110\pi$
$194$		0			0
$195$	−13.6819	+	26.8949i	−0.979782	+	1.92598i
$196$		0			0
$197$	−5.15636	−	5.15636i	−0.367375	−	0.367375i	0.499144	−	0.866519i	$-0.333648\pi$
$197$	−5.15636	−	5.15636i	−0.367375	−	0.367375i	−0.866519	+	0.499144i	$0.833648\pi$
$198$		0			0
$199$	1.48960	+	2.58007i	0.105595	+	0.182896i	0.913981	−	0.405757i	$-0.132992\pi$
$199$	1.48960	+	2.58007i	0.105595	+	0.182896i	−0.808386	+	0.588653i	$0.799659\pi$
$200$		0			0
$201$	13.6037	+	7.85411i	0.959532	+	0.553986i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	10.7679	+	16.5579i	0.752064	+	1.15645i
$206$		0			0
$207$	−2.01362	+	7.51492i	−0.139956	+	0.522323i
$208$		0			0
$209$	27.3299			1.89045
$210$		0			0
$211$	3.43803			0.236684			0.118342	−	0.992973i	$-0.462242\pi$
$211$	3.43803			0.236684			0.118342	+	0.992973i	$0.462242\pi$
$212$		0			0
$213$	8.22505	−	30.6963i	0.563571	−	2.10328i
$214$		0			0
$215$	0.581658	−	2.74514i	0.0396687	−	0.187217i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	15.1347	+	8.73801i	1.02271	+	0.590460i
$220$		0			0
$221$	−11.9090	−	20.6271i	−0.801089	−	1.38753i
$222$		0			0
$223$	−3.16454	−	3.16454i	−0.211913	−	0.211913i	0.593166	−	0.805080i	$-0.297878\pi$
$223$	−3.16454	−	3.16454i	−0.211913	−	0.211913i	−0.805080	+	0.593166i	$0.797878\pi$
$224$		0			0
$225$	−9.30053	+	6.77548i	−0.620035	+	0.451698i
$226$		0			0
$227$	16.8594	+	4.51745i	1.11899	+	0.299834i	0.770477	−	0.637468i	$-0.220018\pi$
$227$	16.8594	+	4.51745i	1.11899	+	0.299834i	0.348518	+	0.937302i	$0.386685\pi$
$228$		0			0
$229$	−13.0351	+	22.5775i	−0.861386	+	1.49196i	0.00920633	+	0.999958i	$0.497069\pi$
$229$	−13.0351	+	22.5775i	−0.861386	+	1.49196i	−0.870592	+	0.492006i	$0.836264\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1.81013	+	6.75551i	0.118586	+	0.442568i	0.999530	−	0.0306518i	$-0.00975828\pi$
$233$	1.81013	+	6.75551i	0.118586	+	0.442568i	−0.880944	+	0.473220i	$0.843092\pi$
$234$		0			0
$235$	−3.33797	−	3.00164i	−0.217745	−	0.195806i
$236$		0			0
$237$	12.5504	−	12.5504i	0.815237	−	0.815237i
$238$		0			0
$239$			14.0957i			0.911773i	0.890038	+	0.455887i	$0.150678\pi$
$239$			14.0957i			0.911773i	−0.890038	+	0.455887i	$0.849322\pi$
$240$		0			0
$241$	−21.5690	+	12.4529i	−1.38938	+	0.802159i	−0.993245	−	0.116034i	$-0.962982\pi$
$241$	−21.5690	+	12.4529i	−1.38938	+	0.802159i	−0.396134	+	0.918193i	$0.629649\pi$
$242$		0			0
$243$	−18.9306	+	5.07244i	−1.21440	+	0.325397i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−35.5533	+	9.52648i	−2.26220	+	0.606155i
$248$		0			0
$249$	−17.6213	+	10.1736i	−1.11670	+	0.644728i
$250$		0			0
$251$		−	7.22642i		−	0.456127i	−0.973646	−	0.228064i	$-0.926761\pi$
$251$		−	7.22642i		−	0.456127i	0.973646	−	0.228064i	$-0.0732395\pi$
$252$		0			0
$253$	10.4028	−	10.4028i	0.654020	−	0.654020i
$254$		0			0
$255$	−1.10841	−	20.8933i	−0.0694113	−	1.30839i
$256$		0			0
$257$	−1.55338	−	5.79731i	−0.0968974	−	0.361626i	0.900403	−	0.435057i	$-0.143272\pi$
$257$	−1.55338	−	5.79731i	−0.0968974	−	0.361626i	−0.997300	+	0.0734310i	$0.976605\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−1.57387	+	2.72602i	−0.0974200	+	0.168736i
$262$		0			0
$263$	8.65695	+	2.31962i	0.533810	+	0.143034i	0.515647	−	0.856801i	$-0.327552\pi$
$263$	8.65695	+	2.31962i	0.533810	+	0.143034i	0.0181632	+	0.999835i	$0.494218\pi$
$264$		0			0
$265$	−11.9869	+	3.90328i	−0.736348	+	0.239776i
$266$		0			0
$267$	14.9349	+	14.9349i	0.914000	+	0.914000i
$268$		0			0
$269$	−1.33084	−	2.30507i	−0.0811424	−	0.140543i	0.822598	−	0.568623i	$-0.192524\pi$
$269$	−1.33084	−	2.30507i	−0.0811424	−	0.140543i	−0.903741	+	0.428080i	$0.859190\pi$
$270$		0			0
$271$	−15.0185	−	8.67094i	−0.912310	−	0.526722i	−0.0311363	−	0.999515i	$-0.509913\pi$
$271$	−15.0185	−	8.67094i	−0.912310	−	0.526722i	−0.881174	+	0.472793i	$0.843246\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	21.6370	−	2.30220i	1.30476	−	0.138828i
$276$		0			0
$277$	0.166267	−	0.620518i	0.00999003	−	0.0372833i	−0.960751	−	0.277412i	$-0.910523\pi$
$277$	0.166267	−	0.620518i	0.00999003	−	0.0372833i	0.970741	+	0.240129i	$0.0771898\pi$
$278$		0			0
$279$	8.05205			0.482064
$280$		0			0
$281$	−17.6729			−1.05428			−0.527139	−	0.849779i	$-0.676735\pi$
$281$	−17.6729			−1.05428			−0.527139	+	0.849779i	$0.676735\pi$
$282$		0			0
$283$	−3.48393	+	13.0022i	−0.207098	+	0.772901i	0.781702	+	0.623653i	$0.214352\pi$
$283$	−3.48393	+	13.0022i	−0.207098	+	0.772901i	−0.988800	+	0.149248i	$0.952315\pi$
$284$		0			0
$285$	−31.6308	−	6.70213i	−1.87365	−	0.397000i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−0.420079	−	0.242532i	−0.0247105	−	0.0142666i
$290$		0			0
$291$	−17.2728	−	29.9174i	−1.01255	−	1.75379i
$292$		0			0
$293$	2.67303	+	2.67303i	0.156160	+	0.156160i	0.780863	−	0.624703i	$-0.214780\pi$
$293$	2.67303	+	2.67303i	0.156160	+	0.156160i	−0.624703	+	0.780863i	$0.714780\pi$
$294$		0			0
$295$	24.7487	+	12.5901i	1.44092	+	0.733023i
$296$		0			0
