LMFDB - Embedded newform 980.2.x.n.667.21

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [980,2,Mod(67,980)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("980.67"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(980, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.x (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [112,4,0,0,0,0,0,-32,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			667.21
Character	$\chi$	$=$	980.667
Dual form			980.2.x.n.263.21

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.02858 - 0.970576i) q^{2} +(-0.517947 + 1.93300i) q^{3} +(0.115964 - 1.99664i) q^{4} +(0.653520 + 2.13844i) q^{5} +(1.34338 + 2.49096i) q^{6} +(-1.81861 - 2.16626i) q^{8} +(-0.870157 - 0.502386i) q^{9} +(2.74771 + 1.56527i) q^{10} +(-4.92166 + 2.84152i) q^{11} +(3.79944 + 1.25831i) q^{12} +(-4.82411 + 4.82411i) q^{13} +(-4.47209 + 0.155660i) q^{15} +(-3.97310 - 0.463075i) q^{16} +(0.979673 - 3.65619i) q^{17} +(-1.38263 + 0.327809i) q^{18} +(0.564422 - 0.977608i) q^{19} +(4.34546 - 1.05686i) q^{20} +(-2.30442 + 7.69959i) q^{22} +(4.70570 - 1.26089i) q^{23} +(5.12932 - 2.39337i) q^{24} +(-4.14582 + 2.79502i) q^{25} +(-0.279829 + 9.64416i) q^{26} +(-2.82336 + 2.82336i) q^{27} -0.781186i q^{29} +(-4.44884 + 4.50062i) q^{30} +(-3.20202 + 1.84869i) q^{31} +(-4.53612 + 3.37989i) q^{32} +(-2.94351 - 10.9853i) q^{33} +(-2.54094 - 4.71154i) q^{34} +(-1.10399 + 1.67913i) q^{36} +(3.32051 - 0.889727i) q^{37} +(-0.368288 - 1.55337i) q^{38} +(-6.82639 - 11.8236i) q^{39} +(3.44390 - 5.30467i) q^{40} -0.451387 q^{41} +(-0.613245 - 0.613245i) q^{43} +(5.10275 + 10.1563i) q^{44} +(0.505655 - 2.18910i) q^{45} +(3.61641 - 5.86417i) q^{46} +(1.10987 + 4.14209i) q^{47} +(2.95298 - 7.44018i) q^{48} +(-1.55154 + 6.89875i) q^{50} +(6.56001 + 3.78742i) q^{51} +(9.07256 + 10.1914i) q^{52} +(-2.03097 - 0.544196i) q^{53} +(-0.163773 + 5.64435i) q^{54} +(-9.29282 - 8.66767i) q^{55} +(1.59738 + 1.59738i) q^{57} +(-0.758200 - 0.803514i) q^{58} +(4.63740 + 8.03221i) q^{59} +(-0.207806 + 8.94719i) q^{60} +(-0.759742 + 1.31591i) q^{61} +(-1.49925 + 5.00933i) q^{62} +(-1.38533 + 7.87914i) q^{64} +(-13.4687 - 7.16340i) q^{65} +(-13.6898 - 8.44243i) q^{66} +(13.1957 + 3.53578i) q^{67} +(-7.18647 - 2.38004i) q^{68} +9.74921i q^{69} +11.8314i q^{71} +(0.494179 + 2.79863i) q^{72} +(1.66308 + 0.445622i) q^{73} +(2.55187 - 4.13796i) q^{74} +(-3.25547 - 9.46156i) q^{75} +(-1.88647 - 1.24031i) q^{76} +(-18.4973 - 5.53607i) q^{78} +(-2.73105 + 4.73031i) q^{79} +(-1.60625 - 8.79886i) q^{80} +(-5.50237 - 9.53039i) q^{81} +(-0.464289 + 0.438106i) q^{82} +(0.968508 + 0.968508i) q^{83} +(8.45877 - 0.294423i) q^{85} +(-1.22597 - 0.0355721i) q^{86} +(1.51003 + 0.404613i) q^{87} +(15.1060 + 5.49396i) q^{88} +(-8.16106 - 4.71179i) q^{89} +(-1.60458 - 2.74244i) q^{90} +(-1.97184 - 9.54179i) q^{92} +(-1.91504 - 7.14703i) q^{93} +(5.16181 + 3.18327i) q^{94} +(2.45942 + 0.568095i) q^{95} +(-4.18387 - 10.5189i) q^{96} +(6.77428 + 6.77428i) q^{97} +5.71016 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 4 q^{2} - 32 q^{8} - 32 q^{16} + 40 q^{22} - 32 q^{25} + 28 q^{30} + 64 q^{32} + 32 q^{36} + 8 q^{37} + 184 q^{46} - 24 q^{50} - 96 q^{53} - 16 q^{57} - 124 q^{58} - 8 q^{60} + 120 q^{65} + 80 q^{72}+ \cdots + 176 q^{93}+O(q^{100}) $ 112 * q + 4 * q^2 - 32 * q^8 - 32 * q^16 + 40 * q^22 - 32 * q^25 + 28 * q^30 + 64 * q^32 + 32 * q^36 + 8 * q^37 + 184 * q^46 - 24 * q^50 - 96 * q^53 - 16 * q^57 - 124 * q^58 - 8 * q^60 + 120 * q^65 + 80 * q^72 - 72 * q^78 + 72 * q^81 + 192 * q^85 - 104 * q^86 - 48 * q^88 - 304 * q^92 + 176 * q^93

Character values

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

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	1.02858	−	0.970576i	0.727318	−	0.686301i
$2$	1.02858	−	0.970576i	0.727318	−	0.686301i
$3$	−0.517947	+	1.93300i	−0.299037	+	1.11602i	0.638922	+	0.769272i	$0.279381\pi$
$3$	−0.517947	+	1.93300i	−0.299037	+	1.11602i	−0.937958	+	0.346748i	$0.887286\pi$
$4$	0.115964	−	1.99664i	0.0579820	−	0.998318i
$5$	0.653520	+	2.13844i	0.292263	+	0.956338i
$5$	0.653520	+	2.13844i	0.292263	+	0.956338i
$6$	1.34338	+	2.49096i	0.548431	+	1.01693i
$7$		0			0
$7$		0			0
$8$	−1.81861	−	2.16626i	−0.642975	−	0.765887i
$9$	−0.870157	−	0.502386i	−0.290052	−	0.167462i
$10$	2.74771	+	1.56527i	0.868904	+	0.494981i
$11$	−4.92166	+	2.84152i	−1.48394	+	0.856751i	−0.999833	−	0.0182593i	$-0.994188\pi$
$11$	−4.92166	+	2.84152i	−1.48394	+	0.856751i	−0.484104	+	0.875011i	$0.660854\pi$
$12$	3.79944	+	1.25831i	1.09680	+	0.363243i
$13$	−4.82411	+	4.82411i	−1.33797	+	1.33797i	−0.439939	+	0.898027i	$0.645000\pi$
$13$	−4.82411	+	4.82411i	−1.33797	+	1.33797i	−0.898027	+	0.439939i	$0.855000\pi$
$14$		0			0
$15$	−4.47209	+	0.155660i	−1.15469	+	0.0401912i
$16$	−3.97310	−	0.463075i	−0.993276	−	0.115769i
$17$	0.979673	−	3.65619i	0.237606	−	0.886756i	−0.739351	−	0.673320i	$-0.764868\pi$
$17$	0.979673	−	3.65619i	0.237606	−	0.886756i	0.976957	−	0.213436i	$-0.0684656\pi$
$18$	−1.38263	+	0.327809i	−0.325889	+	0.0772653i
$19$	0.564422	−	0.977608i	0.129487	−	0.224279i	−0.793991	−	0.607930i	$-0.792000\pi$
$19$	0.564422	−	0.977608i	0.129487	−	0.224279i	0.923478	+	0.383651i	$0.125333\pi$
$20$	4.34546	−	1.05686i	0.971675	−	0.236321i
$21$		0			0
$22$	−2.30442	+	7.69959i	−0.491304	+	1.64156i
$23$	4.70570	−	1.26089i	0.981207	−	0.262914i	0.267654	−	0.963515i	$-0.413752\pi$
$23$	4.70570	−	1.26089i	0.981207	−	0.262914i	0.713553	+	0.700601i	$0.247085\pi$
$24$	5.12932	−	2.39337i	1.04702	−	0.488545i
$25$	−4.14582	+	2.79502i	−0.829165	+	0.559004i
$26$	−0.279829	+	9.64416i	−0.0548790	+	1.89137i
$27$	−2.82336	+	2.82336i	−0.543356	+	0.543356i
$28$		0			0
$29$		−	0.781186i		−	0.145063i	−0.997366	−	0.0725313i	$-0.976892\pi$
$29$		−	0.781186i		−	0.145063i	0.997366	−	0.0725313i	$-0.0231077\pi$
$30$	−4.44884	+	4.50062i	−0.812243	+	0.821696i
$31$	−3.20202	+	1.84869i	−0.575099	+	0.332034i	−0.759183	−	0.650877i	$-0.774401\pi$
$31$	−3.20202	+	1.84869i	−0.575099	+	0.332034i	0.184084	+	0.982911i	$0.441068\pi$
$32$	−4.53612	+	3.37989i	−0.801880	+	0.597486i
$33$	−2.94351	−	10.9853i	−0.512400	−	1.91230i
$34$	−2.54094	−	4.71154i	−0.435767	−	0.808023i
$35$		0			0
$36$	−1.10399	+	1.67913i	−0.183998	+	0.279855i
$37$	3.32051	−	0.889727i	0.545888	−	0.146270i	0.0246729	−	0.999696i	$-0.492146\pi$
$37$	3.32051	−	0.889727i	0.545888	−	0.146270i	0.521215	+	0.853425i	$0.325479\pi$
$38$	−0.368288	−	1.55337i	−0.0597443	−	0.251989i
$39$	−6.82639	−	11.8236i	−1.09310	−	1.89330i
$40$	3.44390	−	5.30467i	0.544529	−	0.838742i
$41$	−0.451387			−0.0704948			−0.0352474	−	0.999379i	$-0.511222\pi$
$41$	−0.451387			−0.0704948			−0.0352474	+	0.999379i	$0.511222\pi$
$42$		0			0
$43$	−0.613245	−	0.613245i	−0.0935189	−	0.0935189i	0.658800	−	0.752319i	$-0.271065\pi$
$43$	−0.613245	−	0.613245i	−0.0935189	−	0.0935189i	−0.752319	+	0.658800i	$0.771065\pi$
$44$	5.10275	+	10.1563i	0.769268	+	1.53112i
$45$	0.505655	−	2.18910i	0.0753785	−	0.326331i
$46$	3.61641	−	5.86417i	0.533211	−	0.864625i
$47$	1.10987	+	4.14209i	0.161891	+	0.604186i	0.998416	+	0.0562577i	$0.0179168\pi$
$47$	1.10987	+	4.14209i	0.161891	+	0.604186i	−0.836525	+	0.547929i	$0.815417\pi$
$48$	2.95298	−	7.44018i	0.426226	−	1.07390i
$49$		0			0
$50$	−1.55154	+	6.89875i	−0.219421	+	0.975630i
$51$	6.56001	+	3.78742i	0.918585	+	0.530345i
$52$	9.07256	+	10.1914i	1.25814	+	1.41329i
$53$	−2.03097	−	0.544196i	−0.278975	−	0.0747511i	0.116619	−	0.993177i	$-0.462794\pi$
$53$	−2.03097	−	0.544196i	−0.278975	−	0.0747511i	−0.395594	+	0.918426i	$0.629461\pi$
$54$	−0.163773	+	5.64435i	−0.0222867	+	0.768099i
$55$	−9.29282	−	8.66767i	−1.25304	−	1.16875i
$56$		0			0
$57$	1.59738	+	1.59738i	0.211578	+	0.211578i
$58$	−0.758200	−	0.803514i	−0.0995566	−	0.105507i
$59$	4.63740	+	8.03221i	0.603738	+	1.04570i	0.992250	+	0.124261i	$0.0396559\pi$
$59$	4.63740	+	8.03221i	0.603738	+	1.04570i	−0.388512	+	0.921444i	$0.627011\pi$
$60$	−0.207806	+	8.94719i	−0.0268276	+	1.15508i
$61$	−0.759742	+	1.31591i	−0.0972751	+	0.168485i	−0.910556	−	0.413386i	$-0.864346\pi$
$61$	−0.759742	+	1.31591i	−0.0972751	+	0.168485i	0.813281	+	0.581871i	$0.197679\pi$
$62$	−1.49925	+	5.00933i	−0.190405	+	0.636185i
$63$		0			0
$64$	−1.38533	+	7.87914i	−0.173166	+	0.984893i
$65$	−13.4687	−	7.16340i	−1.67059	−	0.888510i
$66$	−13.6898	−	8.44243i	−1.68509	−	1.03919i
$67$	13.1957	+	3.53578i	1.61211	+	0.431965i	0.948672	−	0.316263i	$-0.102428\pi$
$67$	13.1957	+	3.53578i	1.61211	+	0.431965i	0.663442	+	0.748228i	$0.269095\pi$
$68$	−7.18647	−	2.38004i	−0.871488	−	0.288622i
$69$			9.74921i			1.17367i
$70$		0			0
$71$			11.8314i			1.40413i	0.712112	+	0.702066i	$0.247739\pi$
$71$			11.8314i			1.40413i	−0.712112	+	0.702066i	$0.752261\pi$
$72$	0.494179	+	2.79863i	0.0582396	+	0.329821i
