LMFDB - Embedded newform 980.2.g.a.391.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [980,2,Mod(391,980)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(980, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("980.391");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.g (of order $2$, degree $1$, 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:	$32$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			391.7
Character	$\chi$	$=$	980.391
Dual form			980.2.g.a.391.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34325 + 0.442358i) q^{2} -0.901278 q^{3} +(1.60864 - 1.18839i) q^{4} -1.00000i q^{5} +(1.21064 - 0.398687i) q^{6} +(-1.63511 + 2.30790i) q^{8} -2.18770 q^{9} +O(q^{10})$	\(q+(-1.34325 + 0.442358i) q^{2} -0.901278 q^{3} +(1.60864 - 1.18839i) q^{4} -1.00000i q^{5} +(1.21064 - 0.398687i) q^{6} +(-1.63511 + 2.30790i) q^{8} -2.18770 q^{9} +(0.442358 + 1.34325i) q^{10} +3.74246i q^{11} +(-1.44983 + 1.07107i) q^{12} -2.41990i q^{13} +0.901278i q^{15} +(1.17544 - 3.82339i) q^{16} +0.583719i q^{17} +(2.93862 - 0.967745i) q^{18} +6.15955 q^{19} +(-1.18839 - 1.60864i) q^{20} +(-1.65551 - 5.02706i) q^{22} -4.31210i q^{23} +(1.47369 - 2.08006i) q^{24} -1.00000 q^{25} +(1.07046 + 3.25054i) q^{26} +4.67556 q^{27} -0.435463 q^{29} +(-0.398687 - 1.21064i) q^{30} +2.53865 q^{31} +(0.112397 + 5.65574i) q^{32} -3.37300i q^{33} +(-0.258212 - 0.784080i) q^{34} +(-3.51922 + 2.59985i) q^{36} -11.3008 q^{37} +(-8.27381 + 2.72472i) q^{38} +2.18101i q^{39} +(2.30790 + 1.63511i) q^{40} -7.35068i q^{41} -5.80096i q^{43} +(4.44752 + 6.02027i) q^{44} +2.18770i q^{45} +(1.90749 + 5.79223i) q^{46} -11.5765 q^{47} +(-1.05940 + 3.44594i) q^{48} +(1.34325 - 0.442358i) q^{50} -0.526093i q^{51} +(-2.87580 - 3.89275i) q^{52} -3.11491 q^{53} +(-6.28044 + 2.06827i) q^{54} +3.74246 q^{55} -5.55147 q^{57} +(0.584935 - 0.192630i) q^{58} +3.47068 q^{59} +(1.07107 + 1.44983i) q^{60} -10.3877i q^{61} +(-3.41004 + 1.12299i) q^{62} +(-2.65284 - 7.54735i) q^{64} -2.41990 q^{65} +(1.49207 + 4.53078i) q^{66} -9.84499i q^{67} +(0.693688 + 0.938993i) q^{68} +3.88640i q^{69} +9.96771i q^{71} +(3.57712 - 5.04900i) q^{72} -9.79892i q^{73} +(15.1798 - 4.99899i) q^{74} +0.901278 q^{75} +(9.90849 - 7.31997i) q^{76} +(-0.964785 - 2.92964i) q^{78} -0.459050i q^{79} +(-3.82339 - 1.17544i) q^{80} +2.34912 q^{81} +(3.25163 + 9.87380i) q^{82} -2.59747 q^{83} +0.583719 q^{85} +(2.56610 + 7.79213i) q^{86} +0.392473 q^{87} +(-8.63724 - 6.11933i) q^{88} -9.88016i q^{89} +(-0.967745 - 2.93862i) q^{90} +(-5.12447 - 6.93662i) q^{92} -2.28803 q^{93} +(15.5502 - 5.12097i) q^{94} -6.15955i q^{95} +(-0.101301 - 5.09739i) q^{96} -4.54044i q^{97} -8.18738i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{2} + 4 q^{4} - 4 q^{8} + 32 q^{9}+O(q^{10}) $ 32 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 + 32 * q^9	$ 32 q - 4 q^{2} + 4 q^{4} - 4 q^{8} + 32 q^{9} + 28 q^{16} - 8 q^{22} - 32 q^{25} - 40 q^{29} - 4 q^{32} + 60 q^{36} - 16 q^{37} + 36 q^{44} - 4 q^{46} + 4 q^{50} + 16 q^{53} + 48 q^{57} - 4 q^{58} - 28 q^{60} + 4 q^{64} - 8 q^{65} - 8 q^{72} - 76 q^{74} + 120 q^{78} + 72 q^{81} - 56 q^{86} - 8 q^{88} - 4 q^{92} + 16 q^{93}+O(q^{100}) $ 32 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 + 32 * q^9 + 28 * q^16 - 8 * q^22 - 32 * q^25 - 40 * q^29 - 4 * q^32 + 60 * q^36 - 16 * q^37 + 36 * q^44 - 4 * q^46 + 4 * q^50 + 16 * q^53 + 48 * q^57 - 4 * q^58 - 28 * q^60 + 4 * q^64 - 8 * q^65 - 8 * q^72 - 76 * q^74 + 120 * q^78 + 72 * q^81 - 56 * q^86 - 8 * q^88 - 4 * q^92 + 16 * q^93

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$197$	$491$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.34325	+	0.442358i	−0.949821	+	0.312794i
$2$	−1.34325	+	0.442358i	−0.949821	+	0.312794i
$3$	−0.901278			−0.520353			−0.260177	−	0.965561i	$-0.583781\pi$
$3$	−0.901278			−0.520353			−0.260177	+	0.965561i	$0.583781\pi$
$4$	1.60864	−	1.18839i	0.804320	−	0.594197i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	1.21064	−	0.398687i	0.494242	−	0.162763i
$7$		0			0
$7$		0			0
$8$	−1.63511	+	2.30790i	−0.578098	+	0.815967i
$9$	−2.18770			−0.729233
$10$	0.442358	+	1.34325i	0.139886	+	0.424773i
$11$			3.74246i			1.12839i	0.825640	+	0.564197i	$0.190814\pi$
$11$			3.74246i			1.12839i	−0.825640	+	0.564197i	$0.809186\pi$
$12$	−1.44983	+	1.07107i	−0.418530	+	0.309192i