$297$	6.76175	+	1.81181i	0.392357	+	0.105132i
$298$		0			0
$299$	−9.90681	+	17.1591i	−0.572926	+	0.992336i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−6.30651	−	23.5362i	−0.362299	−	1.35212i
$304$		0			0
$305$	−17.4731	+	0.926963i	−1.00051	+	0.0530778i
$306$		0			0
$307$	−12.3894	+	12.3894i	−0.707098	+	0.707098i	−0.965924	−	0.258826i	$-0.916664\pi$
$307$	−12.3894	+	12.3894i	−0.707098	+	0.707098i	0.258826	+	0.965924i	$0.416664\pi$
$308$		0			0
$309$		−	28.1136i		−	1.59933i
$310$		0			0
$311$	7.55509	−	4.36193i	0.428410	−	0.247343i	−0.270259	−	0.962788i	$-0.587109\pi$
$311$	7.55509	−	4.36193i	0.428410	−	0.247343i	0.698669	+	0.715445i	$0.253776\pi$
$312$		0			0
$313$	−4.09461	+	1.09715i	−0.231441	+	0.0620145i	−0.372676	−	0.927962i	$-0.621560\pi$
$313$	−4.09461	+	1.09715i	−0.231441	+	0.0620145i	0.141234	+	0.989976i	$0.454893\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	29.7197	−	7.96337i	1.66922	−	0.447267i	0.704323	−	0.709879i	$-0.251251\pi$
$317$	29.7197	−	7.96337i	1.66922	−	0.447267i	0.964902	+	0.262612i	$0.0845839\pi$
$318$		0			0
$319$	5.15483	−	2.97614i	0.288615	−	0.166632i
$320$		0			0
$321$		−	9.85035i		−	0.549793i
$322$		0			0
$323$	18.0464	−	18.0464i	1.00413	−	1.00413i
$324$		0			0
$325$	−27.3449	+	10.5370i	−1.51682	+	0.584486i
$326$		0			0
$327$	7.89373	+	29.4598i	0.436524	+	1.62913i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−9.81308	+	16.9968i	−0.539376	+	0.934226i	0.459562	+	0.888146i	$0.348006\pi$
$331$	−9.81308	+	16.9968i	−0.539376	+	0.934226i	−0.998938	+	0.0460804i	$0.985327\pi$
$332$		0			0
$333$	17.1864	+	4.60508i	0.941809	+	0.252357i
$334$		0			0
$335$	4.72342	+	14.5055i	0.258068	+	0.792522i
$336$		0			0
$337$	5.68650	+	5.68650i	0.309763	+	0.309763i	0.844818	−	0.535054i	$-0.179709\pi$
$337$	5.68650	+	5.68650i	0.309763	+	0.309763i	−0.535054	+	0.844818i	$0.679709\pi$
$338$		0			0
$339$	18.3960	+	31.8628i	0.999134	+	1.73055i
$340$		0			0
$341$	−13.1863	−	7.61311i	−0.714078	−	0.412273i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−14.5910	+	9.48881i	−0.785552	+	0.510860i
$346$		0			0
$347$	−7.92048	+	29.5596i	−0.425194	+	1.58684i	0.338306	+	0.941036i	$0.390146\pi$
$347$	−7.92048	+	29.5596i	−0.425194	+	1.58684i	−0.763500	+	0.645808i	$0.776520\pi$
$348$		0			0
$349$	10.7246			0.574073			0.287036	−	0.957920i	$-0.407330\pi$
$349$	10.7246			0.574073			0.287036	+	0.957920i	$0.407330\pi$
$350$		0			0
$351$	−9.42786			−0.503222
$352$		0			0
$353$	−1.47599	+	5.50849i	−0.0785592	+	0.293187i	−0.994017	−	0.109227i	$-0.965162\pi$
$353$	−1.47599	+	5.50849i	−0.0785592	+	0.293187i	0.915458	+	0.402415i	$0.131829\pi$
$354$		0			0
$355$	25.8728	−	16.8256i	1.37319	−	0.893011i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	8.85535	+	5.11264i	0.467367	+	0.269835i	0.715137	−	0.698984i	$-0.246364\pi$
$359$	8.85535	+	5.11264i	0.467367	+	0.269835i	−0.247770	+	0.968819i	$0.579698\pi$
$360$		0			0
$361$	−10.2199	−	17.7015i	−0.537892	−	0.931656i
$362$		0			0
$363$	12.9243	+	12.9243i	0.678351	+	0.678351i
$364$		0			0
$365$	5.25500	+	16.1380i	0.275059	+	0.844701i
$366$		0			0
$367$	−10.7557	−	2.88198i	−0.561442	−	0.150438i	−0.0330733	−	0.999453i	$-0.510529\pi$
$367$	−10.7557	−	2.88198i	−0.561442	−	0.150438i	−0.528369	+	0.849015i	$0.677196\pi$
$368$		0			0
$369$	10.1640	−	17.6046i	0.529117	−	0.916457i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	3.37644	+	12.6010i	0.174825	+	0.652457i	0.996581	+	0.0826178i	$0.0263281\pi$
$373$	3.37644	+	12.6010i	0.174825	+	0.652457i	−0.821756	+	0.569840i	$0.807005\pi$
$374$		0			0
$375$	−25.6065	−	2.64154i	−1.32231	−	0.136409i
$376$		0			0
$377$	−5.66848	+	5.66848i	−0.291941	+	0.291941i
$378$		0			0
$379$		−	33.9780i		−	1.74533i	−0.488315	−	0.872667i	$-0.662388\pi$
$379$		−	33.9780i		−	1.74533i	0.488315	−	0.872667i	$-0.337612\pi$
$380$		0			0
$381$	21.8153	−	12.5951i	1.11763	−	0.645265i
$382$		0			0
$383$	13.3583	−	3.57934i	0.682576	−	0.182896i	0.0991627	−	0.995071i	$-0.468384\pi$
$383$	13.3583	−	3.57934i	0.682576	−	0.182896i	0.583413	+	0.812176i	$0.301717\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−2.78962	+	0.747477i	−0.141805	+	0.0379964i
$388$		0			0
$389$	−3.11351	+	1.79759i	−0.157861	+	0.0911412i	−0.576850	−	0.816850i	$-0.695718\pi$
$389$	−3.11351	+	1.79759i	−0.157861	+	0.0911412i	0.418988	+	0.907992i	$0.362385\pi$
$390$		0			0
$391$		−	13.7383i		−	0.694777i
$392$		0			0
$393$	−14.9205	+	14.9205i	−0.752639	+	0.752639i
$394$		0			0
$395$	17.2129	−	0.913161i	0.866075	−	0.0459461i
$396$		0			0
$397$	−5.89931	−	22.0165i	−0.296078	−	1.10498i	−0.940358	−	0.340188i	$-0.889509\pi$
$397$	−5.89931	−	22.0165i	−0.296078	−	1.10498i	0.644280	−	0.764790i	$-0.277157\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	4.01271	−	6.95021i	0.200385	−	0.347077i	−0.748268	−	0.663397i	$-0.769114\pi$
$401$	4.01271	−	6.95021i	0.200385	−	0.347077i	0.948652	+	0.316320i	$0.102447\pi$
$402$		0			0
$403$	19.8077	+	5.30745i	0.986690	+	0.264383i
$404$		0			0