$73$	1.66308	+	0.445622i	0.194649	+	0.0521561i	0.354827	−	0.934932i	$-0.384540\pi$
$73$	1.66308	+	0.445622i	0.194649	+	0.0521561i	−0.160177	+	0.987088i	$0.551207\pi$
$74$	2.55187	−	4.13796i	0.296649	−	0.481028i
$75$	−3.25547	−	9.46156i	−0.375909	−	1.09253i
$76$	−1.88647	−	1.24031i	−0.216393	−	0.142274i
$77$		0			0
$78$	−18.4973	−	5.53607i	−2.09440	−	0.626837i
$79$	−2.73105	+	4.73031i	−0.307267	+	0.532201i	−0.977763	−	0.209711i	$-0.932748\pi$
$79$	−2.73105	+	4.73031i	−0.307267	+	0.532201i	0.670497	+	0.741912i	$0.266081\pi$
$80$	−1.60625	−	8.79886i	−0.179584	−	0.983743i
$81$	−5.50237	−	9.53039i	−0.611375	−	1.05893i
$82$	−0.464289	+	0.438106i	−0.0512721	+	0.0483807i
$83$	0.968508	+	0.968508i	0.106308	+	0.106308i	0.758260	−	0.651952i	$-0.226050\pi$
$83$	0.968508	+	0.968508i	0.106308	+	0.106308i	−0.651952	+	0.758260i	$0.726050\pi$
$84$		0			0
$85$	8.45877	−	0.294423i	0.917482	−	0.0319347i
$86$	−1.22597	−	0.0355721i	−0.132200	−	0.00383584i
$87$	1.51003	+	0.404613i	0.161893	+	0.0433790i
$88$	15.1060	+	5.49396i	1.61031	+	0.585658i
$89$	−8.16106	−	4.71179i	−0.865071	−	0.499449i	0.000636335	−	1.00000i	$-0.499797\pi$
$89$	−8.16106	−	4.71179i	−0.865071	−	0.499449i	−0.865707	+	0.500551i	$0.833131\pi$
$90$	−1.60458	−	2.74244i	−0.169137	−	0.289079i
$91$		0			0
$92$	−1.97184	−	9.54179i	−0.205579	−	0.994800i
$93$	−1.91504	−	7.14703i	−0.198581	−	0.741113i
$94$	5.16181	+	3.18327i	0.532400	+	0.328329i
$95$	2.45942	+	0.568095i	0.252331	+	0.0582854i
$96$	−4.18387	−	10.5189i	−0.427015	−	1.07358i
$97$	6.77428	+	6.77428i	0.687824	+	0.687824i	0.961751	−	0.273927i	$-0.0883225\pi$
$97$	6.77428	+	6.77428i	0.687824	+	0.687824i	−0.273927	+	0.961751i	$0.588323\pi$
$98$		0			0
$99$	5.71016			0.573893
$100$	5.09987	+	8.60182i	0.509987	+	0.860182i
$101$	6.03052	+	10.4452i	0.600059	+	1.03933i	0.992811	+	0.119689i	$0.0381897\pi$
$101$	6.03052	+	10.4452i	0.600059	+	1.03933i	−0.392752	+	0.919644i	$0.628477\pi$
$102$	10.4235	−	2.47131i	1.03208	−	0.244696i
$103$	10.5989	−	2.83998i	1.04434	−	0.279831i	0.304432	−	0.952534i	$-0.401533\pi$
$103$	10.5989	−	2.83998i	1.04434	−	0.279831i	0.739913	+	0.672703i	$0.234867\pi$
$104$	19.2234	+	1.67709i	1.88501	+	0.164452i
$105$		0			0
$106$	−2.61720	+	1.41146i	−0.254205	+	0.137093i
$107$	−2.55052	−	9.51868i	−0.246568	−	0.920205i	−0.972589	−	0.232532i	$-0.925299\pi$
$107$	−2.55052	−	9.51868i	−0.246568	−	0.920205i	0.726021	−	0.687673i	$-0.241368\pi$
$108$	5.30982	+	5.96463i	0.510937	+	0.573947i
$109$	−4.43091	+	2.55819i	−0.424404	+	0.245030i	−0.696960	−	0.717110i	$-0.745464\pi$
$109$	−4.43091	+	2.55819i	−0.424404	+	0.245030i	0.272556	+	0.962140i	$0.412131\pi$
$110$	−17.9711	+	0.103975i	−1.71347	+	0.00991360i
$111$			6.87938i			0.652962i
$112$		0			0
$113$	1.98553	−	1.98553i	0.186783	−	0.186783i	−0.607521	−	0.794304i	$-0.707836\pi$
$113$	1.98553	−	1.98553i	0.186783	−	0.186783i	0.794304	+	0.607521i	$0.207836\pi$
$114$	3.19342	+	0.0926582i	0.299091	+	0.00867823i
$115$	5.77160	+	9.23883i	0.538205	+	0.861526i
$116$	−1.55974	−	0.0905894i	−0.144818	−	0.00841101i
$117$	6.62129	−	1.77417i	0.612139	−	0.164022i
$118$	12.5658	+	3.76084i	1.15678	+	0.346213i
$119$		0			0
$120$	8.47019	+	9.40462i	0.773219	+	0.858520i
$121$	10.6485	−	18.4437i	0.968046	−	1.67670i
$122$	0.495736	+	2.09091i	0.0448818	+	0.189302i
$123$	0.233795	−	0.872533i	0.0210805	−	0.0786737i
$124$	3.31983	+	6.60764i	0.298130	+	0.593384i
$125$	−8.68635	−	7.03898i	−0.776931	−	0.629586i
$126$		0			0
$127$	12.1710	−	12.1710i	1.08000	−	1.08000i	0.0834907	−	0.996509i	$-0.473393\pi$
$127$	12.1710	−	12.1710i	1.08000	−	1.08000i	0.996509	−	0.0834907i	$-0.0266069\pi$
$128$	6.22238	+	9.44891i	0.549986	+	0.835174i
$129$	1.50303	−	0.867776i	0.132335	−	0.0764034i
$130$	−20.8063	+	5.70425i	−1.82483	+	0.500296i
$131$	−2.79660	−	1.61462i	−0.244340	−	0.141070i	0.372830	−	0.927900i	$-0.378388\pi$
$131$	−2.79660	−	1.61462i	−0.244340	−	0.141070i	−0.617170	+	0.786830i	$0.711721\pi$
$132$	−22.2751	+	4.60322i	−1.93880	+	0.400659i
$133$		0			0
$134$	17.0046	−	9.17061i	1.46898	−	0.792220i
$135$	−7.88270	−	4.19246i	−0.678435	−	0.360829i
$136$	−9.70189	+	4.52695i	−0.831930	+	0.388183i
$137$	−3.89530	+	14.5375i	−0.332798	+	1.24202i	0.573439	+	0.819248i	$0.305609\pi$
$137$	−3.89530	+	14.5375i	−0.332798	+	1.24202i	−0.906237	+	0.422770i	$0.861058\pi$
$138$	9.46235	+	10.0279i	0.805489	+	0.853629i
$139$	−7.49343			−0.635584			−0.317792	−	0.948160i	$-0.602941\pi$
$139$	−7.49343			−0.635584			−0.317792	+	0.948160i	$0.602941\pi$
$140$		0			0
$141$	−8.58153			−0.722696
$142$	11.4833	+	12.1696i	0.963657	+	1.02125i
$143$	10.0348	−	37.4504i	0.839153	−	3.13176i
$144$	3.22458	+	2.39898i	0.268715	+	0.199915i
$145$	1.67052	−	0.510520i	0.138729	−	0.0423964i
$146$	2.14313	−	1.15579i	0.177367	−	0.0956539i
$147$		0			0
$148$	−1.39140	−	6.73302i	−0.114373	−	0.553451i
$149$	3.75467	+	2.16776i	0.307595	+	0.177590i	0.645850	−	0.763465i	$-0.276503\pi$
$149$	3.75467	+	2.16776i	0.307595	+	0.177590i	−0.338255	+	0.941055i	$0.609837\pi$
$150$	−12.5317	−	6.57232i	−1.02321	−	0.536627i
$151$	12.2708	−	7.08455i	0.998584	−	0.576533i	0.0907547	−	0.995873i	$-0.471072\pi$
$151$	12.2708	−	7.08455i	0.998584	−	0.576533i	0.907829	+	0.419341i	$0.137739\pi$
$152$	−3.14421	+	0.555203i	−0.255029	+	0.0450329i
$153$	−2.68929	+	2.68929i	−0.217416	+	0.217416i
$154$		0			0
$155$	−6.04588	−	5.63916i	−0.485617	−	0.452948i
$156$	−24.3991	+	12.2587i	−1.95349	+	0.981481i
$157$	1.29301	−	4.82557i	0.103193	−	0.385123i	−0.894941	−	0.446185i	$-0.852782\pi$
$157$	1.29301	−	4.82557i	0.103193	−	0.385123i	0.998134	+	0.0610625i	$0.0194489\pi$
$158$	1.78202	+	7.51620i	0.141770	+	0.597957i
$159$	2.10387	−	3.64400i	0.166847	−	0.288988i
$160$	−10.1921	−	7.49137i	−0.805758	−	0.592245i
$161$		0			0
$162$	−14.9096	−	4.46232i	−1.17141	−	0.350593i
$163$	15.6091	−	4.18245i	1.22260	−	0.327595i	0.410906	−	0.911678i	$-0.365212\pi$
$163$	15.6091	−	4.18245i	1.22260	−	0.327595i	0.811694	+	0.584083i	$0.198546\pi$
$164$	−0.0523446	+	0.901256i	−0.00408743	+	0.0703763i
$165$	21.5678	−	13.4737i	1.67905	−	1.04892i
$166$	1.93620	+	0.0561796i	0.150278	+	0.00436038i
$167$	5.33030	−	5.33030i	0.412471	−	0.412471i	−0.470127	−	0.882599i	$-0.655792\pi$
$167$	5.33030	−	5.33030i	0.412471	−	0.412471i	0.882599	+	0.470127i	$0.155792\pi$
$168$		0			0
$169$		−	33.5440i		−	2.58031i
$170$	8.41478	−	8.51272i	0.645384	−	0.652896i
$171$	−0.982273	+	0.567115i	−0.0751163	+	0.0433684i
$172$	−1.29554	+	1.15331i	−0.0987840	+	0.0879392i
$173$	−1.13712	−	4.24379i	−0.0864536	−	0.322649i	0.909132	−	0.416508i	$-0.136746\pi$
$173$	−1.13712	−	4.24379i	−0.0864536	−	0.322649i	−0.995585	+	0.0938592i	$0.970080\pi$
$174$	1.94590	−	1.04943i	0.147518	−	0.0795568i
$175$		0			0
$176$	20.8701	−	9.01057i	1.57314	−	0.679197i
$177$	−17.9282	+	4.80385i	−1.34757	+	0.361079i
$178$	−12.9675	+	3.07447i	−0.971953	+	0.230441i
$179$	0.339543	+	0.588106i	0.0253787	+	0.0439571i	0.878436	−	0.477860i	$-0.158588\pi$
$179$	0.339543	+	0.588106i	0.0253787	+	0.0439571i	−0.853057	+	0.521818i	$0.825254\pi$
$180$	−4.31219	−	1.26346i	−0.321411	−	0.0941730i
$181$	−7.86696			−0.584746			−0.292373	−	0.956304i	$-0.594445\pi$
$181$	−7.86696			−0.584746			−0.292373	+	0.956304i	$0.594445\pi$
$182$		0			0
$183$	−2.15016	−	2.15016i	−0.158944	−	0.158944i
$184$	−11.2892	−	7.90069i	−0.832254	−	0.582447i
$185$	4.07264	+	6.51924i	0.299427	+	0.479304i
$186$	−8.90652	−	5.49262i	−0.653058	−	0.402738i
$187$	5.56753	+	20.7783i	0.407138	+	1.51946i
$188$	8.39895	−	1.73567i	0.612557	−	0.126587i
$189$		0			0
$190$	3.08109	−	1.80272i	0.223526	−	0.130783i
$191$	−9.25179	−	5.34152i	−0.669436	−	0.386499i	0.126427	−	0.991976i	$-0.459649\pi$
$191$	−9.25179	−	5.34152i	−0.669436	−	0.386499i	−0.795863	+	0.605477i	$0.792982\pi$
$192$	−14.5129	−	6.75882i	−1.04738	−	0.487776i
$193$	−10.9000	−	2.92066i	−0.784602	−	0.210233i	−0.155789	−	0.987790i	$-0.549792\pi$
$193$	−10.9000	−	2.92066i	−0.784602	−	0.210233i	−0.628813	+	0.777557i	$0.716459\pi$
$194$	13.5429	+	0.392951i	0.972321	+	0.0282123i
$195$	20.8229	−	22.3248i	1.49116	−	1.59871i
$196$		0			0
$197$	3.29596	+	3.29596i	0.234827	+	0.234827i	0.814704	−	0.579877i	$-0.196899\pi$
$197$	3.29596	+	3.29596i	0.234827	+	0.234827i	−0.579877	+	0.814704i	$0.696899\pi$
$198$	5.87337	−	5.54214i	0.417402	−	0.393863i
$199$	−4.78902	−	8.29482i	−0.339484	−	0.588004i	0.644851	−	0.764308i	$-0.276919\pi$
$199$	−4.78902	−	8.29482i	−0.339484	−	0.588004i	−0.984336	+	0.176304i	$0.943586\pi$
$200$	13.5944	+	3.89787i	0.961266	+	0.275621i
$201$	−13.6694	+	23.6760i	−0.964162	+	1.66998i
$202$	16.3407	+	4.89064i	1.14973	+	0.344104i
$203$		0			0
$204$	8.32283	−	12.6587i	0.582714	−	0.886289i
$205$	−0.294991	−	0.965263i	−0.0206030	−	0.0674169i
$206$	8.14547	−	13.2082i	0.567522	−	0.920261i
$207$	−4.72815	−	1.26690i	−0.328629	−	0.0880560i
$208$	21.4006	−	16.9328i	1.48387	−	1.17408i