$13$		−	2.41990i		−	0.671161i	−0.942012	−	0.335580i	$-0.891068\pi$
$13$		−	2.41990i		−	0.671161i	0.942012	−	0.335580i	$-0.108932\pi$
$14$		0			0
$15$			0.901278i			0.232709i
$16$	1.17544	−	3.82339i	0.293860	−	0.955848i
$17$			0.583719i			0.141573i	0.997492	+	0.0707863i	$0.0225508\pi$
$17$			0.583719i			0.141573i	−0.997492	+	0.0707863i	$0.977449\pi$
$18$	2.93862	−	0.967745i	0.692640	−	0.228100i
$19$	6.15955			1.41310			0.706549	−	0.707664i	$-0.250251\pi$
$19$	6.15955			1.41310			0.706549	+	0.707664i	$0.250251\pi$
$20$	−1.18839	−	1.60864i	−0.265733	−	0.359703i
$21$		0			0
$22$	−1.65551	−	5.02706i	−0.352955	−	1.07177i
$23$		−	4.31210i		−	0.899135i	−0.893246	−	0.449568i	$-0.851578\pi$
$23$		−	4.31210i		−	0.899135i	0.893246	−	0.449568i	$-0.148422\pi$
$24$	1.47369	−	2.08006i	0.300815	−	0.424591i
$25$	−1.00000			−0.200000
$26$	1.07046	+	3.25054i	0.209935	+	0.637482i
$27$	4.67556			0.899812
$28$		0			0
$29$	−0.435463			−0.0808634			−0.0404317	−	0.999182i	$-0.512873\pi$
$29$	−0.435463			−0.0808634			−0.0404317	+	0.999182i	$0.512873\pi$
$30$	−0.398687	−	1.21064i	−0.0727900	−	0.221032i
$31$	2.53865			0.455955			0.227978	−	0.973666i	$-0.426789\pi$
$31$	2.53865			0.455955			0.227978	+	0.973666i	$0.426789\pi$
$32$	0.112397	+	5.65574i	0.0198692	+	0.999803i
$33$		−	3.37300i		−	0.587164i
$34$	−0.258212	−	0.784080i	−0.0442831	−	0.134469i
$35$		0			0
$36$	−3.51922	+	2.59985i	−0.586536	+	0.433308i
$37$	−11.3008			−1.85784			−0.928918	−	0.370285i	$-0.879260\pi$
$37$	−11.3008			−1.85784			−0.928918	+	0.370285i	$0.879260\pi$
$38$	−8.27381	+	2.72472i	−1.34219	+	0.442009i
$39$			2.18101i			0.349241i
$40$	2.30790	+	1.63511i	0.364912	+	0.258533i
$41$		−	7.35068i		−	1.14798i	−0.818861	−	0.573992i	$-0.805394\pi$
$41$		−	7.35068i		−	1.14798i	0.818861	−	0.573992i	$-0.194606\pi$
$42$		0			0
$43$		−	5.80096i		−	0.884637i	−0.896858	−	0.442319i	$-0.854156\pi$
$43$		−	5.80096i		−	0.884637i	0.896858	−	0.442319i	$-0.145844\pi$
$44$	4.44752	+	6.02027i	0.670489	+	0.907590i
$45$			2.18770i			0.326123i
$46$	1.90749	+	5.79223i	0.281244	+	0.854018i
$47$	−11.5765			−1.68861			−0.844305	−	0.535863i	$-0.819986\pi$
$47$	−11.5765			−1.68861			−0.844305	+	0.535863i	$0.819986\pi$
$48$	−1.05940	+	3.44594i	−0.152911	+	0.497379i
$49$		0			0
$50$	1.34325	−	0.442358i	0.189964	−	0.0625588i
$51$		−	0.526093i		−	0.0736677i
$52$	−2.87580	−	3.89275i	−0.398802	−	0.539828i
$53$	−3.11491			−0.427866			−0.213933	−	0.976848i	$-0.568627\pi$
$53$	−3.11491			−0.427866			−0.213933	+	0.976848i	$0.568627\pi$
$54$	−6.28044	+	2.06827i	−0.854660	+	0.281456i
$55$	3.74246			0.504633
$56$		0			0
$57$	−5.55147			−0.735310
$58$	0.584935	−	0.192630i	0.0768057	−	0.0252936i
$59$	3.47068			0.451844			0.225922	−	0.974145i	$-0.427461\pi$
$59$	3.47068			0.451844			0.225922	+	0.974145i	$0.427461\pi$
$60$	1.07107	+	1.44983i	0.138275	+	0.187172i
$61$		−	10.3877i		−	1.33000i	−0.746842	−	0.665001i	$-0.768431\pi$
$61$		−	10.3877i		−	1.33000i	0.746842	−	0.665001i	$-0.231569\pi$
$62$	−3.41004	+	1.12299i	−0.433076	+	0.142620i
$63$		0			0
$64$	−2.65284	−	7.54735i	−0.331605	−	0.943418i
$65$	−2.41990			−0.300152
$66$	1.49207	+	4.53078i	0.183661	+	0.557700i
$67$		−	9.84499i		−	1.20276i	−0.798964	−	0.601379i	$-0.794618\pi$
$67$		−	9.84499i		−	1.20276i	0.798964	−	0.601379i	$-0.205382\pi$
$68$	0.693688	+	0.938993i	0.0841220	+	0.113870i
$69$			3.88640i			0.467868i
$70$		0			0
$71$			9.96771i			1.18295i	0.806324	+	0.591475i	$0.201454\pi$
$71$			9.96771i			1.18295i	−0.806324	+	0.591475i	$0.798546\pi$
$72$	3.57712	−	5.04900i	0.421568	−	0.595030i
$73$		−	9.79892i		−	1.14688i	−0.819249	−	0.573439i	$-0.805609\pi$
$73$		−	9.79892i		−	1.14688i	0.819249	−	0.573439i	$-0.194391\pi$
$74$	15.1798	−	4.99899i	1.76461	−	0.581120i
$75$	0.901278			0.104071
$76$	9.90849	−	7.31997i	1.13658	−	0.839658i
$77$		0			0
$78$	−0.964785	−	2.92964i	−0.109240	−	0.331716i
$79$		−	0.459050i		−	0.0516472i	−0.999667	−	0.0258236i	$-0.991779\pi$
$79$		−	0.459050i		−	0.0516472i	0.999667	−	0.0258236i	$-0.00822082\pi$
$80$	−3.82339	−	1.17544i	−0.427468	−	0.131418i
$81$	2.34912			0.261013
$82$	3.25163	+	9.87380i	0.359083	+	1.09038i
$83$	−2.59747			−0.285109			−0.142554	−	0.989787i	$-0.545532\pi$
$83$	−2.59747			−0.285109			−0.142554	+	0.989787i	$0.545532\pi$
$84$		0			0
$85$	0.583719			0.0633132
$86$	2.56610	+	7.79213i	0.276709	+	0.840247i
$87$	0.392473			0.0420775
$88$	−8.63724	−	6.11933i	−0.920733	−	0.652323i