$405$	−21.1414	−	10.7550i	−1.05052	−	0.534420i
$406$		0			0
$407$	−23.7909	−	23.7909i	−1.17927	−	1.17927i
$408$		0			0
$409$	−6.54852	−	11.3424i	−0.323803	−	0.560844i	0.657466	−	0.753484i	$-0.271628\pi$
$409$	−6.54852	−	11.3424i	−0.323803	−	0.560844i	−0.981269	+	0.192640i	$0.938295\pi$
$410$		0			0
$411$	4.79248	+	2.76694i	0.236396	+	0.136483i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−19.3313	−	4.09604i	−0.948936	−	0.201067i
$416$		0			0
$417$	1.95639	−	7.30133i	0.0958047	−	0.357548i
$418$		0			0
$419$	5.22265			0.255143			0.127572	−	0.991829i	$-0.459282\pi$
$419$	5.22265			0.255143			0.127572	+	0.991829i	$0.459282\pi$
$420$		0			0
$421$	−10.5933			−0.516286			−0.258143	−	0.966107i	$-0.583111\pi$
$421$	−10.5933			−0.516286			−0.258143	+	0.966107i	$0.583111\pi$
$422$		0			0
$423$	−1.19579	+	4.46274i	−0.0581412	+	0.216986i
$424$		0			0
$425$	12.7671	−	15.8074i	0.619294	−	0.766774i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−50.8585	−	29.3632i	−2.45547	−	1.41767i
$430$		0			0
$431$	1.38520	+	2.39923i	0.0667226	+	0.115567i	0.897457	−	0.441102i	$-0.145412\pi$
$431$	1.38520	+	2.39923i	0.0667226	+	0.115567i	−0.830734	+	0.556669i	$0.812079\pi$
$432$		0			0
$433$	4.40498	+	4.40498i	0.211690	+	0.211690i	0.804985	−	0.593295i	$-0.202173\pi$
$433$	4.40498	+	4.40498i	0.211690	+	0.211690i	−0.593295	+	0.804985i	$0.702173\pi$
$434$		0			0
$435$	−6.69588	+	2.18037i	−0.321043	+	0.104541i
$436$		0			0
$437$	−20.5072	−	5.49490i	−0.980994	−	0.262857i
$438$		0			0
$439$	−0.446142	+	0.772741i	−0.0212932	+	0.0368809i	−0.876476	−	0.481446i	$-0.840112\pi$
$439$	−0.446142	+	0.772741i	−0.0212932	+	0.0368809i	0.855182	+	0.518327i	$0.173445\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−5.73847	−	21.4163i	−0.272643	−	1.01752i	−0.957404	−	0.288750i	$-0.906760\pi$
$443$	−5.73847	−	21.4163i	−0.272643	−	1.01752i	0.684761	−	0.728767i	$-0.259906\pi$
$444$		0			0
$445$	1.08665	+	20.4832i	0.0515123	+	0.970997i
$446$		0			0
$447$	−5.70789	+	5.70789i	−0.269974	+	0.269974i
$448$		0			0
$449$		−	5.95434i		−	0.281003i	−0.990080	−	0.140501i	$-0.955129\pi$
$449$		−	5.95434i		−	0.281003i	0.990080	−	0.140501i	$-0.0448714\pi$
$450$		0			0
$451$	−33.2898	+	19.2199i	−1.56755	+	0.905028i
$452$		0			0
$453$	48.9864	−	13.1259i	2.30158	−	0.616706i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−0.422270	+	0.113147i	−0.0197529	+	0.00529278i	−0.268682	−	0.963229i	$-0.586588\pi$
$457$	−0.422270	+	0.113147i	−0.0197529	+	0.00529278i	0.248929	+	0.968522i	$0.419921\pi$
$458$		0			0
$459$	5.66127	−	3.26853i	0.264245	−	0.152562i
$460$		0			0
$461$			2.69522i			0.125529i	0.998028	+	0.0627646i	$0.0199917\pi$
$461$			2.69522i			0.125529i	−0.998028	+	0.0627646i	$0.980008\pi$
$462$		0			0
$463$	−13.2342	+	13.2342i	−0.615046	+	0.615046i	−0.944257	−	0.329211i	$-0.893217\pi$
$463$	−13.2342	+	13.2342i	−0.615046	+	0.615046i	0.329211	+	0.944257i	$0.393217\pi$
$464$		0			0
$465$	13.3944	+	12.0448i	0.621152	+	0.558566i
$466$		0			0
$467$	−0.452047	−	1.68706i	−0.0209182	−	0.0780679i	0.954678	−	0.297642i	$-0.0962000\pi$
$467$	−0.452047	−	1.68706i	−0.0209182	−	0.0780679i	−0.975596	+	0.219574i	$0.929533\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	7.32350	−	12.6847i	0.337449	−	0.584479i
$472$		0			0
$473$	5.27510	+	1.41346i	0.242550	+	0.0649909i
$474$		0			0
$475$	−18.4894	−	25.3799i	−0.848351	−	1.16451i
$476$		0			0
$477$	9.17436	+	9.17436i	0.420065	+	0.420065i
$478$		0			0
$479$	−14.9381	−	25.8735i	−0.682539	−	1.18219i	−0.974204	−	0.225671i	$-0.927542\pi$
$479$	−14.9381	−	25.8735i	−0.682539	−	1.18219i	0.291665	−	0.956521i	$-0.405791\pi$
$480$		0			0
$481$	39.2423	+	22.6566i	1.78930	+	1.03305i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	6.95425	−	32.8207i	0.315776	−	1.49031i
$486$		0			0
$487$	−9.99704	+	37.3095i	−0.453009	+	1.69065i	0.240866	+	0.970558i	$0.422569\pi$
$487$	−9.99704	+	37.3095i	−0.453009	+	1.69065i	−0.693875	+	0.720095i	$0.744098\pi$
$488$		0			0
$489$	−9.52425			−0.430701
$490$		0			0
$491$	−4.60003			−0.207597			−0.103798	−	0.994598i	$-0.533100\pi$
$491$	−4.60003			−0.207597			−0.103798	+	0.994598i	$0.533100\pi$
$492$		0			0
$493$	1.43863	−	5.36902i	0.0647924	−	0.241809i
$494$		0			0
$495$	−12.2090	−	18.7738i	−0.548752	−	0.843818i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	7.55371	+	4.36114i	0.338151	+	0.195231i	0.659454	−	0.751745i	$-0.270788\pi$
$499$	7.55371	+	4.36114i	0.338151	+	0.195231i	−0.321303	+	0.946976i	$0.604121\pi$
$500$		0			0
$501$	7.69381	+	13.3261i	0.343734	+	0.595365i
$502$		0			0
$503$	−5.06191	−	5.06191i	−0.225699	−	0.225699i	0.585194	−	0.810893i	$-0.301018\pi$
$503$	−5.06191	−	5.06191i	−0.225699	−	0.225699i	−0.810893	+	0.585194i	$0.801018\pi$
$504$		0			0
$505$	10.7296	−	21.0914i	0.477461	−	0.938557i
$506$		0			0
$507$	47.4844	+	12.7234i	2.10886	+	0.565067i
$508$		0			0
$509$	9.92930	−	17.1981i	0.440108	−	0.762290i	−0.557589	−	0.830117i	$-0.688273\pi$