$209$			6.41528i			0.443754i
$210$		0			0
$211$			19.2356i			1.32424i	0.749400	+	0.662118i	$0.230342\pi$
$211$			19.2356i			1.32424i	−0.749400	+	0.662118i	$0.769658\pi$
$212$	−1.32208	+	3.99200i	−0.0908009	+	0.274171i
$213$	−22.8702	−	6.12805i	−1.56704	−	0.419887i
$214$	−11.8620	−	7.31527i	−0.810871	−	0.500061i
$215$	0.910617	−	1.71215i	0.0621036	−	0.116768i
$216$	11.2507	+	0.981536i	0.765514	+	0.0667850i
$217$		0			0
$218$	−2.07464	+	6.93184i	−0.140512	+	0.469483i
$219$	−1.72278	+	2.98394i	−0.116415	+	0.201636i
$220$	−18.3838	+	17.5492i	−1.23944	+	1.18317i
$221$	12.9118	+	22.3639i	0.868542	+	1.50436i
$222$	6.67696	+	7.07601i	0.448129	+	0.474911i
$223$	−6.67775	−	6.67775i	−0.447175	−	0.447175i	0.447239	−	0.894414i	$-0.352407\pi$
$223$	−6.67775	−	6.67775i	−0.447175	−	0.447175i	−0.894414	+	0.447239i	$0.852407\pi$
$224$		0			0
$225$	5.01170	−	0.349306i	0.334113	−	0.0232871i
$226$	0.115173	−	3.96938i	0.00766120	−	0.264039i
$227$	−26.3809	−	7.06873i	−1.75096	−	0.469168i	−0.766128	−	0.642688i	$-0.777819\pi$
$227$	−26.3809	−	7.06873i	−1.75096	−	0.469168i	−0.984830	+	0.173520i	$0.944486\pi$
$228$	3.37462	−	3.00415i	0.223490	−	0.198954i
$229$	10.9593	+	6.32735i	0.724210	+	0.418123i	0.816300	−	0.577628i	$-0.196021\pi$
$229$	10.9593	+	6.32735i	0.724210	+	0.418123i	−0.0920901	+	0.995751i	$0.529355\pi$
$230$	14.9036	+	3.90112i	0.982712	+	0.257232i
$231$		0			0
$232$	−1.69225	+	1.42067i	−0.111102	+	0.0932716i
$233$	4.48543	+	16.7399i	0.293850	+	1.09666i	0.942126	+	0.335259i	$0.108824\pi$
$233$	4.48543	+	16.7399i	0.293850	+	1.09666i	−0.648276	+	0.761406i	$0.724510\pi$
$234$	5.08858	−	8.25135i	0.332651	−	0.539408i
$235$	−8.13228	+	5.08033i	−0.530492	+	0.331404i
$236$	16.5752	−	8.32774i	1.07895	−	0.542090i
$237$	−7.72917	−	7.72917i	−0.502064	−	0.502064i
$238$		0			0
$239$	21.7639			1.40779			0.703893	−	0.710306i	$-0.251443\pi$
$239$	21.7639			1.40779			0.703893	+	0.710306i	$0.251443\pi$
$240$	17.8402	+	1.45246i	1.15158	+	0.0937561i
$241$	10.4257	+	18.0579i	0.671579	+	1.16321i	0.977456	+	0.211138i	$0.0677171\pi$
$241$	10.4257	+	18.0579i	0.671579	+	1.16321i	−0.305877	+	0.952071i	$0.598950\pi$
$242$	−6.94820	−	29.3061i	−0.446647	−	1.88387i
$243$	9.70186	−	2.59961i	0.622375	−	0.166765i
$244$	2.53929	+	1.66953i	0.162562	+	0.106881i
$245$		0			0
$246$	−0.606383	−	1.12439i	−0.0386616	−	0.0716883i
$247$	1.99325	+	7.43892i	0.126828	+	0.473327i
$248$	9.82794	+	3.57436i	0.624075	+	0.226972i
$249$	−2.37376	+	1.37049i	−0.150431	+	0.0868515i
$250$	−15.7665	+	1.19060i	−0.997161	+	0.0753000i
$251$			14.6586i			0.925243i	0.886556	+	0.462621i	$0.153091\pi$
$251$			14.6586i			0.925243i	−0.886556	+	0.462621i	$0.846909\pi$
$252$		0			0
$253$	−19.5770	+	19.5770i	−1.23080	+	1.23080i
$254$	0.705994	−	24.3317i	0.0442980	−	1.52671i
$255$	−3.81207	+	16.5033i	−0.238721	+	1.03348i
$256$	15.5711	+	3.67969i	0.973195	+	0.229981i
$257$	13.2421	−	3.54821i	0.826019	−	0.221331i	0.179043	−	0.983841i	$-0.442700\pi$
$257$	13.2421	−	3.54821i	0.826019	−	0.221331i	0.646976	+	0.762510i	$0.276033\pi$
$258$	0.703750	−	2.35139i	0.0438136	−	0.146391i
$259$		0			0
$260$	−15.8646	+	26.0614i	−0.983880	+	1.61626i
$261$	−0.392456	+	0.679754i	−0.0242924	+	0.0420757i
$262$	−4.44364	+	1.05355i	−0.274529	+	0.0650883i
$263$	−5.95878	+	22.2385i	−0.367434	+	1.37128i	0.496657	+	0.867947i	$0.334561\pi$
$263$	−5.95878	+	22.2385i	−0.367434	+	1.37128i	−0.864091	+	0.503335i	$0.832106\pi$
$264$	−18.4440	+	26.3544i	−1.13515	+	1.62200i
$265$	−0.163549	−	4.69874i	−0.0100467	−	0.288641i
$266$		0			0
$267$	13.3349	−	13.3349i	0.816083	−	0.816083i
$268$	8.58989	−	25.9370i	0.524711	−	1.58436i
$269$	−26.1655	+	15.1067i	−1.59534	+	0.921070i	−0.602972	+	0.797762i	$0.706017\pi$
$269$	−26.1655	+	15.1067i	−1.59534	+	0.921070i	−0.992368	+	0.123308i	$0.960650\pi$
$270$	−12.1771	+	3.33848i	−0.741075	+	0.203173i
$271$	−9.31890	−	5.38027i	−0.566083	−	0.326828i	0.189501	−	0.981881i	$-0.439313\pi$
$271$	−9.31890	−	5.38027i	−0.566083	−	0.326828i	−0.755583	+	0.655053i	$0.772646\pi$
$272$	−5.58544	+	14.0728i	−0.338667	+	0.853287i
$273$		0			0
$274$	10.1031	+	18.7337i	0.610349	+	1.13174i
$275$	12.4622	−	25.5366i	0.751500	−	1.53992i
$276$	19.4656	+	1.13056i	1.17169	+	0.0680515i
$277$	8.35362	−	31.1761i	0.501920	−	1.87319i	0.0147379	−	0.999891i	$-0.495309\pi$
$277$	8.35362	−	31.1761i	0.501920	−	1.87319i	0.487182	−	0.873300i	$-0.338025\pi$
$278$	−7.70761	+	7.27294i	−0.462272	+	0.436202i
$279$	3.71501			0.222412
$280$		0			0
$281$	1.05159			0.0627325			0.0313663	−	0.999508i	$-0.490014\pi$
$281$	1.05159			0.0627325			0.0313663	+	0.999508i	$0.490014\pi$
$282$	−8.82682	+	8.32903i	−0.525629	+	0.495987i
$283$	−2.78214	+	10.3831i	−0.165381	+	0.617211i	0.832610	+	0.553860i	$0.186846\pi$
$283$	−2.78214	+	10.3831i	−0.165381	+	0.617211i	−0.997991	+	0.0633515i	$0.979821\pi$
$284$	23.6231	+	1.37202i	1.40177	+	0.0814144i
$285$	−2.37198	+	4.45981i	−0.140504	+	0.264177i
$286$	−26.0269	−	48.2604i	−1.53900	−	2.85370i
$287$		0			0
$288$	5.64514	−	0.662156i	0.332643	−	0.0390179i
$289$	2.31446	+	1.33626i	0.136145	+	0.0786033i
$290$	1.22276	−	2.14648i	0.0718032	−	0.126045i
$291$	−16.6034	+	9.58599i	−0.973310	+	0.561941i
$292$	1.08260	−	3.26890i	0.0633545	−	0.191298i
$293$	19.1160	−	19.1160i	1.11677	−	1.11677i	0.124555	−	0.992213i	$-0.460250\pi$
$293$	19.1160	−	19.1160i	1.11677	−	1.11677i	0.992213	−	0.124555i	$-0.0397502\pi$
$294$		0			0
$295$	−14.1457	+	15.1660i	−0.823597	+	0.882998i
$296$	−7.96608	−	5.57500i	−0.463019	−	0.324040i
$297$	5.87299	−	21.9183i	0.340785	−	1.27183i
$298$	5.96597	−	1.41447i	0.345599	−	0.0819383i
$299$	−16.6182	+	28.7835i	−0.961053	+	1.66459i
$300$	−19.2688	+	5.40279i	−1.11249	+	0.311930i
$301$		0			0
$302$	5.74544	−	19.1968i	0.330613	−	1.10465i
$303$	−23.3140	+	6.24698i	−1.33936	+	0.358879i
$304$	−2.69522	+	3.62277i	−0.154581	+	0.207780i
$305$	−3.31050	−	0.764686i	−0.189559	−	0.0437858i
$306$	−0.155996	+	5.37631i	−0.00891768	+	0.307343i
$307$	−0.726484	+	0.726484i	−0.0414626	+	0.0414626i	−0.727534	−	0.686071i	$-0.759334\pi$
$307$	−0.726484	+	0.726484i	−0.0414626	+	0.0414626i	0.686071	+	0.727534i	$0.259334\pi$
$308$		0			0
$309$			21.9587i			1.24919i
$310$	−11.6919	+	0.0676456i	−0.664057	+	0.00384201i
$311$	−11.5281	+	6.65573i	−0.653697	+	0.377412i	−0.789871	−	0.613273i	$-0.789853\pi$
$311$	−11.5281	+	6.65573i	−0.653697	+	0.377412i	0.136174	+	0.990685i	$0.456519\pi$
$312$	−13.1985	+	36.2903i	−0.747219	+	2.05453i
$313$	−5.62834	−	21.0053i	−0.318133	−	1.18729i	−0.921037	−	0.389474i	$-0.872657\pi$
$313$	−5.62834	−	21.0053i	−0.318133	−	1.18729i	0.602905	−	0.797813i	$-0.294010\pi$
$314$	−3.35362	−	6.21847i	−0.189256	−	0.350928i
$315$		0			0
$316$	9.12800	+	6.00145i	0.513490	+	0.337608i
$317$	14.9105	−	3.99527i	0.837460	−	0.224397i	0.185494	−	0.982645i	$-0.440611\pi$
$317$	14.9105	−	3.99527i	0.837460	−	0.224397i	0.651966	+	0.758249i	$0.273945\pi$
$318$	−1.37278	−	5.79012i	−0.0769818	−	0.324694i
$319$	2.21976	+	3.84473i	0.124283	+	0.215264i
$320$	−17.7544	+	2.18674i	−0.992500	+	0.122242i
$321$	19.7207			1.10070
$322$		0			0
$323$	−3.02137	−	3.02137i	−0.168114	−	0.168114i
$324$	−19.6668	+	9.88105i	−1.09260	+	0.548947i
$325$	6.51642	−	33.4834i	0.361466	−	1.85732i
$326$	11.9959	−	19.4518i	0.664390	−	1.07734i
$327$	−2.65001	−	9.88996i	−0.146546	−	0.546916i
$328$	0.820897	+	0.977820i	0.0453264	+	0.0539911i
$329$		0			0
$330$	9.10707	−	34.7920i	0.501328	−	1.91524i
$331$	22.9196	+	13.2326i	1.25977	+	0.727330i	0.973030	−	0.230677i	$-0.0740941\pi$
$331$	22.9196	+	13.2326i	1.25977	+	0.727330i	0.286743	+	0.958008i	$0.407427\pi$
$332$	2.04607	−	1.82144i	0.112293	−	0.0999648i
$333$	−3.33635	−	0.893972i	−0.182831	−	0.0489894i
$334$	0.309191	−	10.6561i	0.0169182	−	0.583077i
$335$	1.06262	+	30.5289i	0.0580570	+	1.66797i
$336$		0			0
$337$	−10.6349	−	10.6349i	−0.579322	−	0.579322i	0.355394	−	0.934717i	$-0.384347\pi$
$337$	−10.6349	−	10.6349i	−0.579322	−	0.579322i	−0.934717	+	0.355394i	$0.884347\pi$
$338$	−32.5570	−	34.5028i	−1.77087	−	1.87671i
$339$	2.80963	+	4.86642i	0.152598	+	0.264308i
$340$	0.393056	−	16.9232i	0.0213164	−	0.917790i
$341$	10.5062	−	18.1972i	0.568941	−	0.985435i
$342$	−0.459920	+	1.53670i	−0.0248696	+	0.0830950i
$343$		0			0
$344$	−0.213193	+	2.44370i	−0.0114946	+	0.131755i
$345$	−20.8481	+	6.37130i	−1.12242	+	0.343019i
$346$	−5.28854	−	3.26142i	−0.284314	−	0.175335i
$347$	−5.05713	−	1.35506i	−0.271481	−	0.0727432i	0.120510	−	0.992712i	$-0.461547\pi$
$347$	−5.05713	−	1.35506i	−0.271481	−	0.0727432i	−0.391991	+	0.919969i	$0.628214\pi$
$348$	0.982973	−	2.96807i	0.0526929	−	0.159105i
$349$		−	27.3545i		−	1.46426i	−0.681168	−	0.732128i	$-0.738527\pi$
$349$		−	27.3545i		−	1.46426i	0.681168	−	0.732128i	$-0.261473\pi$
$350$		0			0
$351$		−	27.2404i		−	1.45399i
$352$	12.7212	−	29.5241i	0.678042	−	1.57364i