$89$		−	9.88016i		−	1.04730i	−0.851935	−	0.523648i	$-0.824571\pi$
$89$		−	9.88016i		−	1.04730i	0.851935	−	0.523648i	$-0.175429\pi$
$90$	−0.967745	−	2.93862i	−0.102009	−	0.309758i
$91$		0			0
$92$	−5.12447	−	6.93662i	−0.534263	−	0.723192i
$93$	−2.28803			−0.237258
$94$	15.5502	−	5.12097i	1.60388	−	0.528187i
$95$		−	6.15955i		−	0.631956i
$96$	−0.101301	−	5.09739i	−0.0103390	−	0.520250i
$97$		−	4.54044i		−	0.461011i	−0.973071	−	0.230506i	$-0.925962\pi$
$97$		−	4.54044i		−	0.461011i	0.973071	−	0.230506i	$-0.0740380\pi$
$98$		0			0
$99$		−	8.18738i		−	0.822862i
$100$	−1.60864	+	1.18839i	−0.160864	+	0.118839i
$101$		−	9.14442i		−	0.909903i	−0.890516	−	0.454952i	$-0.849657\pi$
$101$		−	9.14442i		−	0.909903i	0.890516	−	0.454952i	$-0.150343\pi$
$102$	0.232721	+	0.706674i	0.0230428	+	0.0699712i
$103$	10.2319			1.00818			0.504092	−	0.863650i	$-0.331827\pi$
$103$	10.2319			1.00818			0.504092	+	0.863650i	$0.331827\pi$
$104$	5.58490	+	3.95681i	0.547645	+	0.387997i
$105$		0			0
$106$	4.18410	−	1.37790i	0.406396	−	0.133834i
$107$		−	6.33201i		−	0.612139i	−0.952009	−	0.306069i	$-0.900986\pi$
$107$		−	6.33201i		−	0.612139i	0.952009	−	0.306069i	$-0.0990139\pi$
$108$	7.52129	−	5.55640i	0.723736	−	0.534665i
$109$	−18.7605			−1.79693			−0.898467	−	0.439040i	$-0.855318\pi$
$109$	−18.7605			−1.79693			−0.898467	+	0.439040i	$0.855318\pi$
$110$	−5.02706	+	1.65551i	−0.479311	+	0.157846i
$111$	10.1851			0.966731
$112$		0			0
$113$	4.17847			0.393077			0.196539	−	0.980496i	$-0.437030\pi$
$113$	4.17847			0.393077			0.196539	+	0.980496i	$0.437030\pi$
$114$	7.45701	−	2.45573i	0.698413	−	0.230001i
$115$	−4.31210			−0.402106
$116$	−0.700502	+	0.517501i	−0.0650400	+	0.0480488i
$117$			5.29402i			0.489432i
$118$	−4.66198	+	1.53528i	−0.429170	+	0.141334i
$119$		0			0
$120$	−2.08006	−	1.47369i	−0.189883	−	0.134529i
$121$	−3.00602			−0.273275
$122$	4.59506	+	13.9532i	0.416017	+	1.26326i
$123$			6.62501i			0.597357i
$124$	4.08377	−	3.01692i	0.366734	−	0.270927i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$		−	4.91036i		−	0.435724i	−0.975980	−	0.217862i	$-0.930092\pi$
$127$		−	4.91036i		−	0.435724i	0.975980	−	0.217862i	$-0.0699083\pi$
$128$	6.90205	+	8.96447i	0.610061	+	0.792355i
$129$			5.22827i			0.460324i
$130$	3.25054	−	1.07046i	0.285091	−	0.0938858i
$131$	15.8745			1.38696			0.693479	−	0.720477i	$-0.256077\pi$
$131$	15.8745			1.38696			0.693479	+	0.720477i	$0.256077\pi$
$132$	−4.00845	−	5.42594i	−0.348891	−	0.472267i
$133$		0			0
$134$	4.35501	+	13.2243i	0.376216	+	1.14240i
$135$		−	4.67556i		−	0.402408i
$136$	−1.34717	−	0.954444i	−0.115519	−	0.0818429i
$137$	−7.84221			−0.670005			−0.335002	−	0.942217i	$-0.608737\pi$
$137$	−7.84221			−0.670005			−0.335002	+	0.942217i	$0.608737\pi$
$138$	−1.71918	−	5.22041i	−0.146346	−	0.444391i
$139$	−17.4044			−1.47623			−0.738113	−	0.674677i	$-0.764283\pi$
$139$	−17.4044			−1.47623			−0.738113	+	0.674677i	$0.764283\pi$
$140$		0			0
$141$	10.4337			0.878674
$142$	−4.40929	−	13.3891i	−0.370020	−	1.12359i
$143$	9.05640			0.757334
$144$	−2.57151	+	8.36443i	−0.214292	+	0.697036i
$145$			0.435463i			0.0361632i
$146$	4.33463	+	13.1624i	0.358736	+	1.08933i
$147$		0			0
$148$	−18.1789	+	13.4298i	−1.49429	+	1.10392i
$149$	1.65155			0.135300			0.0676502	−	0.997709i	$-0.478450\pi$
$149$	1.65155			0.135300			0.0676502	+	0.997709i	$0.478450\pi$
$150$	−1.21064	+	0.398687i	−0.0988485	+	0.0325527i
$151$		−	7.35613i		−	0.598633i	−0.954154	−	0.299317i	$-0.903241\pi$
$151$		−	7.35613i		−	0.598633i	0.954154	−	0.299317i	$-0.0967587\pi$
$152$	−10.0715	+	14.2156i	−0.816909	+	1.15304i
$153$		−	1.27700i		−	0.103239i
$154$		0			0
$155$		−	2.53865i		−	0.203909i
$156$	2.59189	+	3.50845i	0.207518	+	0.280901i
$157$			3.08251i			0.246011i	0.992406	+	0.123005i	$0.0392532\pi$
$157$			3.08251i			0.246011i	−0.992406	+	0.123005i	$0.960747\pi$
$158$	0.203065	+	0.616619i	0.0161549	+	0.0490556i
$159$	2.80740			0.222641
$160$	5.65574	−	0.112397i	0.447125	−	0.00888579i
$161$		0			0
$162$	−3.15545	+	1.03915i	−0.247915	+	0.0816433i
$163$			4.51816i			0.353889i	0.984221	+	0.176945i	$0.0566214\pi$
$163$			4.51816i			0.353889i	−0.984221	+	0.176945i	$0.943379\pi$
$164$	−8.73551	−	11.8246i	−0.682128	−	0.923346i
$165$	−3.37300			−0.262588
$166$	3.48905	−	1.14901i	0.270802	−	0.0891804i
$167$	−16.9358			−1.31053			−0.655266	−	0.755398i	$-0.727444\pi$
$167$	−16.9358			−1.31053			−0.655266	+	0.755398i	$0.727444\pi$