$509$	9.92930	−	17.1981i	0.440108	−	0.762290i	0.997697	+	0.0678272i	$0.0216067\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−2.61462	−	9.75790i	−0.115438	−	0.430822i
$514$		0			0
$515$	18.2561	−	20.3017i	0.804462	−	0.894599i
$516$		0			0
$517$	6.17773	−	6.17773i	0.271696	−	0.271696i
$518$		0			0
$519$		−	24.5008i		−	1.07547i
$520$		0			0
$521$	30.2378	−	17.4578i	1.32474	−	0.764840i	0.340260	−	0.940331i	$-0.389485\pi$
$521$	30.2378	−	17.4578i	1.32474	−	0.764840i	0.984481	+	0.175492i	$0.0561515\pi$
$522$		0			0
$523$	24.7238	−	6.62473i	1.08110	−	0.289679i	0.326053	−	0.945352i	$-0.394281\pi$
$523$	24.7238	−	6.62473i	1.08110	−	0.289679i	0.755046	+	0.655672i	$0.227615\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−13.7342	+	3.68007i	−0.598271	+	0.160306i
$528$		0			0
$529$	10.0212	−	5.78573i	0.435703	−	0.251553i
$530$		0			0
$531$		−	28.5778i		−	1.24017i
$532$		0			0
$533$	36.6069	−	36.6069i	1.58562	−	1.58562i
$534$		0			0
$535$	6.39653	−	7.11323i	0.276546	−	0.307532i
$536$		0			0
$537$	−10.1263	−	37.7917i	−0.436980	−	1.63083i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−21.8231	+	37.7988i	−0.938250	+	1.62510i	−0.169517	+	0.985527i	$0.554221\pi$
$541$	−21.8231	+	37.7988i	−0.938250	+	1.62510i	−0.768733	+	0.639569i	$0.779113\pi$
$542$		0			0
$543$	−28.6221	−	7.66926i	−1.22829	−	0.329120i
$544$		0			0
$545$	−13.4300	+	26.3998i	−0.575279	+	1.13084i
$546$		0			0
$547$	−11.5096	−	11.5096i	−0.492114	−	0.492114i	0.416857	−	0.908972i	$-0.363131\pi$
$547$	−11.5096	−	11.5096i	−0.492114	−	0.492114i	−0.908972	+	0.416857i	$0.863131\pi$
$548$		0			0
$549$	9.00430	+	15.5959i	0.384294	+	0.665617i
$550$		0			0
$551$	−7.43895	−	4.29488i	−0.316910	−	0.182968i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	21.7006	+	33.3691i	0.921140	+	1.41644i
$556$		0			0
$557$	1.14543	−	4.27479i	0.0485333	−	0.181129i	−0.937404	−	0.348243i	$-0.886778\pi$
$557$	1.14543	−	4.27479i	0.0485333	−	0.181129i	0.985937	+	0.167114i	$0.0534450\pi$
$558$		0			0
$559$	−7.35503			−0.311085
$560$		0			0
$561$	40.7196			1.71918
$562$		0			0
$563$	5.96206	−	22.2507i	0.251271	−	0.937756i	−0.718856	−	0.695159i	$-0.755334\pi$
$563$	5.96206	−	22.2507i	0.251271	−	0.937756i	0.970127	−	0.242597i	$-0.0779992\pi$
$564$		0			0
$565$	−7.40647	+	34.9549i	−0.311592	+	1.47056i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−2.78756	−	1.60940i	−0.116861	−	0.0674695i	0.440430	−	0.897787i	$-0.354826\pi$
$569$	−2.78756	−	1.60940i	−0.116861	−	0.0674695i	−0.557291	+	0.830317i	$0.688159\pi$
$570$		0			0
$571$	12.9774	+	22.4775i	0.543088	+	0.940655i	0.998725	+	0.0504895i	$0.0160782\pi$
$571$	12.9774	+	22.4775i	0.543088	+	0.940655i	−0.455637	+	0.890166i	$0.650589\pi$
$572$		0			0
$573$	1.22965	+	1.22965i	0.0513695	+	0.0513695i
$574$		0			0
$575$	−16.6983	−	2.62280i	−0.696369	−	0.109378i
$576$		0			0
$577$	−2.48886	−	0.666889i	−0.103613	−	0.0277629i	0.206640	−	0.978417i	$-0.433747\pi$
$577$	−2.48886	−	0.666889i	−0.103613	−	0.0277629i	−0.310253	+	0.950654i	$0.600414\pi$
$578$		0			0
$579$	31.3669	−	54.3290i	1.30356	−	2.25784i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−6.34998	−	23.6985i	−0.262989	−	0.981490i
$584$		0			0
$585$	22.4266	+	20.1669i	0.927224	+	0.833800i
$586$		0			0
$587$	−0.757263	+	0.757263i	−0.0312556	+	0.0312556i	−0.722562	−	0.691306i	$-0.757036\pi$
$587$	−0.757263	+	0.757263i	−0.0312556	+	0.0312556i	0.691306	+	0.722562i	$0.257036\pi$
$588$		0			0
$589$			21.9730i			0.905381i
$590$		0			0
$591$	−14.5406	+	8.39502i	−0.598121	+	0.345325i
$592$		0			0
$593$	−23.2410	+	6.22741i	−0.954395	+	0.255729i	−0.702226	−	0.711954i	$-0.747810\pi$
$593$	−23.2410	+	6.22741i	−0.954395	+	0.255729i	−0.252169	+	0.967683i	$0.581144\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	6.62580	−	1.77538i	0.271176	−	0.0726613i
$598$		0			0
$599$	−37.4653	+	21.6306i	−1.53079	+	0.883802i	−0.531464	+	0.847081i	$0.678358\pi$
$599$	−37.4653	+	21.6306i	−1.53079	+	0.883802i	−0.999326	+	0.0367207i	$0.988309\pi$
$600$		0			0
$601$			39.5515i			1.61334i	0.591003	+	0.806670i	$0.298732\pi$
$601$			39.5515i			1.61334i	−0.591003	+	0.806670i	$0.701268\pi$
$602$		0			0
$603$	11.1021	−	11.1021i	0.452111	−	0.452111i
$604$		0			0
$605$	0.940367	+	17.7257i	0.0382313	+	0.720653i
$606$		0			0
$607$	−7.24197	−	27.0274i	−0.293943	−	1.09701i	−0.942054	−	0.335463i	$-0.891107\pi$
$607$	−7.24197	−	27.0274i	−0.293943	−	1.09701i	0.648111	−	0.761546i	$-0.275559\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−5.88317	+	10.1899i	−0.238007	+	0.412241i
$612$		0			0
$613$	−37.8456	−	10.1407i	−1.52857	−	0.409579i	−0.606017	−	0.795451i	$-0.707234\pi$
$613$	−37.8456	−	10.1407i	−1.52857	−	0.409579i	−0.922552	+	0.385872i	$0.873901\pi$
$614$		0			0
$615$	43.2418	−	14.0808i	1.74368	−	0.567792i
$616$		0			0
$617$	−33.5984	−	33.5984i	−1.35262	−	1.35262i	−0.882720	−	0.469899i	$-0.844290\pi$
$617$	−33.5984	−	33.5984i	−1.35262	−	1.35262i	−0.469899	−	0.882720i	$-0.655710\pi$
$618$		0			0