$353$	−14.4688	−	3.87689i	−0.770094	−	0.206346i	−0.147681	−	0.989035i	$-0.547181\pi$
$353$	−14.4688	−	3.87689i	−0.770094	−	0.206346i	−0.622413	+	0.782689i	$0.713848\pi$
$354$	−13.7781	+	22.3418i	−0.732300	+	1.18746i
$355$	−25.3008	+	7.73207i	−1.34283	+	0.410376i
$356$	−10.3541	+	15.7483i	−0.548767	+	0.834656i
$357$		0			0
$358$	0.920050	+	0.275363i	0.0486262	+	0.0145534i
$359$	−11.9911	+	20.7692i	−0.632867	+	1.09616i	0.354095	+	0.935209i	$0.384789\pi$
$359$	−11.9911	+	20.7692i	−0.632867	+	1.09616i	−0.986963	+	0.160949i	$0.948545\pi$
$360$	−5.66173	+	2.88573i	−0.298399	+	0.152091i
$361$	8.86285	+	15.3509i	0.466466	+	0.807943i
$362$	−8.09181	+	7.63548i	−0.425296	+	0.401312i
$363$	30.1365	+	30.1365i	1.58175	+	1.58175i
$364$		0			0
$365$	0.133924	+	3.84762i	0.00700989	+	0.201394i
$366$	−4.29851	−	0.124723i	−0.224686	−	0.00651937i
$367$	13.0822	+	3.50537i	0.682887	+	0.182979i	0.583553	−	0.812075i	$-0.301662\pi$
$367$	13.0822	+	3.50537i	0.682887	+	0.182979i	0.0993339	+	0.995054i	$0.468329\pi$
$368$	−19.2801	+	2.83055i	−1.00505	+	0.147553i
$369$	0.392778	+	0.226770i	0.0204472	+	0.0118052i
$370$	10.5165	+	2.75277i	0.546725	+	0.143110i
$371$		0			0
$372$	−14.4921	+	2.99484i	−0.751380	+	0.155275i
$373$	4.76101	+	17.7683i	0.246516	+	0.920010i	0.972615	+	0.232420i	$0.0746645\pi$
$373$	4.76101	+	17.7683i	0.246516	+	0.920010i	−0.726100	+	0.687590i	$0.758669\pi$
$374$	25.8936	+	15.9685i	1.33893	+	0.825711i
$375$	18.1054	−	13.1449i	0.934961	−	0.678802i
$376$	6.95441	−	9.93711i	0.358647	−	0.512467i
$377$	3.76852	+	3.76852i	0.194089	+	0.194089i
$378$		0			0
$379$	−27.8562			−1.43088			−0.715440	−	0.698675i	$-0.753774\pi$
$379$	−27.8562			−1.43088			−0.715440	+	0.698675i	$0.753774\pi$
$380$	1.41948	−	4.84468i	0.0728179	−	0.248527i
$381$	17.2226	+	29.8304i	0.882341	+	1.52826i
$382$	−14.7006	+	3.48537i	−0.752147	+	0.178327i
$383$	12.7702	−	3.42176i	0.652527	−	0.174844i	0.0826556	−	0.996578i	$-0.473660\pi$
$383$	12.7702	−	3.42176i	0.652527	−	0.174844i	0.569871	+	0.821734i	$0.306993\pi$
$384$	−21.4876	+	7.13385i	−1.09654	+	0.364048i
$385$		0			0
$386$	−14.0463	+	7.57518i	−0.714938	+	0.385567i
$387$	0.225534	+	0.841705i	0.0114645	+	0.0427862i
$388$	14.3113	−	12.7402i	0.726548	−	0.646786i
$389$	−14.5751	+	8.41493i	−0.738986	+	0.426654i	−0.821701	−	0.569919i	$-0.806974\pi$
$389$	−14.5751	+	8.41493i	−0.738986	+	0.426654i	0.0827144	+	0.996573i	$0.473641\pi$
$390$	−0.249786	−	43.1731i	−0.0126484	−	2.18616i
$391$		−	18.4402i		−	0.932561i
$392$		0			0
$393$	4.56955	−	4.56955i	0.230503	−	0.230503i
$394$	6.58914	+	0.191186i	0.331956	+	0.00963183i
$395$	−11.9003	−	2.74882i	−0.598767	−	0.138308i
$396$	0.662173	−	11.4011i	0.0332754	−	0.572927i
$397$	−10.0371	+	2.68943i	−0.503748	+	0.134979i	−0.501739	−	0.865019i	$-0.667306\pi$
$397$	−10.0371	+	2.68943i	−0.503748	+	0.134979i	−0.00200883	+	0.999998i	$0.500639\pi$
$398$	−12.9767	−	3.88380i	−0.650461	−	0.194677i
$399$		0			0
$400$	17.7661	−	9.18508i	0.888305	−	0.459254i
$401$	−11.0986	+	19.2234i	−0.554239	+	0.959969i	0.443724	+	0.896164i	$0.353657\pi$
$401$	−11.0986	+	19.2234i	−0.554239	+	0.959969i	−0.997962	+	0.0638058i	$0.979676\pi$
$402$	8.91932	+	37.6199i	0.444855	+	1.87631i
$403$	6.52862	−	24.3651i	0.325214	−	1.21371i
$404$	21.5545	−	10.8295i	1.07238	−	0.538787i
$405$	16.7842	−	17.9948i	0.834015	−	0.894168i
$406$		0			0
$407$	−13.8142	+	13.8142i	−0.684746	+	0.684746i
$408$	−3.72556	−	21.0985i	−0.184443	−	1.04453i
$409$	−7.98006	+	4.60729i	−0.394589	+	0.227816i	−0.684147	−	0.729345i	$-0.739825\pi$
$409$	−7.98006	+	4.60729i	−0.394589	+	0.227816i	0.289558	+	0.957161i	$0.406492\pi$
$410$	−1.24028	−	0.706542i	−0.0612532	−	0.0348936i
$411$	−26.0834	−	15.0593i	−1.28660	−	0.742818i
$412$	−4.44130	−	21.4916i	−0.218807	−	1.05881i
$413$		0			0
$414$	−6.09292	+	3.28592i	−0.299451	+	0.161494i
$415$	−1.43815	+	2.70403i	−0.0705962	+	0.132736i
$416$	5.57776	−	38.1877i	0.273472	−	1.87230i
$417$	3.88120	−	14.4848i	0.190063	−	0.709325i
$418$	6.22652	+	6.59864i	0.304549	+	0.322750i
$419$	−18.5156			−0.904546			−0.452273	−	0.891880i	$-0.649387\pi$
$419$	−18.5156			−0.904546			−0.452273	+	0.891880i	$0.649387\pi$
$420$		0			0
$421$	25.5501			1.24524			0.622619	−	0.782525i	$-0.286069\pi$
$421$	25.5501			1.24524			0.622619	+	0.782525i	$0.286069\pi$
$422$	18.6697	+	19.7854i	0.908824	+	0.963140i
$423$	1.11517	−	4.16186i	0.0542212	−	0.202356i
$424$	2.51467	+	5.38928i	0.122123	+	0.261726i
$425$	6.15758	+	17.8961i	0.298686	+	0.868090i
$426$	−29.4716	+	15.8941i	−1.42790	+	0.770070i
$427$		0			0
$428$	−19.3011	+	3.98864i	−0.932953	+	0.192798i
$429$	67.1943	+	38.7947i	3.24417	+	1.87302i
$430$	−0.725129	−	2.64491i	−0.0349688	−	0.127549i
$431$	−9.02515	+	5.21067i	−0.434726	+	0.250989i	−0.701358	−	0.712809i	$-0.747423\pi$
$431$	−9.02515	+	5.21067i	−0.434726	+	0.250989i	0.266632	+	0.963798i	$0.414089\pi$
$432$	12.5249	−	9.91008i	0.602607	−	0.476799i
$433$	−20.3802	+	20.3802i	−0.979412	+	0.979412i	−0.999792	−	0.0203805i	$-0.993512\pi$
$433$	−20.3802	+	20.3802i	−0.979412	+	0.979412i	0.0203805	+	0.999792i	$0.493512\pi$
$434$		0			0
$435$	0.121599	+	3.49354i	0.00583023	+	0.167502i
$436$	4.59394	+	9.14356i	0.220010	+	0.437897i
$437$	1.42335	−	5.31201i	0.0680880	−	0.254108i
$438$	1.12412	+	4.74131i	0.0537126	+	0.226549i
$439$	10.4182	−	18.0448i	0.497233	−	0.861233i	−0.502762	−	0.864425i	$-0.667683\pi$
$439$	10.4182	−	18.0448i	0.497233	−	0.861233i	0.999995	+	0.00319202i	$0.00101605\pi$
$440$	−1.87640	+	35.8937i	−0.0894537	+	1.71117i
$441$		0			0
$442$	34.9867	+	10.4712i	1.66415	+	0.498066i
$443$	−25.8052	+	6.91448i	−1.22604	+	0.328517i	−0.813037	−	0.582212i	$-0.802187\pi$
$443$	−25.8052	+	6.91448i	−1.22604	+	0.328517i	−0.413004	+	0.910729i	$0.635521\pi$
$444$	13.7356	+	0.797760i	0.651864	+	0.0378600i
$445$	4.74245	−	20.5312i	0.224814	−	0.973270i
$446$	−13.3499	−	0.387352i	−0.632135	−	0.0183416i
$447$	−6.13501	+	6.13501i	−0.290176	+	0.290176i
$448$		0			0
$449$			27.5815i			1.30165i	0.759227	+	0.650826i	$0.225577\pi$
$449$			27.5815i			1.30165i	−0.759227	+	0.650826i	$0.774423\pi$
$450$	4.81592	−	5.22352i	0.227024	−	0.246239i
$451$	2.22158	−	1.28263i	0.104610	−	0.0603966i
$452$	−3.73412	−	4.19462i	−0.175638	−	0.197298i
$453$	7.33884	+	27.3889i	0.344809	+	1.28684i
$454$	−33.9956	+	18.3339i	−1.59549	+	0.860451i
$455$		0			0
$456$	0.555326	−	6.36534i	0.0260055	−	0.298084i
$457$	−1.32882	+	0.356056i	−0.0621596	+	0.0166556i	−0.289765	−	0.957098i	$-0.593577\pi$
$457$	−1.32882	+	0.356056i	−0.0621596	+	0.0166556i	0.227605	+	0.973753i	$0.426910\pi$
$458$	17.4137	−	4.12863i	0.813689	−	0.192918i
$459$	7.55678	+	13.0887i	0.352720	+	0.610929i
$460$	19.1159	−	10.4524i	0.891282	−	0.487346i
$461$	17.6688			0.822918			0.411459	−	0.911428i	$-0.365019\pi$
$461$	17.6688			0.822918			0.411459	+	0.911428i	$0.365019\pi$
$462$		0			0
$463$	−5.55471	−	5.55471i	−0.258149	−	0.258149i	0.566152	−	0.824301i	$-0.308432\pi$
$463$	−5.55471	−	5.55471i	−0.258149	−	0.258149i	−0.824301	+	0.566152i	$0.808432\pi$
$464$	−0.361748	+	3.10373i	−0.0167937	+	0.144087i
$465$	14.0320	−	8.76592i	0.650717	−	0.406510i
$466$	20.8609	+	12.8649i	0.966365	+	0.595954i
$467$	−3.39345	−	12.6645i	−0.157030	−	0.586045i	−0.998923	−	0.0463998i	$-0.985225\pi$
$467$	−3.39345	−	12.6645i	−0.157030	−	0.586045i	0.841893	−	0.539645i	$-0.181441\pi$
$468$	−2.77454	−	13.4261i	−0.128253	−	0.620619i
$469$		0			0
$470$	−3.43388	+	13.1185i	−0.158393	+	0.605113i
$471$	8.65814	+	4.99878i	0.398946	+	0.230332i
$472$	8.96621	−	24.6532i	0.412703	−	1.13476i
$473$	4.76073	+	1.27563i	0.218899	+	0.0586537i
$474$	−15.4518	−	0.448341i	−0.709726	−	0.0205930i
$475$	0.392441	+	5.63057i	0.0180064	+	0.258348i
$476$		0			0
$477$	1.49387	+	1.49387i	0.0683994	+	0.0683994i
$478$	22.3859	−	21.1235i	1.02391	−	0.966165i
$479$	−1.27174	−	2.20272i	−0.0581072	−	0.100645i	0.835509	−	0.549477i	$-0.185173\pi$
$479$	−1.27174	−	2.20272i	−0.0581072	−	0.100645i	−0.893616	+	0.448833i	$0.851840\pi$
$480$	19.7598	−	15.8213i	0.901908	−	0.722139i
$481$	−11.7263	+	20.3106i	−0.534675	+	0.926085i
$482$	28.2502	+	8.45506i	1.28676	+	0.385117i
$483$		0			0
$484$	−35.5906	−	23.4000i	−1.61775	−	1.06364i
$485$	−10.0592	+	18.9135i	−0.456767	+	0.858818i
$486$	7.45605	−	12.0903i	0.338213	−	0.548427i
$487$	3.55528	+	0.952635i	0.161105	+	0.0431680i	0.338470	−	0.940977i	$-0.390091\pi$
$487$	3.55528	+	0.952635i	0.161105	+	0.0431680i	−0.177365	+	0.984145i	$0.556757\pi$
$488$	4.23228	−	0.747333i	0.191586	−	0.0338302i
$489$			32.3388i			1.46241i
$490$		0			0
$491$		−	22.3410i		−	1.00823i	−0.863635	−	0.504117i	$-0.831818\pi$
$491$		−	22.3410i		−	1.00823i	0.863635	−	0.504117i	$-0.168182\pi$
$492$	−1.71502	−	0.567985i	−0.0773190	−	0.0256067i
$493$	−2.85616	−	0.765307i	−0.128635	−	0.0344677i
$494$	9.27027	+	5.71694i	0.417089	+	0.257217i