$168$		0			0
$169$	7.14406			0.549543
$170$	−0.784080	+	0.258212i	−0.0601362	+	0.0198040i
$171$	−13.4752			−1.03048
$172$	−6.89382	−	9.33165i	−0.525649	−	0.711531i
$173$			0.132697i			0.0100888i	0.999987	+	0.00504439i	$0.00160569\pi$
$173$			0.132697i			0.0100888i	−0.999987	+	0.00504439i	$0.998394\pi$
$174$	−0.527189	+	0.173613i	−0.0399661	+	0.0131616i
$175$		0			0
$176$	14.3089	+	4.39904i	1.07857	+	0.331590i
$177$	−3.12804			−0.235118
$178$	4.37057	+	13.2715i	0.327588	+	0.994743i
$179$		−	16.0991i		−	1.20330i	−0.798760	−	0.601650i	$-0.794510\pi$
$179$		−	16.0991i		−	1.20330i	0.798760	−	0.601650i	$-0.205490\pi$
$180$	2.59985	+	3.51922i	0.193781	+	0.262307i
$181$		−	3.99317i		−	0.296810i	−0.988927	−	0.148405i	$-0.952586\pi$
$181$		−	3.99317i		−	0.296810i	0.988927	−	0.148405i	$-0.0474139\pi$
$182$		0			0
$183$			9.36216i			0.692071i
$184$	9.95191	+	7.05076i	0.733665	+	0.519789i
$185$			11.3008i			0.830850i
$186$	3.07340	−	1.01213i	0.225352	−	0.0742128i
$187$	−2.18455			−0.159750
$188$	−18.6225	+	13.7575i	−1.35818	+	1.00337i
$189$		0			0
$190$	2.72472	+	8.27381i	0.197672	+	0.600245i
$191$			20.0500i			1.45077i	0.688344	+	0.725385i	$0.258338\pi$
$191$			20.0500i			1.45077i	−0.688344	+	0.725385i	$0.741662\pi$
$192$	2.39094	+	6.80226i	0.172552	+	0.490911i
$193$	19.3392			1.39206			0.696032	−	0.718011i	$-0.254947\pi$
$193$	19.3392			1.39206			0.696032	+	0.718011i	$0.254947\pi$
$194$	2.00850	+	6.09894i	0.144202	+	0.437878i
$195$	2.18101			0.156185
$196$		0			0
$197$	−1.63738			−0.116659			−0.0583293	−	0.998297i	$-0.518577\pi$
$197$	−1.63738			−0.116659			−0.0583293	+	0.998297i	$0.518577\pi$
$198$	3.62175	+	10.9977i	0.257386	+	0.781572i
$199$	−0.783264			−0.0555241			−0.0277621	−	0.999615i	$-0.508838\pi$
$199$	−0.783264			−0.0555241			−0.0277621	+	0.999615i	$0.508838\pi$
$200$	1.63511	−	2.30790i	0.115620	−	0.163193i
$201$			8.87308i			0.625859i
$202$	4.04510	+	12.2832i	0.284612	+	0.864245i
$203$		0			0
$204$	−0.625205	−	0.846294i	−0.0437731	−	0.0592524i
$205$	−7.35068			−0.513394
$206$	−13.7441	+	4.52618i	−0.957594	+	0.315354i
$207$			9.43358i			0.655679i
$208$	−9.25225	−	2.84445i	−0.641528	−	0.197227i
$209$			23.0519i			1.59453i
$210$		0			0
$211$			9.22534i			0.635099i	0.948242	+	0.317549i	$0.102860\pi$
$211$			9.22534i			0.635099i	−0.948242	+	0.317549i	$0.897140\pi$
$212$	−5.01077	+	3.70174i	−0.344141	+	0.254237i
$213$		−	8.98368i		−	0.615551i
$214$	2.80101	+	8.50547i	0.191473	+	0.581422i
$215$	−5.80096			−0.395622
$216$	−7.64505	+	10.7907i	−0.520180	+	0.734217i
$217$		0			0
$218$	25.2001	−	8.29887i	1.70677	−	0.562071i
$219$			8.83155i			0.596781i
$220$	6.02027	−	4.44752i	0.405887	−	0.299852i
$221$	1.41254			0.0950179
$222$	−13.6812	+	4.50548i	−0.918221	+	0.302388i
$223$	24.2380			1.62310			0.811550	−	0.584284i	$-0.198624\pi$
$223$	24.2380			1.62310			0.811550	+	0.584284i	$0.198624\pi$
$224$		0			0
$225$	2.18770			0.145847
$226$	−5.61273	+	1.84838i	−0.373353	+	0.122952i
$227$	−10.6325			−0.705701			−0.352851	−	0.935680i	$-0.614788\pi$
$227$	−10.6325			−0.705701			−0.352851	+	0.935680i	$0.614788\pi$
$228$	−8.93031	+	6.59733i	−0.591424	+	0.436919i
$229$		−	29.5128i		−	1.95026i	−0.221626	−	0.975132i	$-0.571136\pi$
$229$		−	29.5128i		−	1.95026i	0.221626	−	0.975132i	$-0.428864\pi$
$230$	5.79223	−	1.90749i	0.381928	−	0.125776i
$231$		0			0
$232$	0.712029	−	1.00501i	0.0467470	−	0.0659819i
$233$	28.0703			1.83894			0.919472	−	0.393155i	$-0.128616\pi$
$233$	28.0703			1.83894			0.919472	+	0.393155i	$0.128616\pi$
$234$	−2.34185	−	7.11119i	−0.153092	−	0.464873i
$235$			11.5765i			0.755169i
$236$	5.58307	−	4.12453i	0.363427	−	0.268484i
$237$			0.413732i			0.0268748i
$238$		0			0
$239$			13.6279i			0.881512i	0.897627	+	0.440756i	$0.145290\pi$
$239$			13.6279i			0.881512i	−0.897627	+	0.440756i	$0.854710\pi$
$240$	3.44594	+	1.05940i	0.222435	+	0.0683839i
$241$			4.20741i			0.271023i	0.990776	+	0.135512i	$0.0432678\pi$
$241$			4.20741i			0.271023i	−0.990776	+	0.135512i	$0.956732\pi$
$242$	4.03784	−	1.32974i	0.259562	−	0.0854787i
$243$	−16.1439			−1.03563
$244$	−12.3446	−	16.7100i	−0.790283	−	1.06975i
$245$		0			0
$246$	−2.93062	−	8.89904i	−0.186850	−	0.567382i
$247$		−	14.9055i		−	0.948415i
$248$	−4.15097	+	5.85896i	−0.263587	+	0.372044i
$249$	2.34104			0.148357
$250$	−0.442358	−	1.34325i	−0.0279772	−	0.0849546i
$251$	−18.8826			−1.19186			−0.595928	−	0.803038i	$-0.703216\pi$