$619$	−0.378048	−	0.654799i	−0.0151951	−	0.0263186i	0.858328	−	0.513102i	$-0.171504\pi$
$619$	−0.378048	−	0.654799i	−0.0151951	−	0.0263186i	−0.873523	+	0.486783i	$0.838170\pi$
$620$		0			0
$621$	−4.70946	−	2.71901i	−0.188984	−	0.109110i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−16.7759	−	18.5356i	−0.671035	−	0.741426i
$626$		0			0
$627$	16.2865	−	60.7822i	0.650422	−	2.42741i
$628$		0			0
$629$	−31.4191			−1.25276
$630$		0			0
$631$	7.09588			0.282482			0.141241	−	0.989975i	$-0.454891\pi$
$631$	7.09588			0.282482			0.141241	+	0.989975i	$0.454891\pi$
$632$		0			0
$633$	2.04880	−	7.64622i	0.0814325	−	0.303910i
$634$		0			0
$635$	23.9323	+	5.07093i	0.949726	+	0.201234i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−27.5084	−	15.8820i	−1.08821	−	0.628281i
$640$		0			0
$641$	−4.92761	−	8.53488i	−0.194629	−	0.337107i	0.752150	−	0.658992i	$-0.229017\pi$
$641$	−4.92761	−	8.53488i	−0.194629	−	0.337107i	−0.946779	+	0.321885i	$0.895684\pi$
$642$		0			0
$643$	−14.2434	−	14.2434i	−0.561704	−	0.561704i	0.368087	−	0.929791i	$-0.380013\pi$
$643$	−14.2434	−	14.2434i	−0.561704	−	0.561704i	−0.929791	+	0.368087i	$0.880013\pi$
$644$		0			0
$645$	−5.75861	−	2.92951i	−0.226745	−	0.115349i
$646$		0			0
$647$	−43.1440	−	11.5604i	−1.69617	−	0.454487i	−0.724198	−	0.689593i	$-0.757790\pi$
$647$	−43.1440	−	11.5604i	−1.69617	−	0.454487i	−0.971970	+	0.235106i	$0.924456\pi$
$648$		0			0
$649$	−27.0200	+	46.7999i	−1.06063	+	1.83706i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	2.35139	+	8.77551i	0.0920170	+	0.343412i	0.996550	−	0.0829908i	$-0.0264472\pi$
$653$	2.35139	+	8.77551i	0.0920170	+	0.343412i	−0.904533	+	0.426403i	$0.859781\pi$
$654$		0			0
$655$	−20.4635	+	1.08561i	−0.799573	+	0.0424181i
$656$		0			0
$657$	12.3515	−	12.3515i	0.481877	−	0.481877i
$658$		0			0
$659$			37.6874i			1.46809i	0.679099	+	0.734046i	$0.262371\pi$
$659$			37.6874i			1.46809i	−0.679099	+	0.734046i	$0.737629\pi$
$660$		0			0
$661$	−14.4385	+	8.33605i	−0.561591	+	0.324235i	−0.753784	−	0.657122i	$-0.771773\pi$
$661$	−14.4385	+	8.33605i	−0.561591	+	0.324235i	0.192193	+	0.981357i	$0.438440\pi$
$662$		0			0
$663$	−52.9718	+	14.1937i	−2.05725	+	0.551239i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−4.46635	+	1.19675i	−0.172938	+	0.0463385i
$668$		0			0
$669$	−8.92381	+	5.15216i	−0.345014	+	0.199194i
$670$		0			0
$671$		−	34.0538i		−	1.31463i
$672$		0			0
$673$	12.4425	−	12.4425i	0.479624	−	0.479624i	−0.425387	−	0.905011i	$-0.639862\pi$
$673$	12.4425	−	12.4425i	0.479624	−	0.479624i	0.905011	+	0.425387i	$0.139862\pi$
$674$		0			0
$675$	−2.89196	−	7.50502i	−0.111312	−	0.288868i
$676$		0			0
$677$	5.81870	+	21.7157i	0.223631	+	0.834602i	0.982948	+	0.183882i	$0.0588663\pi$
$677$	5.81870	+	21.7157i	0.223631	+	0.834602i	−0.759318	+	0.650720i	$0.774467\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	20.0937	−	34.8034i	0.769994	−	1.33367i
$682$		0			0
$683$	−31.4583	−	8.42924i	−1.20372	−	0.322536i	−0.399425	−	0.916766i	$-0.630790\pi$
$683$	−31.4583	−	8.42924i	−1.20372	−	0.322536i	−0.804295	+	0.594230i	$0.797457\pi$
$684$		0			0
$685$	1.66402	+	5.11018i	0.0635791	+	0.195250i
$686$		0			0
$687$	42.4448	+	42.4448i	1.61937	+	1.61937i
$688$		0			0
$689$	16.5213	+	28.6157i	0.629411	+	1.09017i
$690$		0			0
$691$	−2.36602	−	1.36602i	−0.0900078	−	0.0519660i	0.454321	−	0.890838i	$-0.349882\pi$
$691$	−2.36602	−	1.36602i	−0.0900078	−	0.0519660i	−0.544328	+	0.838872i	$0.683215\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	6.15404	−	4.00209i	0.233436	−	0.151808i
$696$		0			0
$697$	−9.29060	+	34.6730i	−0.351907	+	1.31333i
$698$		0			0
$699$	16.1030			0.609073
$700$		0			0
$701$	−22.4517			−0.847989			−0.423994	−	0.905665i	$-0.639372\pi$
$701$	−22.4517			−0.847989			−0.423994	+	0.905665i	$0.639372\pi$
$702$		0			0
$703$	−12.5667	+	46.8994i	−0.473960	+	1.76884i
$704$		0			0
$705$	−8.66487	+	5.63494i	−0.326338	+	0.212224i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	18.5428	+	10.7057i	0.696390	+	0.402061i	0.806002	−	0.591913i	$-0.201627\pi$
$709$	18.5428	+	10.7057i	0.696390	+	0.402061i	−0.109611	+	0.993975i	$0.534961\pi$
$710$		0			0
$711$	−8.87023	−	15.3637i	−0.332660	−	0.576183i
$712$		0			0
$713$	8.36376	+	8.36376i	0.313225	+	0.313225i
$714$		0			0
$715$	−17.6589	−	54.2300i	−0.660404	−	2.02809i
$716$		0			0
$717$	31.3490	+	8.39993i	1.17075	+	0.313701i
$718$		0			0
$719$	7.53973	−	13.0592i	0.281185	−	0.487026i	−0.690492	−	0.723340i	$-0.742606\pi$
$719$	7.53973	−	13.0592i	0.281185	−	0.487026i	0.971677	+	0.236314i	$0.0759393\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	14.8419	+	55.3906i	0.551975	+	2.06000i
$724$		0			0
$725$	−6.25116	−	2.77359i	−0.232162	−	0.103009i
$726$		0			0
$727$	11.3016	−	11.3016i	0.419152	−	0.419152i	−0.465759	−	0.884911i	$-0.654219\pi$
$727$	11.3016	−	11.3016i	0.419152	−	0.419152i	0.884911	+	0.465759i	$0.154219\pi$
$728$		0			0
$729$			13.3013i			0.492640i
$730$		0			0