$495$	3.73170	+	12.2108i	0.167728	+	0.548835i
$496$	13.5780	−	5.86225i	0.609672	−	0.263223i
$497$		0			0
$498$	−1.11144	+	3.71358i	−0.0498050	+	0.166410i
$499$	−4.97828	+	8.62263i	−0.222858	+	0.386002i	−0.955675	−	0.294424i	$-0.904872\pi$
$499$	−4.97828	+	8.62263i	−0.222858	+	0.386002i	0.732816	+	0.680426i	$0.238205\pi$
$500$	−15.0616	+	16.5272i	−0.673574	+	0.739120i
$501$	7.54268	+	13.0643i	0.336982	+	0.583670i
$502$	14.2273	+	15.0776i	0.634995	+	0.672945i
$503$	−8.22634	−	8.22634i	−0.366794	−	0.366794i	0.499512	−	0.866307i	$-0.333513\pi$
$503$	−8.22634	−	8.22634i	−0.366794	−	0.366794i	−0.866307	+	0.499512i	$0.833513\pi$
$504$		0			0
$505$	−18.3953	+	19.7220i	−0.818579	+	0.877618i
$506$	−1.13559	+	39.1376i	−0.0504832	+	1.73988i
$507$	64.8407	+	17.3740i	2.87968	+	0.771608i
$508$	−22.8896	−	25.7124i	−1.01556	−	1.14080i
$509$	28.4455	+	16.4230i	1.26083	+	0.727938i	0.973234	−	0.229815i	$-0.0738122\pi$
$509$	28.4455	+	16.4230i	1.26083	+	0.727938i	0.287591	+	0.957753i	$0.407146\pi$
$510$	12.0967	+	20.6749i	0.535651	+	0.915501i
$511$		0			0
$512$	19.5876	−	11.3281i	0.865658	−	0.500636i
$513$	1.16657	+	4.35371i	0.0515055	+	0.192221i
$514$	10.1768	−	16.5021i	0.448879	−	0.727876i
$515$	12.9997	+	20.8092i	0.572837	+	0.916962i
$516$	−1.55833	−	3.10164i	−0.0686019	−	0.136542i
$517$	−17.2323	−	17.2323i	−0.757874	−	0.757874i
$518$		0			0
$519$	8.79222			0.385936
$520$	8.97653	+	42.2041i	0.393647	+	1.85077i
$521$	−0.899013	−	1.55714i	−0.0393865	−	0.0682194i	0.845660	−	0.533722i	$-0.179207\pi$
$521$	−0.899013	−	1.55714i	−0.0393865	−	0.0682194i	−0.885047	+	0.465502i	$0.845874\pi$
$522$	0.256080	+	1.08009i	0.0112083	+	0.0472743i
$523$	24.7912	−	6.64278i	1.08404	−	0.290468i	0.327792	−	0.944750i	$-0.393696\pi$
$523$	24.7912	−	6.64278i	1.08404	−	0.290468i	0.756251	+	0.654282i	$0.227029\pi$
$524$	−3.54811	+	5.39655i	−0.155000	+	0.235750i
$525$		0			0
$526$	15.4550	+	28.6575i	0.673871	+	1.24953i
$527$	3.62222	+	13.5183i	0.157786	+	0.588866i
$528$	6.60785	+	45.0090i	0.287570	+	1.95877i
$529$	0.635213	−	0.366740i	0.0276179	−	0.0159452i
$530$	−4.72871	−	4.67431i	−0.205402	−	0.203039i
$531$		−	9.31904i		−	0.404412i
$532$		0			0
$533$	2.17754	−	2.17754i	0.0943198	−	0.0943198i
$534$	0.773509	−	26.6586i	0.0334730	−	1.15363i
$535$	18.6883	−	11.6748i	0.807964	−	0.504744i
$536$	−16.3384	−	35.0155i	−0.705713	−	1.51244i
$537$	−1.31268	+	0.351731i	−0.0566462	+	0.0151783i
$538$	−12.2512	+	40.9341i	−0.528188	+	1.76479i
$539$		0			0
$540$	−9.28492	+	15.2527i	−0.399559	+	0.656372i
$541$	12.6660	−	21.9381i	0.544552	−	0.943192i	−0.454083	−	0.890959i	$-0.650033\pi$
$541$	12.6660	−	21.9381i	0.544552	−	0.943192i	0.998635	−	0.0522324i	$-0.0166336\pi$
$542$	−14.8072	+	3.51065i	−0.636024	+	0.150795i
$543$	4.07466	−	15.2069i	0.174861	−	0.652589i
$544$	7.91361	+	19.8961i	0.339293	+	0.853038i
$545$	−8.36620	−	7.80339i	−0.358369	−	0.334261i
$546$		0			0
$547$	−17.3594	+	17.3594i	−0.742233	+	0.742233i	−0.973007	−	0.230774i	$-0.925874\pi$
$547$	−17.3594	+	17.3594i	−0.742233	+	0.742233i	0.230774	+	0.973007i	$0.425874\pi$
$548$	28.5743	+	9.46331i	1.22063	+	0.404253i
$549$	1.32219	−	0.763367i	0.0564297	−	0.0325797i
$550$	−11.9668	−	38.3620i	−0.510266	−	1.63576i
$551$	−0.763694	−	0.440919i	−0.0325344	−	0.0187838i
$552$	21.1193	−	17.7300i	0.898897	−	0.754639i
$553$		0			0
$554$	−21.6664	−	40.1750i	−0.920518	−	1.70687i
$555$	−14.7111	+	4.49581i	−0.624452	+	0.190837i
$556$	−0.868968	+	14.9616i	−0.0368524	+	0.634515i
$557$	−7.28440	+	27.1858i	−0.308650	+	1.15190i	0.621108	+	0.783725i	$0.286683\pi$
$557$	−7.28440	+	27.1858i	−0.308650	+	1.15190i	−0.929758	+	0.368172i	$0.879984\pi$
$558$	3.82120	−	3.60570i	0.161764	−	0.152642i
$559$	5.91672			0.250250
$560$		0			0
$561$	−43.0482			−1.81750
$562$	1.08165	−	1.02065i	0.0456265	−	0.0430534i
$563$	−6.32985	+	23.6233i	−0.266772	+	0.995605i	0.694386	+	0.719603i	$0.255676\pi$
$563$	−6.32985	+	23.6233i	−0.266772	+	0.995605i	−0.961157	+	0.276002i	$0.910990\pi$
$564$	−0.995148	+	17.1342i	−0.0419033	+	0.721480i
$565$	5.54350	+	2.94834i	0.233217	+	0.124038i
$566$	7.21592	+	13.3802i	0.303308	+	0.562410i
$567$		0			0
$568$	25.6299	−	21.5167i	1.07541	−	0.902822i
$569$	−34.9968	−	20.2054i	−1.46714	−	0.847055i	−0.467818	−	0.883825i	$-0.654960\pi$
$569$	−34.9968	−	20.2054i	−1.46714	−	0.847055i	−0.999324	+	0.0367696i	$0.988293\pi$
$570$	1.88882	+	6.88947i	0.0791138	+	0.288568i
$571$	−13.5653	+	7.83192i	−0.567690	+	0.327756i	−0.756226	−	0.654310i	$-0.772959\pi$
$571$	−13.5653	+	7.83192i	−0.567690	+	0.327756i	0.188536	+	0.982066i	$0.439626\pi$
$572$	−73.6112	−	24.3788i	−3.07784	−	1.01933i
$573$	15.1171	−	15.1171i	0.631526	−	0.631526i
$574$		0			0
$575$	−15.9848	+	18.3800i	−0.666612	+	0.766498i
$576$	5.16382	−	6.16012i	0.215159	−	0.256672i
$577$	2.94861	−	11.0044i	0.122752	−	0.458118i	−0.876997	−	0.480495i	$-0.840457\pi$
$577$	2.94861	−	11.0044i	0.122752	−	0.458118i	0.999750	+	0.0223775i	$0.00712358\pi$
$578$	3.67756	−	0.871914i	0.152966	−	0.0362668i
$579$	11.2913	−	19.5571i	0.469250	−	0.812764i
$580$	−0.825603	−	3.39461i	−0.0342813	−	0.140954i
$581$		0			0
$582$	−7.77406	+	25.9749i	−0.322245	+	1.07669i
$583$	11.5421	−	3.09269i	0.478024	−	0.128086i
$584$	−2.05917	−	4.41308i	−0.0852089	−	0.182614i
$585$	8.12110	+	12.9998i	0.335766	+	0.537474i
$586$	1.10885	−	38.2159i	0.0458061	−	1.57868i
$587$	10.0769	−	10.0769i	0.415916	−	0.415916i	−0.467877	−	0.883794i	$-0.654981\pi$
$587$	10.0769	−	10.0769i	0.415916	−	0.415916i	0.883794	+	0.467877i	$0.154981\pi$
$588$		0			0
$589$			4.17376i			0.171977i
$590$	0.169688	+	29.3290i	0.00698594	+	1.20746i
$591$	−8.07822	+	4.66396i	−0.332294	+	0.191850i
$592$	−13.6047	+	1.99733i	−0.559151	+	0.0820899i
$593$	−2.87691	−	10.7368i	−0.118141	−	0.440907i	0.881362	−	0.472442i	$-0.156627\pi$
$593$	−2.87691	−	10.7368i	−0.118141	−	0.440907i	−0.999503	+	0.0315347i	$0.989961\pi$
$594$	−15.2325	−	28.2449i	−0.624997	−	1.15890i
$595$		0			0
$596$	4.76363	−	7.24533i	0.195126	−	0.296780i
$597$	18.5144	−	4.96091i	0.757743	−	0.203037i
$598$	10.8434	+	45.7354i	0.443421	+	1.87026i
$599$	−5.65333	−	9.79185i	−0.230989	−	0.400084i	0.727111	−	0.686520i	$-0.240863\pi$
$599$	−5.65333	−	9.79185i	−0.230989	−	0.400084i	−0.958099	+	0.286436i	$0.907529\pi$
$600$	−14.5757	+	24.2591i	−0.595052	+	0.990372i
$601$	37.1086			1.51369			0.756846	−	0.653593i	$-0.226739\pi$
$601$	37.1086			1.51369			0.756846	+	0.653593i	$0.226739\pi$
$602$		0			0
$603$	−9.70602	−	9.70602i	−0.395260	−	0.395260i
$604$	−12.7223	−	25.3219i	−0.517663	−	1.03033i
$605$	46.3998	+	10.7178i	1.88642	+	0.435740i
$606$	−17.9172	+	29.0536i	−0.727838	+	1.18022i
$607$	7.66535	+	28.6075i	0.311127	+	1.16114i	0.927541	+	0.373720i	$0.121918\pi$
$607$	7.66535	+	28.6075i	0.311127	+	1.16114i	−0.616414	+	0.787422i	$0.711415\pi$
$608$	0.743923	+	6.34223i	0.0301700	+	0.257211i
$609$		0			0
$610$	−4.14731	+	2.42655i	−0.167920	+	0.0982482i
$611$	−25.3360	−	14.6278i	−1.02499	−	0.591776i
$612$	5.05766	+	5.68138i	0.204444	+	0.229656i
$613$	4.51998	+	1.21113i	0.182560	+	0.0489169i	0.348941	−	0.937145i	$-0.386541\pi$
$613$	4.51998	+	1.21113i	0.182560	+	0.0489169i	−0.166381	+	0.986062i	$0.553208\pi$
$614$	−0.0421407	+	1.45236i	−0.00170066	+	0.0586123i
$615$	2.01865	−	0.0702628i	0.0813997	−	0.00283327i
$616$		0			0
$617$	7.18275	+	7.18275i	0.289167	+	0.289167i	0.836751	−	0.547584i	$-0.184452\pi$
$617$	7.18275	+	7.18275i	0.289167	+	0.289167i	−0.547584	+	0.836751i	$0.684452\pi$
$618$	21.3126	+	22.5864i	0.857320	+	0.908557i
$619$	−16.0406	−	27.7831i	−0.644725	−	1.11670i	−0.984365	−	0.176141i	$-0.943639\pi$
$619$	−16.0406	−	27.7831i	−0.644725	−	1.11670i	0.339640	−	0.940556i	$-0.389695\pi$
$620$	−11.9605	+	11.4175i	−0.480343	+	0.458537i
$621$	−9.72596	+	16.8459i	−0.390289	+	0.676001i
$622$	−5.39767	+	18.0348i	−0.216427	+	0.723131i
$623$		0			0
$624$	21.6467	+	50.1377i	0.866562	+	2.00712i
$625$	9.37571	−	23.1753i	0.375028	−	0.927013i
$626$	−26.1764	−	16.1429i	−1.04622	−	0.645200i
$627$	−12.4008	−	3.32277i	−0.495238	−	0.132699i
$628$	−9.48497	−	3.14126i	−0.378492	−	0.125350i
$629$		−	13.0120i		−	0.518824i
$630$		0			0
$631$		−	18.7069i		−	0.744710i	−0.928090	−	0.372355i	$-0.878550\pi$
$631$		−	18.7069i		−	0.744710i	0.928090	−	0.372355i	$-0.121450\pi$
$632$	15.2138	−	2.68644i	0.605171	−	0.106861i
$633$	−37.1826	−	9.96304i	−1.47787	−	0.395995i
$634$	11.4590	−	18.5813i	0.455096	−	0.737957i
$635$	33.9808	+	18.0729i	1.34849	+	0.717201i
$636$	−7.03177	−	4.62323i	−0.278828	−	0.183323i
$637$		0			0
$638$	6.01481	+	1.80018i	0.238129	+	0.0712698i
$639$	5.94394	−	10.2952i	0.235139	−	0.407272i
$640$	−16.1395	+	19.4812i	−0.637968	+	0.770063i
$641$	14.8043	+	25.6419i	0.584736	+	1.01279i	0.994908	+	0.100785i	$0.0321353\pi$
$641$	14.8043	+	25.6419i	0.584736	+	1.01279i	−0.410172	+	0.912008i	$0.634531\pi$