$251$	−18.8826			−1.19186			−0.595928	+	0.803038i	$0.703216\pi$
$252$		0			0
$253$	16.1379			1.01458
$254$	2.17214	+	6.59584i	0.136292	+	0.413860i
$255$	−0.526093			−0.0329452
$256$	−13.2367	−	8.98835i	−0.827292	−	0.561772i
$257$			25.8345i			1.61151i	0.592247	+	0.805757i	$0.298241\pi$
$257$			25.8345i			1.61151i	−0.592247	+	0.805757i	$0.701759\pi$
$258$	−2.31277	−	7.02288i	−0.143987	−	0.437225i
$259$		0			0
$260$	−3.89275	+	2.87580i	−0.241418	+	0.178349i
$261$	0.952661			0.0589682
$262$	−21.3234	+	7.02219i	−1.31736	+	0.433832i
$263$			10.6971i			0.659614i	0.944048	+	0.329807i	$0.106984\pi$
$263$			10.6971i			0.659614i	−0.944048	+	0.329807i	$0.893016\pi$
$264$	7.78456	+	5.51522i	0.479106	+	0.339438i
$265$			3.11491i			0.191347i
$266$		0			0
$267$			8.90478i			0.544963i
$268$	−11.6997	−	15.8370i	−0.714675	−	0.967402i
$269$			8.36512i			0.510030i	0.966937	+	0.255015i	$0.0820805\pi$
$269$			8.36512i			0.510030i	−0.966937	+	0.255015i	$0.917920\pi$
$270$	2.06827	+	6.28044i	0.125871	+	0.382216i
$271$	−27.1113			−1.64690			−0.823448	−	0.567392i	$-0.807952\pi$
$271$	−27.1113			−1.64690			−0.823448	+	0.567392i	$0.807952\pi$
$272$	2.23179	+	0.686127i	0.135322	+	0.0416025i
$273$		0			0
$274$	10.5340	−	3.46906i	0.636385	−	0.209574i
$275$		−	3.74246i		−	0.225679i
$276$	4.61858	+	6.25182i	0.278006	+	0.376315i
$277$	3.35983			0.201872			0.100936	−	0.994893i	$-0.467816\pi$
$277$	3.35983			0.201872			0.100936	+	0.994893i	$0.467816\pi$
$278$	23.3785	−	7.69899i	1.40215	−	0.461755i
$279$	−5.55380			−0.332497
$280$		0			0
$281$	−7.33947			−0.437836			−0.218918	−	0.975743i	$-0.570253\pi$
$281$	−7.33947			−0.437836			−0.218918	+	0.975743i	$0.570253\pi$
$282$	−14.0150	+	4.61542i	−0.834583	+	0.274844i
$283$	7.20564			0.428331			0.214165	−	0.976797i	$-0.431297\pi$
$283$	7.20564			0.428331			0.214165	+	0.976797i	$0.431297\pi$
$284$	11.8456	+	16.0344i	0.702905	+	0.951469i
$285$			5.55147i			0.328841i
$286$	−12.1650	+	4.00617i	−0.719332	+	0.236890i
$287$		0			0
$288$	−0.245892	−	12.3730i	−0.0144893	−	0.729089i
$289$	16.6593			0.979957
$290$	−0.192630	−	0.584935i	−0.0113116	−	0.0343486i
$291$			4.09220i			0.239889i
$292$	−11.6450	−	15.7629i	−0.681471	−	0.922456i
$293$		−	8.47879i		−	0.495336i	−0.968845	−	0.247668i	$-0.920336\pi$
$293$		−	8.47879i		−	0.495336i	0.968845	−	0.247668i	$-0.0796642\pi$
$294$		0			0
$295$		−	3.47068i		−	0.202071i
$296$	18.4780	−	26.0811i	1.07401	−	1.51593i
$297$			17.4981i			1.01534i
$298$	−2.21845	+	0.730577i	−0.128511	+	0.0423212i
$299$	−10.4349			−0.603464
$300$	1.44983	−	1.07107i	0.0837060	−	0.0618384i
$301$		0			0
$302$	3.25404	+	9.88112i	0.187249	+	0.568595i
$303$			8.24166i			0.473471i
$304$	7.24018	−	23.5504i	0.415253	−	1.35071i
$305$	−10.3877			−0.594795
$306$	0.564891	+	1.71533i	0.0322927	+	0.0980589i
$307$	10.4271			0.595104			0.297552	−	0.954706i	$-0.403830\pi$
$307$	10.4271			0.595104			0.297552	+	0.954706i	$0.403830\pi$
$308$		0			0
$309$	−9.22183			−0.524612
$310$	1.12299	+	3.41004i	0.0637817	+	0.193677i
$311$	7.92592			0.449437			0.224719	−	0.974424i	$-0.427854\pi$
$311$	7.92592			0.449437			0.224719	+	0.974424i	$0.427854\pi$
$312$	−5.03355	−	3.56618i	−0.284969	−	0.201895i
$313$			14.4667i			0.817703i	0.912601	+	0.408852i	$0.134071\pi$
$313$			14.4667i			0.817703i	−0.912601	+	0.408852i	$0.865929\pi$
$314$	−1.36357	−	4.14058i	−0.0769507	−	0.233666i
$315$		0			0
$316$	−0.545533	−	0.738447i	−0.0306886	−	0.0415409i
$317$	3.53706			0.198661			0.0993305	−	0.995054i	$-0.468330\pi$
$317$	3.53706			0.198661			0.0993305	+	0.995054i	$0.468330\pi$
$318$	−3.77104	+	1.24188i	−0.211469	+	0.0696409i
$319$		−	1.62970i		−	0.0912458i
$320$	−7.54735	+	2.65284i	−0.421910	+	0.148298i
$321$			5.70690i			0.318528i
$322$		0			0
$323$			3.59544i			0.200056i
$324$	3.77888	−	2.79167i	0.209938	−	0.155093i
$325$			2.41990i			0.134232i
$326$	−1.99864	−	6.06901i	−0.110695	−	0.336131i
$327$	16.9085			0.935041
$328$	16.9647	+	12.0192i	0.936717	+	0.663648i
$329$		0			0
$330$	4.53078	−	1.49207i	0.249411	−	0.0821359i
$331$		−	23.5297i		−	1.29331i	−0.762782	−	0.646655i	$-0.776167\pi$
$331$		−	23.5297i		−	1.29331i	0.762782	−	0.646655i	$-0.223833\pi$
$332$	−4.17839	+	3.08681i	−0.229319	+	0.169411i
$333$	24.7227			1.35479
$334$	22.7490	−	7.49169i	1.24477	−	0.409927i
$335$	−9.84499			−0.537890
$336$		0			0
$337$	5.10057			0.277846			0.138923	−	0.990303i	$-0.455636\pi$