$731$	4.41657	−	2.54991i	0.163353	−	0.0943118i
$732$		0			0
$733$	−12.3672	+	3.31377i	−0.456791	+	0.122397i	−0.479875	−	0.877337i	$-0.659318\pi$
$733$	−12.3672	+	3.31377i	−0.456791	+	0.122397i	0.0230840	+	0.999734i	$0.492651\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−28.6779	+	7.68422i	−1.05636	+	0.283052i
$738$		0			0
$739$	20.1257	−	11.6196i	0.740335	−	0.427433i	−0.0818559	−	0.996644i	$-0.526085\pi$
$739$	20.1257	−	11.6196i	0.740335	−	0.427433i	0.822191	+	0.569211i	$0.192751\pi$
$740$		0			0
$741$			84.7481i			3.11330i
$742$		0			0
$743$	−28.5381	+	28.5381i	−1.04696	+	1.04696i	−0.0481196	+	0.998842i	$0.515323\pi$
$743$	−28.5381	+	28.5381i	−1.04696	+	1.04696i	−0.998842	+	0.0481196i	$0.984677\pi$
$744$		0			0
$745$	−7.82838	+	0.415303i	−0.286810	+	0.0152155i
$746$		0			0
$747$	5.26374	+	19.6445i	0.192590	+	0.718756i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	23.2379	−	40.2493i	0.847965	−	1.46872i	−0.0350566	−	0.999385i	$-0.511161\pi$
$751$	23.2379	−	40.2493i	0.847965	−	1.46872i	0.883021	−	0.469333i	$-0.155506\pi$
$752$		0			0
$753$	−16.0717	−	4.30639i	−0.585684	−	0.156933i
$754$		0			0
$755$	43.8981	+	22.3317i	1.59761	+	0.812735i
$756$		0			0
$757$	19.4978	+	19.4978i	0.708661	+	0.708661i	0.966254	−	0.257592i	$-0.0829292\pi$
$757$	19.4978	+	19.4978i	0.708661	+	0.708661i	−0.257592	+	0.966254i	$0.582929\pi$
$758$		0			0
$759$	−16.9368	−	29.3353i	−0.614765	−	1.06480i
$760$		0			0
$761$	−15.5856	−	8.99836i	−0.564978	−	0.326190i	0.190163	−	0.981753i	$-0.439098\pi$
$761$	−15.5856	−	8.99836i	−0.564978	−	0.326190i	−0.755141	+	0.655562i	$0.772432\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−20.4584	−	4.33486i	−0.739676	−	0.156727i
$766$		0			0
$767$	18.8369	−	70.3001i	0.680159	−	2.53839i
$768$		0			0
$769$	−7.17459			−0.258722			−0.129361	−	0.991598i	$-0.541293\pi$
$769$	−7.17459			−0.258722			−0.129361	+	0.991598i	$0.541293\pi$
$770$		0			0
$771$	−13.8190			−0.497679
$772$		0			0
$773$	−11.8419	+	44.1947i	−0.425925	+	1.58957i	0.335970	+	0.941873i	$0.390936\pi$
$773$	−11.8419	+	44.1947i	−0.425925	+	1.58957i	−0.761895	+	0.647701i	$0.775731\pi$
$774$		0			0
$775$	1.85095	+	17.3959i	0.0664880	+	0.624879i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	48.0405	+	27.7362i	1.72123	+	0.993753i
$780$		0			0
$781$	30.0324	+	52.0176i	1.07464	+	1.86134i
$782$		0			0
$783$	−1.55576	−	1.55576i	−0.0555983	−	0.0555983i
$784$		0			0
$785$	13.5256	−	4.40432i	0.482748	−	0.157197i
$786$		0			0
$787$	−20.0866	−	5.38218i	−0.716009	−	0.191854i	−0.117619	−	0.993059i	$-0.537526\pi$
$787$	−20.0866	−	5.38218i	−0.716009	−	0.191854i	−0.598390	+	0.801205i	$0.704193\pi$
$788$		0			0
$789$	10.3177	−	17.8709i	0.367322	−	0.636220i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	11.8702	+	44.3003i	0.421524	+	1.57315i
$794$		0			0
$795$	1.53768	+	28.9850i	0.0545361	+	1.02799i
$796$		0			0
$797$	−28.4657	+	28.4657i	−1.00831	+	1.00831i	−0.00834254	+	0.999965i	$0.502656\pi$
$797$	−28.4657	+	28.4657i	−1.00831	+	1.00831i	−0.999965	+	0.00834254i	$0.997344\pi$
$798$		0			0
$799$		−	8.15852i		−	0.288628i
$800$		0			0
$801$	18.2826	−	10.5555i	0.645986	−	0.372960i
$802$		0			0
$803$	−31.9054	+	8.54901i	−1.12592	+	0.301688i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−5.91959	+	1.58615i	−0.208380	+	0.0558351i
$808$		0			0
$809$	32.5718	−	18.8053i	1.14516	−	0.661161i	0.197460	−	0.980311i	$-0.436731\pi$
$809$	32.5718	−	18.8053i	1.14516	−	0.661161i	0.947704	+	0.319150i	$0.103397\pi$
$810$		0			0
$811$			25.6605i			0.901060i	0.892761	+	0.450530i	$0.148765\pi$
$811$			25.6605i			0.901060i	−0.892761	+	0.450530i	$0.851235\pi$
$812$		0			0
$813$	−28.2342	+	28.2342i	−0.990216	+	0.990216i
$814$		0			0
$815$	−6.87774	−	6.18476i	−0.240917	−	0.216643i
$816$		0			0
$817$	−2.03977	−	7.61251i	−0.0713624	−	0.266328i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1.78971	+	3.09987i	−0.0624614	+	0.108186i	−0.895565	−	0.444931i	$-0.853228\pi$
$821$	−1.78971	+	3.09987i	−0.0624614	+	0.108186i	0.833104	+	0.553117i	$0.186562\pi$
$822$		0			0
$823$	−6.03583	−	1.61730i	−0.210396	−	0.0563754i	0.152082	−	0.988368i	$-0.451402\pi$
$823$	−6.03583	−	1.61730i	−0.210396	−	0.0563754i	−0.362477	+	0.931993i	$0.618069\pi$
$824$		0			0
$825$	7.77383	−	49.4929i	0.270650	−	1.72312i
$826$		0			0
$827$	−19.5077	−	19.5077i	−0.678350	−	0.678350i	0.281277	−	0.959627i	$-0.409242\pi$
$827$	−19.5077	−	19.5077i	−0.678350	−	0.678350i	−0.959627	+	0.281277i	$0.909242\pi$
$828$		0			0
$829$	−7.47729	−	12.9510i	−0.259697	−	0.449808i	0.706464	−	0.707749i	$-0.250289\pi$
$829$	−7.47729	−	12.9510i	−0.259697	−	0.449808i	−0.966161	+	0.257941i	$0.916956\pi$
$830$		0			0
$831$	−1.28096	−	0.739561i	−0.0444359	−	0.0256551i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−3.09762	+	14.6193i	−0.107198	+	0.505921i
$836$		0			0
$837$	−1.45667	+	5.43638i	−0.0503500	+	0.187909i
$838$		0			0
$839$	−10.7062			−0.369618			−0.184809	−	0.982774i	$-0.559167\pi$