$642$	20.2843	−	19.1404i	0.800559	−	0.755412i
$643$	−15.8819	−	15.8819i	−0.626323	−	0.626323i	0.320818	−	0.947141i	$-0.396042\pi$
$643$	−15.8819	−	15.8819i	−0.626323	−	0.626323i	−0.947141	+	0.320818i	$0.896042\pi$
$644$		0			0
$645$	2.83795	+	2.64703i	0.111744	+	0.104227i
$646$	−6.04020	−	0.175259i	−0.237649	−	0.00689547i
$647$	24.1531	+	6.47181i	0.949557	+	0.254433i	0.700174	−	0.713972i	$-0.253106\pi$
$647$	24.1531	+	6.47181i	0.949557	+	0.254433i	0.249383	+	0.968405i	$0.419772\pi$
$648$	−10.6386	+	29.2516i	−0.417924	+	1.14911i
$649$	−45.6474	−	26.3545i	−1.79182	−	1.03451i
$650$	−25.7955	−	40.7651i	−1.01178	−	1.59894i
$651$		0			0
$652$	−6.54073	−	31.6507i	−0.256155	−	1.23954i
$653$	10.7091	+	39.9668i	0.419079	+	1.56402i	0.776523	+	0.630088i	$0.216981\pi$
$653$	10.7091	+	39.9668i	0.419079	+	1.56402i	−0.357445	+	0.933934i	$0.616352\pi$
$654$	−12.3247	−	7.60061i	−0.481934	−	0.297207i
$655$	1.62512	−	7.03554i	0.0634989	−	0.274901i
$656$	1.79341	+	0.209026i	0.0700209	+	0.00816111i
$657$	−1.22327	−	1.22327i	−0.0477243	−	0.0477243i
$658$		0			0
$659$	−32.9086			−1.28194			−0.640968	−	0.767568i	$-0.721467\pi$
$659$	−32.9086			−1.28194			−0.640968	+	0.767568i	$0.721467\pi$
$660$	−24.4009	−	44.6255i	−0.949804	−	1.73705i
$661$	−8.98502	−	15.5625i	−0.349477	−	0.605311i	0.636680	−	0.771128i	$-0.280307\pi$
$661$	−8.98502	−	15.5625i	−0.349477	−	0.605311i	−0.986157	+	0.165817i	$0.946974\pi$
$662$	36.4179	−	8.63434i	1.41542	−	0.335583i
$663$	−49.9171	+	13.3753i	−1.93862	+	0.519452i
$664$	0.336700	−	3.85937i	0.0130665	−	0.149773i
$665$		0			0
$666$	−4.29938	+	2.31866i	−0.166598	+	0.0898461i
$667$	−0.984989	−	3.67603i	−0.0381389	−	0.142336i
$668$	−10.0245	−	11.2608i	−0.387861	−	0.435693i
$669$	16.3668	−	9.44939i	0.632778	−	0.365335i
$670$	30.7236	+	30.3702i	1.18696	+	1.17330i
$671$		−	8.63530i		−	0.333362i
$672$		0			0
$673$	6.28219	−	6.28219i	0.242161	−	0.242161i	−0.575583	−	0.817744i	$-0.695225\pi$
$673$	6.28219	−	6.28219i	0.242161	−	0.242161i	0.817744	+	0.575583i	$0.195225\pi$
$674$	−21.2609	−	0.616894i	−0.818941	−	0.0237619i
$675$	3.81380	−	19.5965i	0.146793	−	0.754270i
$676$	−66.9752	−	3.88990i	−2.57597	−	0.149611i
$677$	26.2432	−	7.03183i	1.00861	−	0.270255i	0.283560	−	0.958955i	$-0.408485\pi$
$677$	26.2432	−	7.03183i	1.00861	−	0.270255i	0.725047	+	0.688699i	$0.241818\pi$
$678$	7.61317	+	2.27856i	0.292382	+	0.0875075i
$679$		0			0
$680$	−16.0210	−	17.7884i	−0.614377	−	0.682155i
$681$	27.3278	−	47.3331i	1.04720	−	1.81381i
$682$	−6.85532	−	28.9144i	−0.262504	−	1.10719i
$683$	5.82534	−	21.7405i	0.222900	−	0.831876i	−0.760334	−	0.649532i	$-0.774965\pi$
$683$	5.82534	−	21.7405i	0.222900	−	0.831876i	0.983235	−	0.182344i	$-0.0583684\pi$
$684$	1.01841	+	2.02701i	0.0389400	+	0.0775045i
$685$	−33.6331	+	1.17066i	−1.28505	+	0.0447287i
$686$		0			0
$687$	−17.9071	+	17.9071i	−0.683199	+	0.683199i
$688$	2.15251	+	2.72046i	0.0820636	+	0.103717i
$689$	12.4229	−	7.17235i	0.473274	−	0.273245i
$690$	−15.2601	+	26.7881i	−0.580943	+	1.01980i
$691$	−9.95579	−	5.74798i	−0.378736	−	0.218663i	0.298532	−	0.954400i	$-0.403503\pi$
$691$	−9.95579	−	5.74798i	−0.378736	−	0.218663i	−0.677268	+	0.735736i	$0.736836\pi$
$692$	−8.60516	+	1.77829i	−0.327119	+	0.0676003i
$693$		0			0
$694$	−6.51686	+	3.51455i	−0.247377	+	0.133410i
$695$	−4.89710	−	16.0242i	−0.185758	−	0.607834i
$696$	−1.86967	−	4.00695i	−0.0708695	−	0.151883i
$697$	−0.442212	+	1.65036i	−0.0167500	+	0.0625118i
$698$	−26.5497	−	28.1364i	−1.00492	−	1.06498i
$699$	−34.6814			−1.31177
$700$		0			0
$701$	−2.54230			−0.0960214			−0.0480107	−	0.998847i	$-0.515288\pi$
$701$	−2.54230			−0.0960214			−0.0480107	+	0.998847i	$0.515288\pi$
$702$	−26.4389	−	28.0190i	−0.997872	−	1.05751i
$703$	1.00436	−	3.74834i	0.0378803	−	0.141371i
$704$	−15.5706	−	42.7149i	−0.586840	−	1.60988i
$705$	−5.60820	−	18.3511i	−0.211217	−	0.691141i
$706$	−18.6451	+	10.0553i	−0.701719	+	0.378437i
$707$		0			0
$708$	7.51251	+	36.3532i	0.282337	+	1.36624i
$709$	8.79409	+	5.07727i	0.330269	+	0.190681i	0.655960	−	0.754795i	$-0.272264\pi$
$709$	8.79409	+	5.07727i	0.330269	+	0.190681i	−0.325692	+	0.945476i	$0.605597\pi$
$710$	−18.5194	+	32.5094i	−0.695019	+	1.22006i
$711$	4.75288	−	2.74408i	0.178247	−	0.102911i
$712$	4.63483	+	26.2478i	0.173697	+	0.983680i
$713$	−12.7368	+	12.7368i	−0.476995	+	0.476995i
$714$		0			0
$715$	86.6434	−	3.01579i	3.24028	−	0.112784i
$716$	1.21361	−	0.609745i	0.0453547	−	0.0227872i
$717$	−11.2725	+	42.0696i	−0.420980	+	1.57112i
$718$	7.82426	+	33.0012i	0.291999	+	1.23159i
$719$	−18.7042	+	32.3967i	−0.697550	+	1.20819i	0.271763	+	0.962364i	$0.412393\pi$
$719$	−18.7042	+	32.3967i	−0.697550	+	1.20819i	−0.969313	+	0.245828i	$0.920940\pi$
$720$	−3.02273	+	8.46335i	−0.112651	+	0.315410i
$721$		0			0
$722$	24.0154	+	7.18761i	0.893761	+	0.267495i
$723$	−40.3059	+	10.7999i	−1.49899	+	0.401654i
$724$	−0.912283	+	15.7074i	−0.0339047	+	0.583762i
$725$	2.18343	+	3.23866i	0.0810906	+	0.120281i
$726$	60.2476	+	1.74811i	2.23600	+	0.0648783i
$727$	8.42845	−	8.42845i	0.312594	−	0.312594i	−0.533320	−	0.845914i	$-0.679056\pi$
$727$	8.42845	−	8.42845i	0.312594	−	0.312594i	0.845914	+	0.533320i	$0.179056\pi$
$728$		0			0
$729$		−	12.9141i		−	0.478298i
$730$	3.87216	+	3.82761i	0.143315	+	0.141666i
$731$	−2.84292	+	1.64136i	−0.105149	+	0.0607079i
$732$	−4.54242	+	4.04374i	−0.167893	+	0.149461i
$733$	1.93333	+	7.21528i	0.0714092	+	0.266503i	0.992395	−	0.123093i	$-0.0392814\pi$
$733$	1.93333	+	7.21528i	0.0714092	+	0.266503i	−0.920986	+	0.389596i	$0.872615\pi$
$734$	16.8584	−	9.09173i	0.622254	−	0.335582i
$735$		0			0
$736$	−17.0839	+	21.6243i	−0.629723	+	0.797082i
$737$	−74.9919	+	20.0940i	−2.76236	+	0.740172i
$738$	0.624102	−	0.147969i	0.0229735	−	0.00544681i
$739$	1.19432	+	2.06863i	0.0439339	+	0.0760957i	0.887156	−	0.461469i	$-0.152678\pi$
$739$	1.19432	+	2.06863i	0.0439339	+	0.0760957i	−0.843222	+	0.537565i	$0.819344\pi$
$740$	13.4888	−	7.37558i	0.495859	−	0.271132i
$741$	−15.4119			−0.566169
$742$		0			0
$743$	14.6605	+	14.6605i	0.537841	+	0.537841i	0.922894	−	0.385053i	$-0.125817\pi$
$743$	14.6605	+	14.6605i	0.537841	+	0.537841i	−0.385053	+	0.922894i	$0.625817\pi$
$744$	−11.9996	+	17.1461i	−0.439926	+	0.628607i
$745$	−2.18187	+	9.44580i	−0.0799374	+	0.346067i
$746$	22.1426	+	13.6553i	0.810699	+	0.499955i
$747$	−0.356190	−	1.32932i	−0.0130323	−	0.0486372i
$748$	42.1323	−	8.70679i	1.54051	−	0.318352i
$749$		0			0
$750$	5.86478	−	31.0934i	0.214151	−	1.13537i
$751$	−0.704630	−	0.406818i	−0.0257123	−	0.0148450i	0.487089	−	0.873352i	$-0.338059\pi$
$751$	−0.704630	−	0.406818i	−0.0257123	−	0.0148450i	−0.512801	+	0.858507i	$0.671392\pi$
$752$	−2.49153	−	16.9709i	−0.0908568	−	0.618866i
$753$	−28.3351	−	7.59237i	−1.03259	−	0.276681i
$754$	7.53388	+	0.218598i	0.274368	+	0.00796088i
$755$	23.1691	+	21.6104i	0.843209	+	0.786484i
$756$		0			0
$757$	11.0046	+	11.0046i	0.399968	+	0.399968i	0.878222	−	0.478254i	$-0.158730\pi$
$757$	11.0046	+	11.0046i	0.399968	+	0.399968i	−0.478254	+	0.878222i	$0.658730\pi$
$758$	−28.6524	+	27.0366i	−1.04070	+	0.982014i
$759$	−27.7026	−	47.9823i	−1.00554	−	1.74165i
$760$	−3.24207	−	6.36087i	−0.117602	−	0.230733i
$761$	−1.15696	+	2.00391i	−0.0419397	+	0.0726418i	−0.886233	−	0.463239i	$-0.846687\pi$
$761$	−1.15696	+	2.00391i	−0.0419397	+	0.0726418i	0.844294	+	0.535881i	$0.180020\pi$
$762$	46.6676	+	13.9672i	1.69059	+	0.505979i
$763$		0			0
$764$	−11.7379	+	17.8530i	−0.424664	+	0.645900i
$765$	−7.50837	−	3.99337i	−0.271466	−	0.144381i
$766$	9.81412	−	15.9140i	0.354598	−	0.574997i
$767$	−61.1195	−	16.3769i	−2.20690	−	0.591337i
$768$	−15.1779	+	28.1931i	−0.547684	+	1.01733i
$769$			18.4165i			0.664117i	0.943259	+	0.332059i	$0.107743\pi$
$769$			18.4165i			0.664117i	−0.943259	+	0.332059i	$0.892257\pi$
$770$		0			0
$771$			27.4348i			0.988040i
$772$	−7.09550	+	21.4247i	−0.255373	+	0.771092i
$773$	16.8978	+	4.52774i	0.607770	+	0.162852i	0.549562	−	0.835453i	$-0.314795\pi$
$773$	16.8978	+	4.52774i	0.607770	+	0.162852i	0.0582081	+	0.998304i	$0.481461\pi$
$774$	1.04892	+	0.646865i	0.0377026	+	0.0232511i
$775$	8.10789	−	16.6140i	0.291244	−	0.596794i
$776$	2.35506	−	26.9946i	0.0845419	−	0.969049i
$777$		0			0
$778$	−6.82435	+	22.8017i	−0.244665	+	0.817480i
$779$	−0.254773	+	0.441280i	−0.00912819	+	0.0158105i
$780$	−42.1597	−	44.1647i	−1.50956	−	1.58135i
$781$	−33.6193	−	58.2303i	−1.20299	−	2.08364i
$782$	−17.8976	−	18.9673i	−0.640018	−	0.678268i
$783$	2.20557	+	2.20557i	0.0788206	+	0.0788206i
$784$		0			0
$785$	11.1642	−	0.388591i	0.398467	−	0.0138694i
$786$	0.265063	−	9.13526i	0.00945449	−	0.325844i
$787$	−22.1789	−	5.94282i	−0.790592	−	0.211838i	−0.159143	−	0.987256i	$-0.550873\pi$
$787$	−22.1789	−	5.94282i	−0.790592	−	0.211838i	−0.631449	+	0.775417i	$0.717540\pi$
$788$	6.96303	−	6.19861i	0.248048	−	0.220816i