$337$	5.10057			0.277846			0.138923	+	0.990303i	$0.455636\pi$
$338$	−9.59626	+	3.16023i	−0.521968	+	0.171894i
$339$	−3.76596			−0.204539
$340$	0.938993	−	0.693688i	0.0509240	−	0.0376205i
$341$			9.50081i			0.514497i
$342$	18.1006	−	5.96087i	0.978768	−	0.322327i
$343$		0			0
$344$	13.3880	+	9.48520i	0.721835	+	0.511407i
$345$	3.88640			0.209237
$346$	−0.0586997	−	0.178246i	−0.00315571	−	0.00958254i
$347$			1.66642i			0.0894580i	0.998999	+	0.0447290i	$0.0142424\pi$
$347$			1.66642i			0.0894580i	−0.998999	+	0.0447290i	$0.985758\pi$
$348$	0.631347	−	0.466412i	0.0338438	−	0.0250023i
$349$			27.6081i			1.47783i	0.673801	+	0.738913i	$0.264661\pi$
$349$			27.6081i			1.47783i	−0.673801	+	0.738913i	$0.735339\pi$
$350$		0			0
$351$		−	11.3144i		−	0.603918i
$352$	−21.1664	+	0.420643i	−1.12817	+	0.0224203i
$353$		−	27.1577i		−	1.44546i	−0.691131	−	0.722730i	$-0.742887\pi$
$353$		−	27.1577i		−	1.44546i	0.691131	−	0.722730i	$-0.257113\pi$
$354$	4.20174	−	1.38371i	0.223320	−	0.0735436i
$355$	9.96771			0.529031
$356$	−11.7415	−	15.8936i	−0.622300	−	0.842360i
$357$		0			0
$358$	7.12154	+	21.6251i	0.376385	+	1.14292i
$359$			16.7549i			0.884292i	0.896943	+	0.442146i	$0.145783\pi$
$359$			16.7549i			0.884292i	−0.896943	+	0.442146i	$0.854217\pi$
$360$	−5.04900	−	3.57712i	−0.266105	−	0.188531i
$361$	18.9400			0.996845
$362$	1.76641	+	5.36382i	0.0928404	+	0.281916i
$363$	2.70926			0.142199
$364$		0			0
$365$	−9.79892			−0.512899
$366$	−4.14142	−	12.5757i	−0.216476	−	0.657344i
$367$	−8.44425			−0.440787			−0.220393	−	0.975411i	$-0.570734\pi$
$367$	−8.44425			−0.440787			−0.220393	+	0.975411i	$0.570734\pi$
$368$	−16.4869	−	5.06862i	−0.859437	−	0.264220i
$369$			16.0811i			0.837147i
$370$	−4.99899	−	15.1798i	−0.259885	−	0.789158i
$371$		0			0
$372$	−3.68062	+	2.71908i	−0.190831	+	0.140978i
$373$	−10.3772			−0.537312			−0.268656	−	0.963236i	$-0.586580\pi$
$373$	−10.3772			−0.537312			−0.268656	+	0.963236i	$0.586580\pi$
$374$	2.93439	−	0.966350i	0.151734	−	0.0499688i
$375$		−	0.901278i		−	0.0465418i
$376$	18.9289	−	26.7175i	0.976183	−	1.37785i
$377$			1.05378i			0.0542723i
$378$		0			0
$379$			11.7976i			0.606002i	0.952990	+	0.303001i	$0.0979886\pi$
$379$			11.7976i			0.606002i	−0.952990	+	0.303001i	$0.902011\pi$
$380$	−7.31997	−	9.90849i	−0.375507	−	0.508295i
$381$			4.42560i			0.226730i
$382$	−8.86929	−	26.9322i	−0.453792	−	1.37797i
$383$	0.957045			0.0489027			0.0244514	−	0.999701i	$-0.492216\pi$
$383$	0.957045			0.0489027			0.0244514	+	0.999701i	$0.492216\pi$
$384$	−6.22067	−	8.07948i	−0.317447	−	0.412304i
$385$		0			0
$386$	−25.9773	+	8.55483i	−1.32221	+	0.435430i
$387$			12.6907i			0.645107i
$388$	−5.39583	−	7.30392i	−0.273932	−	0.370801i
$389$	−30.1641			−1.52938			−0.764689	−	0.644399i	$-0.777107\pi$
$389$	−30.1641			−1.52938			−0.764689	+	0.644399i	$0.777107\pi$
$390$	−2.92964	+	0.964785i	−0.148348	+	0.0488538i
$391$	2.51705			0.127293
$392$		0			0
$393$	−14.3073			−0.721708
$394$	2.19941	−	0.724308i	0.110805	−	0.0364901i
$395$	−0.459050			−0.0230973
$396$	−9.72983	−	13.1705i	−0.488942	−	0.661844i
$397$		−	6.20697i		−	0.311519i	−0.987795	−	0.155760i	$-0.950217\pi$
$397$		−	6.20697i		−	0.311519i	0.987795	−	0.155760i	$-0.0497825\pi$
$398$	1.05212	−	0.346483i	0.0527380	−	0.0173676i
$399$		0			0
$400$	−1.17544	+	3.82339i	−0.0587720	+	0.191170i
$401$	26.3130			1.31401			0.657004	−	0.753887i	$-0.271824\pi$
$401$	26.3130			1.31401			0.657004	+	0.753887i	$0.271824\pi$
$402$	−3.92507	−	11.9188i	−0.195765	−	0.594454i
$403$		−	6.14329i		−	0.306019i
$404$	−10.8672	−	14.7101i	−0.540662	−	0.731853i
$405$		−	2.34912i		−	0.116728i
$406$		0			0
$407$		−	42.2927i		−	2.09637i
$408$	1.21417	+	0.860219i	0.0601105	+	0.0425872i
$409$			18.4030i			0.909968i	0.890500	+	0.454984i	$0.150355\pi$
$409$			18.4030i			0.909968i	−0.890500	+	0.454984i	$0.849645\pi$
$410$	9.87380	−	3.25163i	0.487632	−	0.160587i
$411$	7.06801			0.348639
$412$	16.4595	−	12.1596i	0.810902	−	0.599060i
$413$		0			0
$414$	−4.17302	−	12.6716i	−0.205093	−	0.622777i
$415$			2.59747i			0.127505i
$416$	13.6863	−	0.271991i	0.671028	−	0.0133355i
$417$	15.6862			0.768158
$418$	−10.1972	−	30.9644i	−0.498760	−	1.51452i
$419$	35.2426			1.72171			0.860856	−	0.508848i	$-0.169928\pi$
$419$	35.2426			1.72171			0.860856	+	0.508848i	$0.169928\pi$
$420$		0			0
$421$	−15.6669			−0.763558			−0.381779	−	0.924254i	$-0.624688\pi$