$839$	−10.7062			−0.369618			−0.184809	+	0.982774i	$0.559167\pi$
$840$		0			0
$841$	27.1292			0.935490
$842$		0			0
$843$	−10.5317	+	39.3048i	−0.362731	+	1.35373i
$844$		0			0
$845$	26.0277	+	40.0230i	0.895381	+	1.37683i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	26.8409	+	15.4966i	0.921178	+	0.531843i
$850$		0			0
$851$	13.0684	+	22.6351i	0.447978	+	0.775920i
$852$		0			0
$853$	18.9196	+	18.9196i	0.647794	+	0.647794i	0.952460	−	0.304665i	$-0.0985446\pi$
$853$	18.9196	+	18.9196i	0.647794	+	0.647794i	−0.304665	+	0.952460i	$0.598545\pi$
$854$		0			0
$855$	−14.6534	+	28.8045i	−0.501135	+	0.985094i
$856$		0			0
$857$	−30.3505	−	8.13239i	−1.03675	−	0.277797i	−0.299986	−	0.953944i	$-0.596982\pi$
$857$	−30.3505	−	8.13239i	−1.03675	−	0.277797i	−0.736767	+	0.676147i	$0.763649\pi$
$858$		0			0
$859$	4.98015	−	8.62588i	0.169921	−	0.294311i	−0.768471	−	0.639884i	$-0.778982\pi$
$859$	4.98015	−	8.62588i	0.169921	−	0.294311i	0.938392	+	0.345573i	$0.112316\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−3.74592	−	13.9800i	−0.127513	−	0.475883i	0.872404	−	0.488785i	$-0.162560\pi$
$863$	−3.74592	−	13.9800i	−0.127513	−	0.475883i	−0.999917	+	0.0129019i	$0.995893\pi$
$864$		0			0
$865$	15.9101	−	17.6928i	0.540961	−	0.601573i
$866$		0			0
$867$	−0.789730	+	0.789730i	−0.0268206	+	0.0268206i
$868$		0			0
$869$			33.5467i			1.13800i
$870$		0			0
$871$	34.6284	−	19.9927i	1.17334	−	0.677426i
$872$		0			0
$873$	−33.3525	+	8.93676i	−1.12881	+	0.302464i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	38.0410	−	10.1930i	1.28455	−	0.344195i	0.448963	−	0.893550i	$-0.351793\pi$
$877$	38.0410	−	10.1930i	1.28455	−	0.344195i	0.835589	+	0.549356i	$0.185127\pi$
$878$		0			0
$879$	7.53776	−	4.35193i	0.254242	−	0.146787i
$880$		0			0
$881$		−	6.28420i		−	0.211720i	−0.994381	−	0.105860i	$-0.966240\pi$
$881$		−	6.28420i		−	0.211720i	0.994381	−	0.105860i	$-0.0337595\pi$
$882$		0			0
$883$	−11.1314	+	11.1314i	−0.374602	+	0.374602i	−0.869150	−	0.494548i	$-0.835333\pi$
$883$	−11.1314	+	11.1314i	−0.374602	+	0.374602i	0.494548	+	0.869150i	$0.335333\pi$
$884$		0			0
$885$	42.7488	−	47.5386i	1.43699	−	1.59799i
$886$		0			0
$887$	14.6173	+	54.5526i	0.490802	+	1.83170i	0.552376	+	0.833595i	$0.313721\pi$
$887$	14.6173	+	54.5526i	0.490802	+	1.83170i	−0.0615739	+	0.998103i	$0.519612\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	23.0816	−	39.9786i	0.773264	−	1.33933i
$892$		0			0
$893$	−12.1782	−	3.26315i	−0.407529	−	0.109197i
$894$		0			0
$895$	17.2283	−	33.8662i	0.575880	−	1.13202i
$896$		0			0
$897$	32.2584	+	32.2584i	1.07708	+	1.07708i
$898$		0			0
$899$	2.39279	+	4.14443i	0.0798039	+	0.138224i
$900$		0			0
$901$	−19.8415	−	11.4555i	−0.661016	−	0.381638i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−15.6887	−	24.1245i	−0.521509	−	0.801927i
$906$		0			0
$907$	13.2513	−	49.4545i	0.440002	−	1.64211i	−0.288803	−	0.957389i	$-0.593257\pi$
$907$	13.2513	−	49.4545i	0.440002	−	1.64211i	0.728805	−	0.684721i	$-0.240076\pi$
$908$		0			0
$909$	−24.3548			−0.807797
$910$		0			0
$911$	15.1833			0.503046			0.251523	−	0.967851i	$-0.419069\pi$
$911$	15.1833			0.503046			0.251523	+	0.967851i	$0.419069\pi$
$912$		0			0
$913$	9.95359	−	37.1473i	0.329416	−	1.22940i
$914$		0			0
$915$	−8.35102	+	39.4128i	−0.276076	+	1.30295i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−2.22759	−	1.28610i	−0.0734814	−	0.0424245i	0.462809	−	0.886458i	$-0.346842\pi$
$919$	−2.22759	−	1.28610i	−0.0734814	−	0.0424245i	−0.536291	+	0.844033i	$0.680175\pi$
$920$		0			0
$921$	20.1710	+	34.9372i	0.664658	+	1.15122i
$922$		0			0
$923$	−57.2008	−	57.2008i	−1.88279	−	1.88279i
$924$		0			0
$925$	−5.99827	+	38.1886i	−0.197222	+	1.25563i
$926$		0			0
$927$	−27.1426	−	7.27285i	−0.891481	−	0.238872i
$928$		0			0
$929$	−16.9500	+	29.3582i	−0.556111	+	0.963212i	0.441706	+	0.897160i	$0.354374\pi$
$929$	−16.9500	+	29.3582i	−0.556111	+	0.963212i	−0.997816	+	0.0660518i	$0.978960\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−5.19875	−	19.4020i	−0.170199	−	0.635193i
$934$		0			0
$935$	29.4048	+	26.4421i	0.961640	+	0.864748i
$936$		0			0
$937$	10.7525	−	10.7525i	0.351269	−	0.351269i	−0.509313	−	0.860581i	$-0.670100\pi$
$937$	10.7525	−	10.7525i	0.351269	−	0.351269i	0.860581	+	0.509313i	$0.170100\pi$
$938$		0			0
$939$			9.76029i			0.318515i
$940$		0			0
$941$	22.5287	−	13.0070i	0.734415	−	0.424015i	−0.0856201	−	0.996328i	$-0.527287\pi$
$941$	22.5287	−	13.0070i	0.734415	−	0.424015i	0.820035	+	0.572313i	$0.193954\pi$
$942$		0			0
$943$	28.8435	−	7.72860i	0.939275	−	0.251678i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−37.3367	+	10.0043i	−1.21328	+	0.325097i	−0.808048	−	0.589117i	$-0.799476\pi$
$947$	−37.3367	+	10.0043i	−1.21328	+	0.325097i	−0.405231	+	0.914214i	$0.632809\pi$
$948$		0			0
$949$	38.5255	−	22.2427i	1.25059	−	0.722028i
$950$		0			0
$951$		−	70.8426i		−	2.29723i
$952$		0			0
$953$	14.8931	−	14.8931i	0.482435	−	0.482435i	−0.423473	−	0.905909i	$-0.639189\pi$