$789$	−39.9007	−	23.0367i	−1.42050	−	0.820127i
$790$	−14.9083	+	8.72272i	−0.530415	+	0.310341i
$791$		0			0
$792$	−10.3845	−	12.3697i	−0.368999	−	0.439537i
$793$	−2.68302	−	10.0132i	−0.0952770	−	0.355579i
$794$	−7.71368	+	12.5081i	−0.273748	+	0.443895i
$795$	9.16739	+	2.11756i	0.325134	+	0.0751020i
$796$	−17.1171	+	8.60002i	−0.606699	+	0.304820i
$797$	2.27256	+	2.27256i	0.0804981	+	0.0804981i	0.746209	−	0.665711i	$-0.231872\pi$
$797$	2.27256	+	2.27256i	0.0804981	+	0.0804981i	−0.665711	+	0.746209i	$0.731872\pi$
$798$		0			0
$799$	16.2316			0.574232
$800$	9.35907	−	26.6910i	0.330893	−	0.943668i
$801$	4.73427	+	8.20000i	0.167277	+	0.289733i
$802$	7.24190	+	30.5449i	0.255720	+	1.07858i
$803$	−9.45138	+	2.53249i	−0.333532	+	0.0893697i
$804$	45.6872	+	30.0383i	1.61126	+	1.05937i
$805$		0			0
$806$	−16.9330	−	31.3981i	−0.596440	−	1.10595i
$807$	−15.6489	−	58.4025i	−0.550868	−	2.05587i
$808$	11.6598	−	32.0593i	0.410189	−	1.12784i
$809$	−9.03218	+	5.21473i	−0.317555	+	0.183340i	−0.650302	−	0.759676i	$-0.725358\pi$
$809$	−9.03218	+	5.21473i	−0.317555	+	0.183340i	0.332747	+	0.943016i	$0.392024\pi$
$810$	−0.201338	−	34.7995i	−0.00707431	−	1.22273i
$811$			13.6718i			0.480081i	0.970763	+	0.240040i	$0.0771607\pi$
$811$			13.6718i			0.480081i	−0.970763	+	0.240040i	$0.922839\pi$
$812$		0			0
$813$	15.2268	−	15.2268i	0.534026	−	0.534026i
$814$	−0.801313	+	27.6168i	−0.0280860	+	0.967970i
$815$	19.1448	+	30.6458i	0.670612	+	1.07348i
$816$	−24.3097	−	18.0856i	−0.851011	−	0.633123i
$817$	−0.945642	+	0.253384i	−0.0330838	+	0.00886479i
$818$	−3.73643	+	12.4842i	−0.130641	+	0.436501i
$819$		0			0
$820$	−1.96149	+	0.477053i	−0.0684981	+	0.0166594i
$821$	15.7490	−	27.2781i	0.549645	−	0.952012i	−0.448654	−	0.893705i	$-0.648097\pi$
$821$	15.7490	−	27.2781i	0.549645	−	0.952012i	0.998299	−	0.0583068i	$-0.0185702\pi$
$822$	−41.4451	+	9.82623i	−1.44556	+	0.342729i
$823$	−2.05757	+	7.67895i	−0.0717223	+	0.267671i	−0.992470	−	0.122487i	$-0.960913\pi$
$823$	−2.05757	+	7.67895i	−0.0717223	+	0.267671i	0.920748	+	0.390158i	$0.127580\pi$
$824$	−25.4274	−	17.7952i	−0.885807	−	0.619926i
$825$	42.9076	+	37.3161i	1.49385	+	1.29918i
$826$		0			0
$827$	4.54203	−	4.54203i	0.157942	−	0.157942i	−0.623712	−	0.781654i	$-0.714376\pi$
$827$	4.54203	−	4.54203i	0.157942	−	0.157942i	0.781654	+	0.623712i	$0.214376\pi$
$828$	−3.07784	+	9.29348i	−0.106962	+	0.322971i
$829$	−10.3234	+	5.96019i	−0.358545	+	0.207006i	−0.668442	−	0.743764i	$-0.733039\pi$
$829$	−10.3234	+	5.96019i	−0.358545	+	0.207006i	0.309897	+	0.950770i	$0.399705\pi$
$830$	1.14521	+	4.17716i	0.0397508	+	0.144991i
$831$	55.9368	+	32.2951i	1.94043	+	1.12031i
$832$	−31.3269	−	44.6928i	−1.08606	−	1.54944i
$833$		0			0
$834$	−10.0665	−	18.6658i	−0.348574	−	0.646345i
$835$	14.8820	+	7.91506i	0.515012	+	0.273912i
$836$	12.8090	+	0.743941i	0.443007	+	0.0257297i
$837$	3.82095	−	14.2600i	0.132071	−	0.492897i
$838$	−19.0448	+	17.9708i	−0.657892	+	0.620790i
$839$	26.9117			0.929095			0.464548	−	0.885548i	$-0.346217\pi$
$839$	26.9117			0.929095			0.464548	+	0.885548i	$0.346217\pi$
$840$		0			0
$841$	28.3897			0.978957
$842$	26.2804	−	24.7984i	0.905683	−	0.854608i
$843$	−0.544667	+	2.03272i	−0.0187593	+	0.0700107i
$844$	38.4066	+	2.23064i	1.32201	+	0.0767818i
$845$	71.7318	−	21.9217i	2.46765	−	0.754129i
$846$	−2.89236	−	5.36316i	−0.0994413	−	0.184389i
$847$		0			0
$848$	7.81725	+	3.10264i	0.268445	+	0.106545i
$849$	−18.6296	−	10.7558i	−0.639365	−	0.369138i
$850$	23.7031	+	12.4312i	0.813011	+	0.426388i
$851$	14.5035	−	8.37358i	0.497173	−	0.287043i
$852$	−14.8876	+	44.9528i	−0.510041	+	1.54006i
$853$	17.1543	−	17.1543i	0.587353	−	0.587353i	−0.349561	−	0.936914i	$-0.613669\pi$
$853$	17.1543	−	17.1543i	0.587353	−	0.587353i	0.936914	+	0.349561i	$0.113669\pi$
$854$		0			0
$855$	−1.85467	−	1.72991i	−0.0634285	−	0.0591616i
$856$	−15.9815	+	22.8358i	−0.546236	+	0.780512i
$857$	−9.49933	+	35.4520i	−0.324491	+	1.21102i	0.590331	+	0.807161i	$0.298997\pi$
$857$	−9.49933	+	35.4520i	−0.324491	+	1.21102i	−0.914823	+	0.403856i	$0.867670\pi$
$858$	106.768	−	25.3137i	3.64500	−	0.864196i
$859$	16.9027	−	29.2764i	0.576714	−	0.998897i	−0.419140	−	0.907922i	$-0.637668\pi$
$859$	16.9027	−	29.2764i	0.576714	−	0.998897i	0.995853	−	0.0909754i	$-0.0289985\pi$
$860$	−3.31295	−	2.01672i	−0.112970	−	0.0687695i
$861$		0			0
$862$	−4.22576	+	14.1192i	−0.143930	+	0.480902i
$863$	31.1439	−	8.34499i	1.06015	−	0.284067i	0.313710	−	0.949519i	$-0.398428\pi$
$863$	31.1439	−	8.34499i	1.06015	−	0.284067i	0.746441	+	0.665452i	$0.231761\pi$
$864$	3.26445	−	22.3498i	0.111059	−	0.760354i
$865$	8.33194	−	5.20506i	0.283294	−	0.176977i
$866$	−1.18218	+	40.7433i	−0.0401722	+	1.38451i
$867$	−3.78176	+	3.78176i	−0.128435	+	0.128435i
$868$		0			0
$869$		−	31.0413i		−	1.05300i
$870$	3.51582	+	3.47537i	0.119197	+	0.117826i
$871$	−80.7146	+	46.6006i	−2.73491	+	1.57900i
$872$	13.5998	+	4.94614i	0.460546	+	0.167498i
$873$	−2.49139	−	9.29799i	−0.0843208	−	0.314689i
$874$	−3.69168	−	6.84531i	−0.124873	−	0.231546i
$875$		0			0
$876$	5.75806	+	3.78579i	0.194547	+	0.127910i
$877$	−15.4565	+	4.14155i	−0.521928	+	0.139850i	−0.510158	−	0.860080i	$-0.670413\pi$
$877$	−15.4565	+	4.14155i	−0.521928	+	0.139850i	−0.0117699	+	0.999931i	$0.503747\pi$
$878$	−6.79792	−	28.6722i	−0.229419	−	0.967641i
$879$	27.0502	+	46.8523i	0.912380	+	1.58029i
$880$	32.9076	+	38.7408i	1.10931	+	1.30595i
$881$	−52.7104			−1.77586			−0.887929	−	0.459981i	$-0.847856\pi$
$881$	−52.7104			−1.77586			−0.887929	+	0.459981i	$0.847856\pi$
$882$		0			0
$883$	−5.34754	−	5.34754i	−0.179959	−	0.179959i	0.611379	−	0.791338i	$-0.290615\pi$
$883$	−5.34754	−	5.34754i	−0.179959	−	0.179959i	−0.791338	+	0.611379i	$0.790615\pi$
$884$	46.1499	−	23.1868i	1.55219	−	0.779855i
$885$	−21.9892	−	35.1989i	−0.739158	−	1.18320i
$886$	−19.8317	+	32.1580i	−0.666260	+	1.08037i
$887$	−11.9600	−	44.6354i	−0.401578	−	1.49871i	−0.810281	−	0.586042i	$-0.800685\pi$
$887$	−11.9600	−	44.6354i	−0.401578	−	1.49871i	0.408703	−	0.912668i	$-0.365981\pi$
$888$	14.9025	−	12.5109i	0.500095	−	0.419838i
$889$		0			0
$890$	−15.0491	−	25.7209i	−0.504445	−	0.862167i
$891$	54.1616	+	31.2702i	1.81448	+	1.04759i
$892$	−14.1074	+	12.5586i	−0.472351	+	0.420495i
$893$	4.67578	+	1.25287i	0.156469	+	0.0419258i
$894$	−0.355870	+	12.2649i	−0.0119021	+	0.410198i
$895$	−1.03573	+	1.11043i	−0.0346206	+	0.0371176i
$896$		0			0
$897$	−47.0313	−	47.0313i	−1.57033	−	1.57033i
$898$	26.7699	+	28.3699i	0.893325	+	0.946714i
$899$	1.44417	+	2.50137i	0.0481657	+	0.0834254i
$900$	−0.116262	−	10.0470i	−0.00387539	−	0.334901i
$901$	−3.97937	+	6.89247i	−0.132572	+	0.229622i
$902$	1.04019	−	3.47550i	0.0346344	−	0.115721i
$903$		0			0
$904$	−7.91205	−	0.690264i	−0.263151	−	0.0229578i
$905$	−5.14121	−	16.8230i	−0.170900	−	0.559215i
$906$	34.1316	+	21.0489i	1.13395	+	0.699302i
$907$	57.5368	+	15.4169i	1.91048	+	0.511911i	0.993633	+	0.112668i	$0.0359396\pi$
$907$	57.5368	+	15.4169i	1.91048	+	0.511911i	0.916845	+	0.399243i	$0.130727\pi$
$908$	−17.1729	+	51.8532i	−0.569903	+	1.72081i
$909$		−	12.1186i		−	0.401948i
$910$		0			0
$911$		−	45.5865i		−	1.51035i	−0.655524	−	0.755174i	$-0.727552\pi$
$911$		−	45.5865i		−	1.51035i	0.655524	−	0.755174i	$-0.272448\pi$
$912$	−5.60685	−	7.08626i	−0.185661	−	0.234650i
$913$	−7.51871	−	2.01463i	−0.248833	−	0.0666746i
$914$	−1.02122	+	1.65595i	−0.0337790	+	0.0547741i
$915$	3.19281	−	6.00315i	0.105551	−	0.198458i
$916$	13.9043	−	21.1480i	0.459411	−	0.698748i
$917$		0			0
$918$	20.4764	+	6.12840i	0.675821	+	0.202267i
$919$	24.3756	−	42.2197i	0.804076	−	1.39270i	−0.112837	−	0.993613i	$-0.535994\pi$
$919$	24.3756	−	42.2197i	0.804076	−	1.39270i	0.916913	−	0.399087i	$-0.130673\pi$
$920$	9.51739	−	29.3046i	0.313779	−	0.966143i
$921$	−1.02802	−	1.78058i	−0.0338743	−	0.0586720i
$922$	18.1738	−	17.1489i	0.598523	−	0.564770i
$923$	−57.0761	−	57.0761i	−1.87868	−	1.87868i
$924$		0			0
$925$	−11.2794	+	12.9695i	−0.370865	+	0.426436i
$926$	−11.1048	−	0.322209i	−0.364925	−	0.0105884i
$927$	−10.6495	−	2.85353i	−0.349776	−	0.0937221i
$928$	2.64032	+	3.54355i	0.0866728	+	0.116323i
$929$	12.2678	+	7.08280i	0.402493	+	0.232379i	0.687559	−	0.726129i	$-0.258682\pi$
$929$	12.2678	+	7.08280i	0.402493	+	0.232379i	−0.285066	+	0.958508i	$0.592016\pi$
$930$	5.92503	−	22.6356i	0.194290	−	0.742249i
$931$		0			0
$932$	33.9435	−	7.01455i	1.11186	−	0.229769i
$933$	−6.89463	−	25.7311i	−0.225720	−	0.842398i
$934$	−15.7823	−	9.73291i	−0.516414	−	0.318471i
$935$	−40.7946	+	25.4848i	−1.33413	+	0.833443i
$936$	−15.8848	−	11.1169i	−0.519212	−	0.363367i
$937$	10.0190	+	10.0190i	0.327306	+	0.327306i	0.851561	−	0.524255i	$-0.175656\pi$
$937$	10.0190	+	10.0190i	0.327306	+	0.327306i	−0.524255	+	0.851561i	$0.675656\pi$
$938$		0			0
$939$	43.5184			1.42017
$940$	9.20051	+	16.8263i	0.300088	+	0.548815i