$421$	−15.6669			−0.763558			−0.381779	+	0.924254i	$0.624688\pi$
$422$	−4.08090	−	12.3919i	−0.198655	−	0.603230i
$423$	25.3259			1.23139
$424$	5.09322	−	7.18891i	0.247349	−	0.349124i
$425$		−	0.583719i		−	0.0283145i
$426$	3.97400	+	12.0673i	0.192541	+	0.584664i
$427$		0			0
$428$	−7.52492	−	10.1859i	−0.363731	−	0.492355i
$429$	−8.16233			−0.394081
$430$	7.79213	−	2.56610i	0.375770	−	0.123748i
$431$			2.00541i			0.0965970i	0.998833	+	0.0482985i	$0.0153799\pi$
$431$			2.00541i			0.0965970i	−0.998833	+	0.0482985i	$0.984620\pi$
$432$	5.49584	−	17.8765i	0.264419	−	0.860083i
$433$		−	13.5978i		−	0.653469i	−0.945116	−	0.326734i	$-0.894052\pi$
$433$		−	13.5978i		−	0.653469i	0.945116	−	0.326734i	$-0.105948\pi$
$434$		0			0
$435$		−	0.392473i		−	0.0188176i
$436$	−30.1790	+	22.2949i	−1.44531	+	1.06773i
$437$		−	26.5606i		−	1.27057i
$438$	−3.90671	−	11.8630i	−0.186670	−	0.566835i
$439$	29.0493			1.38645			0.693224	−	0.720722i	$-0.256190\pi$
$439$	29.0493			1.38645			0.693224	+	0.720722i	$0.256190\pi$
$440$	−6.11933	+	8.63724i	−0.291728	+	0.411764i
$441$		0			0
$442$	−1.89740	+	0.624849i	−0.0902500	+	0.0297211i
$443$			14.6366i			0.695406i	0.937605	+	0.347703i	$0.113038\pi$
$443$			14.6366i			0.695406i	−0.937605	+	0.347703i	$0.886962\pi$
$444$	16.3842	−	12.1040i	0.777561	−	0.574428i
$445$	−9.88016			−0.468365
$446$	−32.5577	+	10.7219i	−1.54165	+	0.507696i
$447$	−1.48851			−0.0704040
$448$		0			0
$449$	−27.0699			−1.27751			−0.638754	−	0.769411i	$-0.720550\pi$
$449$	−27.0699			−1.27751			−0.638754	+	0.769411i	$0.720550\pi$
$450$	−2.93862	+	0.967745i	−0.138528	+	0.0456199i
$451$	27.5097			1.29538
$452$	6.72165	−	4.96567i	0.316160	−	0.233565i
$453$			6.62992i			0.311501i
$454$	14.2820	−	4.70335i	0.670290	−	0.220739i
$455$		0			0
$456$	9.07725	−	12.8122i	0.425081	−	0.599989i
$457$	−7.60612			−0.355799			−0.177900	−	0.984049i	$-0.556930\pi$
$457$	−7.60612			−0.355799			−0.177900	+	0.984049i	$0.556930\pi$
$458$	13.0552	+	39.6431i	0.610031	+	1.85240i
$459$			2.72921i			0.127389i
$460$	−6.93662	+	5.12447i	−0.323421	+	0.238930i
$461$		−	12.7953i		−	0.595936i	−0.954576	−	0.297968i	$-0.903691\pi$
$461$		−	12.7953i		−	0.595936i	0.954576	−	0.297968i	$-0.0963089\pi$
$462$		0			0
$463$		−	27.9178i		−	1.29745i	−0.761024	−	0.648724i	$-0.775303\pi$
$463$		−	27.9178i		−	1.29745i	0.761024	−	0.648724i	$-0.224697\pi$
$464$	−0.511861	+	1.66495i	−0.0237625	+	0.0772931i
$465$			2.28803i			0.106105i
$466$	−37.7054	+	12.4171i	−1.74667	+	0.575211i
$467$	−22.6108			−1.04630			−0.523152	−	0.852239i	$-0.675244\pi$
$467$	−22.6108			−1.04630			−0.523152	+	0.852239i	$0.675244\pi$
$468$	6.29138	+	8.51617i	0.290819	+	0.393660i
$469$		0			0
$470$	−5.12097	−	15.5502i	−0.236213	−	0.717276i
$471$		−	2.77820i		−	0.128012i
$472$	−5.67493	+	8.00999i	−0.261210	+	0.368689i
$473$	21.7099			0.998220
$474$	−0.183018	−	0.555745i	−0.00840628	−	0.0255262i
$475$	−6.15955			−0.282620
$476$		0			0
$477$	6.81448			0.312014
$478$	−6.02838	−	18.3056i	−0.275732	−	0.837279i
$479$	−21.9815			−1.00436			−0.502180	−	0.864763i	$-0.667468\pi$
$479$	−21.9815			−1.00436			−0.502180	+	0.864763i	$0.667468\pi$
$480$	−5.09739	+	0.101301i	−0.232663	+	0.00462375i
$481$			27.3468i			1.24691i
$482$	−1.86118	−	5.65160i	−0.0847744	−	0.257423i
$483$		0			0
$484$	−4.83560	+	3.57234i	−0.219800	+	0.162379i
$485$	−4.54044			−0.206171
$486$	21.6853	−	7.14137i	0.983663	−	0.323939i
$487$			25.3829i			1.15021i	0.818081	+	0.575103i	$0.195038\pi$
$487$			25.3829i			1.15021i	−0.818081	+	0.575103i	$0.804962\pi$
$488$	23.9737	+	16.9849i	1.08524	+	0.768872i
$489$		−	4.07212i		−	0.184147i
$490$		0			0
$491$		−	36.4635i		−	1.64557i	−0.568350	−	0.822787i	$-0.692418\pi$
$491$		−	36.4635i		−	1.64557i	0.568350	−	0.822787i	$-0.307582\pi$
$492$	7.87312	+	10.6573i	0.354948	+	0.480466i
$493$		−	0.254188i		−	0.0114480i
$494$	6.59357	+	20.0218i	0.296659	+	0.900825i
$495$	−8.18738			−0.367995
$496$	2.98403	−	9.70626i	0.133987	−	0.435824i
$497$		0			0
$498$	−3.14460	+	1.03558i	−0.140913	+	0.0464053i
$499$		−	11.8789i		−	0.531772i	−0.964004	−	0.265886i	$-0.914335\pi$
$499$		−	11.8789i		−	0.531772i	0.964004	−	0.265886i	$-0.0856646\pi$
$500$	1.18839	+	1.60864i	0.0531466	+	0.0719405i
$501$	15.2639			0.681940
$502$	25.3640	−	8.35284i	1.13205	−	0.372806i
$503$	−17.3055			−0.771614			−0.385807	−	0.922580i	$-0.626077\pi$
$503$	−17.3055			−0.771614			−0.385807	+	0.922580i	$0.626077\pi$