$953$	14.8931	−	14.8931i	0.482435	−	0.482435i	0.905909	+	0.423473i	$0.139189\pi$
$954$		0			0
$955$	0.0894689	+	1.68647i	0.00289515	+	0.0545729i
$956$		0			0
$957$	−3.54710	−	13.2380i	−0.114662	−	0.427923i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−9.37914	+	16.2452i	−0.302553	+	0.524037i
$962$		0			0
$963$	−9.51015	−	2.54824i	−0.306460	−	0.0821158i
$964$		0			0
$965$	57.9306	−	18.8639i	1.86485	−	0.607250i
$966$		0			0
$967$	−17.1574	−	17.1574i	−0.551744	−	0.551744i	0.375200	−	0.926944i	$-0.377574\pi$
$967$	−17.1574	−	17.1574i	−0.551744	−	0.551744i	−0.926944	+	0.375200i	$0.877574\pi$
$968$		0			0
$969$	−29.3812	−	50.8898i	−0.943861	−	1.63482i
$970$		0			0
$971$	3.66822	+	2.11785i	0.117719	+	0.0679649i	0.557703	−	0.830040i	$-0.311683\pi$
$971$	3.66822	+	2.11785i	0.117719	+	0.0679649i	−0.439985	+	0.898005i	$0.645016\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	7.13896	+	67.0946i	0.228630	+	2.14875i
$976$		0			0
$977$	−6.33228	+	23.6324i	−0.202587	+	0.756067i	0.787584	+	0.616207i	$0.211332\pi$
$977$	−6.33228	+	23.6324i	−0.202587	+	0.756067i	−0.990171	+	0.139859i	$0.955335\pi$
$978$		0			0
$979$	−39.9203			−1.27586
$980$		0			0
$981$	30.4844			0.973292
$982$		0			0
$983$	9.14176	−	34.1175i	0.291577	−	1.08818i	−0.652321	−	0.757943i	$-0.726205\pi$
$983$	9.14176	−	34.1175i	0.291577	−	1.08818i	0.943898	−	0.330237i	$-0.107129\pi$
$984$		0			0
$985$	−15.9517	−	3.37994i	−0.508263	−	0.107694i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−3.67403	−	2.12120i	−0.116827	−	0.0674503i
$990$		0			0
$991$	2.45968	+	4.26030i	0.0781345	+	0.135333i	0.902445	−	0.430805i	$-0.141770\pi$
$991$	2.45968	+	4.26030i	0.0781345	+	0.135333i	−0.824311	+	0.566138i	$0.808437\pi$
$992$		0			0
$993$	31.9532	+	31.9532i	1.01400	+	1.01400i
$994$		0			0
$995$	5.93756	+	3.02054i	0.188233	+	0.0957577i
$996$		0			0
$997$	−27.5398	−	7.37927i	−0.872195	−	0.233704i	−0.205158	−	0.978729i	$-0.565771\pi$
$997$	−27.5398	−	7.37927i	−0.872195	−	0.233704i	−0.667037	+	0.745025i	$0.732438\pi$
$998$		0			0
$999$	−6.21828	+	10.7704i	−0.196738	+	0.340760i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.v.c.117.11		48
5.3	odd	4	inner	980.2.v.c.313.11		48
7.2	even	3		980.2.m.b.97.11	yes	24
7.3	odd	6	inner	980.2.v.c.717.11		48
7.4	even	3	inner	980.2.v.c.717.2		48
7.5	odd	6		980.2.m.b.97.2	✓	24
7.6	odd	2	inner	980.2.v.c.117.2		48
35.3	even	12	inner	980.2.v.c.913.11		48
35.13	even	4	inner	980.2.v.c.313.2		48
35.18	odd	12	inner	980.2.v.c.913.2		48
35.23	odd	12		980.2.m.b.293.2	yes	24
35.33	even	12		980.2.m.b.293.11	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
980.2.m.b.97.2	✓	24	7.5	odd	6
980.2.m.b.97.11	yes	24	7.2	even	3
980.2.m.b.293.2	yes	24	35.23	odd	12
980.2.m.b.293.11	yes	24	35.33	even	12
980.2.v.c.117.2		48	7.6	odd	2	inner
980.2.v.c.117.11		48	1.1	even	1	trivial
980.2.v.c.313.2		48	35.13	even	4	inner
980.2.v.c.313.11		48	5.3	odd	4	inner
980.2.v.c.717.2		48	7.4	even	3	inner
980.2.v.c.717.11		48	7.3	odd	6	inner
980.2.v.c.913.2		48	35.18	odd	12	inner
980.2.v.c.913.11		48	35.3	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:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.v (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.595923 - 2.22401i) q^{3} +(1.87454 - 1.21905i) q^{5} +(-1.99304 - 1.15068i) q^{9} +O(q^{10})\)	\(q+(0.595923 - 2.22401i) q^{3} +(1.87454 - 1.21905i) q^{5} +(-1.99304 - 1.15068i) q^{9} +(2.17591 + 3.76879i) q^{11} +(-4.14432 - 4.14432i) q^{13} +(-1.59411 - 4.89547i) q^{15} +(3.92538 + 1.05180i) q^{17} +(3.14006 - 5.43874i) q^{19} +(-0.874967 - 3.26542i) q^{23} +(2.02782 - 4.57033i) q^{25} +(1.13744 - 1.13744i) q^{27} -1.36777i q^{29} +(-3.03006 + 1.74941i) q^{31} +(9.67851 - 2.59335i) q^{33} +(-7.46792 + 2.00102i) q^{37} +(-11.6867 + 6.74733i) q^{39} +8.83302i q^{41} +(0.887363 - 0.887363i) q^{43} +(-5.13878 + 0.272617i) q^{45} +(-0.519600 - 1.93917i) q^{47} +(4.67845 - 8.10332i) q^{51} +(-5.44564 - 1.45916i) q^{53} +(8.67318 + 4.41220i) q^{55} +(-10.2246 - 10.2246i) q^{57} +(6.20889 + 10.7541i) q^{59} +(-6.77681 - 3.91259i) q^{61} +(-12.8208 - 2.71656i) q^{65} +(-1.76575 + 6.58987i) q^{67} -7.78376 q^{69} +13.8022 q^{71} +(-1.96447 + 7.33150i) q^{73} +(-8.95606 - 7.23347i) q^{75} +(6.67590 + 3.85434i) q^{79} +(-5.30391 - 9.18664i) q^{81} +(-6.24881 - 6.24881i) q^{83} +(8.64051 - 2.81360i) q^{85} +(-3.04194 - 0.815086i) q^{87} +(-4.58662 + 7.94426i) q^{89} +(2.08502 + 7.78142i) q^{93} +(-0.743936 - 14.0231i) q^{95} +(10.6092 - 10.6092i) q^{97} -10.0151i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 16 q^{11} + 48 q^{23} - 32 q^{25} + 32 q^{37} + 32 q^{43} - 48 q^{51} + 24 q^{53} - 64 q^{65} + 32 q^{67} - 8 q^{81} - 128 q^{85} + 96 q^{93} - 64 q^{95}+O(q^{100}) \) 48 * q - 16 * q^11 + 48 * q^23 - 32 * q^25 + 32 * q^37 + 32 * q^43 - 48 * q^51 + 24 * q^53 - 64 * q^65 + 32 * q^67 - 8 * q^81 - 128 * q^85 + 96 * q^93 - 64 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more