$941$	−13.9028	−	24.0804i	−0.453219	−	0.784998i	0.545365	−	0.838199i	$-0.316391\pi$
$941$	−13.9028	−	24.0804i	−0.453219	−	0.784998i	−0.998584	+	0.0532008i	$0.983058\pi$
$942$	13.7573	−	3.26173i	0.448237	−	0.106273i
$943$	−2.12409	+	0.569149i	−0.0691700	+	0.0185341i
$944$	−14.7053	−	34.0603i	−0.478618	−	1.10857i
$945$		0			0
$946$	6.13491	−	3.30856i	0.199463	−	0.107570i
$947$	7.51380	+	28.0419i	0.244166	+	0.911239i	0.973801	+	0.227402i	$0.0730233\pi$
$947$	7.51380	+	28.0419i	0.244166	+	0.911239i	−0.729635	+	0.683837i	$0.760310\pi$
$948$	−16.3286	+	14.5360i	−0.530330	+	0.472108i
$949$	−10.1726	+	5.87317i	−0.330217	+	0.190651i
$950$	5.86855	+	5.41061i	0.190401	+	0.175543i
$951$			30.8915i			1.00172i
$952$		0			0
$953$	33.2622	−	33.2622i	1.07747	−	1.07747i	0.0807336	−	0.996736i	$-0.474274\pi$
$953$	33.2622	−	33.2622i	1.07747	−	1.07747i	0.996736	−	0.0807336i	$-0.0257263\pi$
$954$	2.98647	+	0.0866537i	0.0966907	+	0.00280552i
$955$	5.37628	−	23.2752i	0.173972	−	0.753166i
$956$	2.52382	−	43.4545i	0.0816262	−	1.40542i
$957$	−8.58159	+	2.29943i	−0.277404	+	0.0743301i
$958$	−3.44599	−	1.03136i	−0.111335	−	0.0333216i
$959$		0			0
$960$	4.96886	−	35.4519i	0.160369	−	1.14421i
$961$	−8.66472	+	15.0077i	−0.279507	+	0.484120i
$962$	7.65149	+	32.2725i	0.246694	+	1.04051i
$963$	−2.56269	+	9.56409i	−0.0825815	+	0.308198i
$964$	37.2640	−	18.7223i	1.20019	−	0.603004i
$965$	−0.877752	−	25.2178i	−0.0282558	−	0.811788i
$966$		0			0
$967$	−8.70456	+	8.70456i	−0.279920	+	0.279920i	−0.833077	−	0.553157i	$-0.813423\pi$
$967$	−8.70456	+	8.70456i	−0.279920	+	0.279920i	0.553157	+	0.833077i	$0.313423\pi$
$968$	−59.3193	+	10.4746i	−1.90660	+	0.336665i
$969$	7.40523	−	4.27541i	0.237890	−	0.137346i
$970$	8.01023	+	29.2174i	0.257193	+	0.938113i
$971$	43.9465	+	25.3725i	1.41031	+	0.814243i	0.995417	−	0.0956276i	$-0.0304858\pi$
$971$	43.9465	+	25.3725i	1.41031	+	0.814243i	0.414893	+	0.909870i	$0.363819\pi$
$972$	−4.06540	−	19.6725i	−0.130398	−	0.630997i
$973$		0			0
$974$	4.58151	−	2.47081i	0.146801	−	0.0791698i
$975$	61.3483	+	29.9389i	1.96472	+	0.958811i
$976$	3.62790	−	4.87644i	0.116126	−	0.156091i
$977$	−0.0440753	+	0.164491i	−0.00141009	+	0.00526254i	−0.966627	−	0.256187i	$-0.917534\pi$
$977$	−0.0440753	+	0.164491i	−0.00141009	+	0.00526254i	0.965217	+	0.261449i	$0.0842004\pi$
$978$	31.3872	+	33.2631i	1.00365	+	1.06364i
$979$	53.5546			1.71161
$980$		0			0
$981$	5.14078			0.164133
$982$	−21.6836	−	22.9795i	−0.691952	−	0.733306i
$983$	−5.81741	+	21.7109i	−0.185546	+	0.692469i	0.808966	+	0.587855i	$0.200027\pi$
$983$	−5.81741	+	21.7109i	−0.185546	+	0.692469i	−0.994513	+	0.104614i	$0.966639\pi$
$984$	−2.31531	+	1.08034i	−0.0738094	+	0.0344399i
$985$	−4.89422	+	9.20216i	−0.155943	+	0.293205i
$986$	−3.68059	+	1.98494i	−0.117214	+	0.0632135i
$987$		0			0
$988$	15.0840	−	3.11715i	0.479885	−	0.0991699i
$989$	−3.65898	−	2.11251i	−0.116349	−	0.0671740i
$990$	15.6899	+	8.93793i	0.498657	+	0.284066i
$991$	12.0154	−	6.93708i	0.381681	−	0.220364i	−0.296869	−	0.954918i	$-0.595942\pi$
$991$	12.0154	−	6.93708i	0.381681	−	0.220364i	0.678549	+	0.734555i	$0.262609\pi$
$992$	8.27637	−	19.2083i	0.262775	−	0.609865i
$993$	−37.4498	+	37.4498i	−1.18843	+	1.18843i
$994$		0			0
$995$	14.6082	−	15.6618i	0.463112	−	0.496514i
$996$	2.46110	+	4.89847i	0.0779831	+	0.155214i
$997$	4.08361	−	15.2402i	0.129329	−	0.482663i	−0.870628	−	0.491942i	$-0.836287\pi$
$997$	4.08361	−	15.2402i	0.129329	−	0.482663i	0.999957	+	0.00927934i	$0.00295375\pi$
$998$	3.24835	+	13.7009i	0.102825	+	0.433694i
$999$	−6.86297	+	11.8870i	−0.217135	+	0.376089i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.x.n.667.21		112
4.3	odd	2	inner	980.2.x.n.667.28		112
5.3	odd	4	inner	980.2.x.n.863.9		112
7.2	even	3		980.2.k.m.687.5	✓	56
7.3	odd	6	inner	980.2.x.n.67.15		112
7.4	even	3	inner	980.2.x.n.67.16		112
7.5	odd	6		980.2.k.m.687.6	yes	56
7.6	odd	2	inner	980.2.x.n.667.22		112
20.3	even	4	inner	980.2.x.n.863.16		112
28.3	even	6	inner	980.2.x.n.67.10		112
28.11	odd	6	inner	980.2.x.n.67.9		112
28.19	even	6		980.2.k.m.687.11	yes	56
28.23	odd	6		980.2.k.m.687.12	yes	56
28.27	even	2	inner	980.2.x.n.667.27		112
35.3	even	12	inner	980.2.x.n.263.27		112
35.13	even	4	inner	980.2.x.n.863.10		112
35.18	odd	12	inner	980.2.x.n.263.28		112
35.23	odd	12		980.2.k.m.883.12	yes	56
35.33	even	12		980.2.k.m.883.11	yes	56
140.3	odd	12	inner	980.2.x.n.263.22		112
140.23	even	12		980.2.k.m.883.5	yes	56
140.83	odd	4	inner	980.2.x.n.863.15		112
140.103	odd	12		980.2.k.m.883.6	yes	56
140.123	even	12	inner	980.2.x.n.263.21		112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
980.2.k.m.687.5	✓	56	7.2	even	3
980.2.k.m.687.6	yes	56	7.5	odd	6
980.2.k.m.687.11	yes	56	28.19	even	6
980.2.k.m.687.12	yes	56	28.23	odd	6
980.2.k.m.883.5	yes	56	140.23	even	12
980.2.k.m.883.6	yes	56	140.103	odd	12
980.2.k.m.883.11	yes	56	35.33	even	12
980.2.k.m.883.12	yes	56	35.23	odd	12
980.2.x.n.67.9		112	28.11	odd	6	inner
980.2.x.n.67.10		112	28.3	even	6	inner
980.2.x.n.67.15		112	7.3	odd	6	inner
980.2.x.n.67.16		112	7.4	even	3	inner
980.2.x.n.263.21		112	140.123	even	12	inner
980.2.x.n.263.22		112	140.3	odd	12	inner
980.2.x.n.263.27		112	35.3	even	12	inner
980.2.x.n.263.28		112	35.18	odd	12	inner
980.2.x.n.667.21		112	1.1	even	1	trivial
980.2.x.n.667.22		112	7.6	odd	2	inner
980.2.x.n.667.27		112	28.27	even	2	inner
980.2.x.n.667.28		112	4.3	odd	2	inner
980.2.x.n.863.9		112	5.3	odd	4	inner
980.2.x.n.863.10		112	35.13	even	4	inner
980.2.x.n.863.15		112	140.83	odd	4	inner
980.2.x.n.863.16		112	20.3	even	4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.02858 - 0.970576i) q^{2} +(-0.517947 + 1.93300i) q^{3} +(0.115964 - 1.99664i) q^{4} +(0.653520 + 2.13844i) q^{5} +(1.34338 + 2.49096i) q^{6} +(-1.81861 - 2.16626i) q^{8} +(-0.870157 - 0.502386i) q^{9} +(2.74771 + 1.56527i) q^{10} +(-4.92166 + 2.84152i) q^{11} +(3.79944 + 1.25831i) q^{12} +(-4.82411 + 4.82411i) q^{13} +(-4.47209 + 0.155660i) q^{15} +(-3.97310 - 0.463075i) q^{16} +(0.979673 - 3.65619i) q^{17} +(-1.38263 + 0.327809i) q^{18} +(0.564422 - 0.977608i) q^{19} +(4.34546 - 1.05686i) q^{20} +(-2.30442 + 7.69959i) q^{22} +(4.70570 - 1.26089i) q^{23} +(5.12932 - 2.39337i) q^{24} +(-4.14582 + 2.79502i) q^{25} +(-0.279829 + 9.64416i) q^{26} +(-2.82336 + 2.82336i) q^{27} -0.781186i q^{29} +(-4.44884 + 4.50062i) q^{30} +(-3.20202 + 1.84869i) q^{31} +(-4.53612 + 3.37989i) q^{32} +(-2.94351 - 10.9853i) q^{33} +(-2.54094 - 4.71154i) q^{34} +(-1.10399 + 1.67913i) q^{36} +(3.32051 - 0.889727i) q^{37} +(-0.368288 - 1.55337i) q^{38} +(-6.82639 - 11.8236i) q^{39} +(3.44390 - 5.30467i) q^{40} -0.451387 q^{41} +(-0.613245 - 0.613245i) q^{43} +(5.10275 + 10.1563i) q^{44} +(0.505655 - 2.18910i) q^{45} +(3.61641 - 5.86417i) q^{46} +(1.10987 + 4.14209i) q^{47} +(2.95298 - 7.44018i) q^{48} +(-1.55154 + 6.89875i) q^{50} +(6.56001 + 3.78742i) q^{51} +(9.07256 + 10.1914i) q^{52} +(-2.03097 - 0.544196i) q^{53} +(-0.163773 + 5.64435i) q^{54} +(-9.29282 - 8.66767i) q^{55} +(1.59738 + 1.59738i) q^{57} +(-0.758200 - 0.803514i) q^{58} +(4.63740 + 8.03221i) q^{59} +(-0.207806 + 8.94719i) q^{60} +(-0.759742 + 1.31591i) q^{61} +(-1.49925 + 5.00933i) q^{62} +(-1.38533 + 7.87914i) q^{64} +(-13.4687 - 7.16340i) q^{65} +(-13.6898 - 8.44243i) q^{66} +(13.1957 + 3.53578i) q^{67} +(-7.18647 - 2.38004i) q^{68} +9.74921i q^{69} +11.8314i q^{71} +(0.494179 + 2.79863i) q^{72} +(1.66308 + 0.445622i) q^{73} +(2.55187 - 4.13796i) q^{74} +(-3.25547 - 9.46156i) q^{75} +(-1.88647 - 1.24031i) q^{76} +(-18.4973 - 5.53607i) q^{78} +(-2.73105 + 4.73031i) q^{79} +(-1.60625 - 8.79886i) q^{80} +(-5.50237 - 9.53039i) q^{81} +(-0.464289 + 0.438106i) q^{82} +(0.968508 + 0.968508i) q^{83} +(8.45877 - 0.294423i) q^{85} +(-1.22597 - 0.0355721i) q^{86} +(1.51003 + 0.404613i) q^{87} +(15.1060 + 5.49396i) q^{88} +(-8.16106 - 4.71179i) q^{89} +(-1.60458 - 2.74244i) q^{90} +(-1.97184 - 9.54179i) q^{92} +(-1.91504 - 7.14703i) q^{93} +(5.16181 + 3.18327i) q^{94} +(2.45942 + 0.568095i) q^{95} +(-4.18387 - 10.5189i) q^{96} +(6.77428 + 6.77428i) q^{97} +5.71016 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 4 q^{2} - 32 q^{8} - 32 q^{16} + 40 q^{22} - 32 q^{25} + 28 q^{30} + 64 q^{32} + 32 q^{36} + 8 q^{37} + 184 q^{46} - 24 q^{50} - 96 q^{53} - 16 q^{57} - 124 q^{58} - 8 q^{60} + 120 q^{65} + 80 q^{72}+ \cdots + 176 q^{93}+O(q^{100}) \) 112 * q + 4 * q^2 - 32 * q^8 - 32 * q^16 + 40 * q^22 - 32 * q^25 + 28 * q^30 + 64 * q^32 + 32 * q^36 + 8 * q^37 + 184 * q^46 - 24 * q^50 - 96 * q^53 - 16 * q^57 - 124 * q^58 - 8 * q^60 + 120 * q^65 + 80 * q^72 - 72 * q^78 + 72 * q^81 + 192 * q^85 - 104 * q^86 - 48 * q^88 - 304 * q^92 + 176 * q^93

Introduction

L-functions

Modular forms

Varieties

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