$504$		0			0
$505$	−9.14442			−0.406921
$506$	−21.6772	+	7.13871i	−0.963669	+	0.317355i
$507$	−6.43879			−0.285957
$508$	−5.83544	−	7.89900i	−0.258906	−	0.350462i
$509$		−	13.7083i		−	0.607609i	−0.952734	−	0.303805i	$-0.901743\pi$
$509$		−	13.7083i		−	0.607609i	0.952734	−	0.303805i	$-0.0982570\pi$
$510$	0.706674	−	0.232721i	0.0312921	−	0.0103051i
$511$		0			0
$512$	21.7562	+	6.21824i	0.961498	+	0.274810i
$513$	28.7993			1.27152
$514$	−11.4281	−	34.7022i	−0.504072	−	1.53065i
$515$		−	10.2319i		−	0.450873i
$516$	6.21325	+	8.41041i	0.273523	+	0.370248i
$517$		−	43.3247i		−	1.90542i
$518$		0			0
$519$		−	0.119597i		−	0.00524973i
$520$	3.95681	−	5.58490i	0.173517	−	0.244914i
$521$		−	36.3519i		−	1.59261i	−0.604897	−	0.796304i	$-0.706786\pi$
$521$		−	36.3519i		−	1.59261i	0.604897	−	0.796304i	$-0.293214\pi$
$522$	−1.27966	+	0.421417i	−0.0560093	+	0.0184449i
$523$	−4.26422			−0.186461			−0.0932306	−	0.995645i	$-0.529719\pi$
$523$	−4.26422			−0.186461			−0.0932306	+	0.995645i	$0.529719\pi$
$524$	25.5363	−	18.8651i	1.11556	−	0.824126i
$525$		0			0
$526$	−4.73196	−	14.3689i	−0.206323	−	0.626515i
$527$			1.48186i			0.0645508i
$528$	−12.8963	−	3.96476i	−0.561239	−	0.172544i
$529$	4.40578			0.191556
$530$	−1.37790	−	4.18410i	−0.0598523	−	0.181746i
$531$	−7.59279			−0.329499
$532$		0			0
$533$	−17.7879			−0.770482
$534$	−3.93910	−	11.9613i	−0.170461	−	0.517618i
$535$	−6.33201			−0.273757
$536$	22.7213	+	16.0976i	0.981411	+	0.695312i
$537$			14.5097i			0.626141i
$538$	−3.70038	−	11.2364i	−0.159535	−	0.484438i
$539$		0			0
$540$	−5.55640	−	7.52129i	−0.239110	−	0.323665i
$541$	−6.68266			−0.287310			−0.143655	−	0.989628i	$-0.545886\pi$
$541$	−6.68266			−0.287310			−0.143655	+	0.989628i	$0.545886\pi$
$542$	36.4173	−	11.9929i	1.56426	−	0.515139i
$543$			3.59895i			0.154446i
$544$	−3.30136	+	0.0656085i	−0.141545	+	0.00281294i
$545$			18.7605i			0.803614i
$546$		0			0
$547$			45.6888i			1.95351i	0.214353	+	0.976756i	$0.431236\pi$
$547$			45.6888i			1.95351i	−0.214353	+	0.976756i	$0.568764\pi$
$548$	−12.6153	+	9.31963i	−0.538898	+	0.398115i
$549$			22.7250i			0.969881i
$550$	1.65551	+	5.02706i	0.0705910	+	0.214355i
$551$	−2.68225			−0.114268
$552$	−8.96944	−	6.35469i	−0.381765	−	0.270474i
$553$		0			0
$554$	−4.51309	+	1.48625i	−0.191743	+	0.0631445i
$555$		−	10.1851i		−	0.432335i
$556$	−27.9975	+	20.6833i	−1.18736	+	0.877168i
$557$	4.88406			0.206944			0.103472	−	0.994632i	$-0.467005\pi$
$557$	4.88406			0.206944			0.103472	+	0.994632i	$0.467005\pi$
$558$	7.46014	−	2.45677i	0.315813	−	0.104003i
$559$	−14.0378			−0.593734
$560$		0			0
$561$	1.96888			0.0831263
$562$	9.85875	−	3.24667i	0.415866	−	0.136953i
$563$	−2.73584			−0.115302			−0.0576509	−	0.998337i	$-0.518361\pi$
$563$	−2.73584			−0.115302			−0.0576509	+	0.998337i	$0.518361\pi$
$564$	16.7840	−	12.3993i	0.706734	−	0.522105i
$565$		−	4.17847i		−	0.175789i
$566$	−9.67897	+	3.18747i	−0.406838	+	0.133979i
$567$		0			0
$568$	−23.0045	−	16.2983i	−0.965248	−	0.683861i
$569$	4.59348			0.192569			0.0962843	−	0.995354i	$-0.469304\pi$
$569$	4.59348			0.192569			0.0962843	+	0.995354i	$0.469304\pi$
$570$	−2.45573	−	7.45701i	−0.102859	−	0.312340i
$571$			5.61846i			0.235125i	0.993065	+	0.117563i	$0.0375081\pi$
$571$			5.61846i			0.235125i	−0.993065	+	0.117563i	$0.962492\pi$
$572$	14.5685	−	10.7626i	0.609139	−	0.450006i
$573$		−	18.0707i		−	0.754912i
$574$		0			0
$575$			4.31210i			0.179827i
$576$	5.80361	+	16.5113i	0.241817	+	0.687972i
$577$			34.3461i			1.42985i	0.699203	+	0.714924i	$0.253539\pi$
$577$			34.3461i			1.42985i	−0.699203	+	0.714924i	$0.746461\pi$
$578$	−22.3776	+	7.36936i	−0.930784	+	0.306525i
$579$	−17.4300			−0.724365
$580$	0.517501	+	0.700502i	0.0214881	+	0.0290868i
$581$		0			0
$582$	−1.81021	−	5.49684i	−0.0750358	−	0.227851i
$583$		−	11.6574i		−	0.482801i
$584$	22.6150	+	16.0223i	0.935814	+	0.663008i
$585$	5.29402			0.218881
$586$	3.75066	+	11.3891i	0.154938	+	0.470481i
$587$	40.1422			1.65685			0.828423	−	0.560103i	$-0.189238\pi$
$587$	40.1422			1.65685			0.828423	+	0.560103i	$0.189238\pi$
$588$		0			0
$589$	15.6369			0.644309
$590$	1.53528	+	4.66198i	0.0632065	+	0.191931i
$591$	1.47574			0.0607036
$592$	−13.2834	+	43.2073i	−0.545944	+	1.77581i
$593$			10.9337i			0.448992i	0.974475	+	0.224496i	$0.0720736\pi$
$593$			10.9337i			0.448992i	−0.974475	+	0.224496i	$0.927926\pi$
$594$	−7.74042	−	23.5043i	−0.317593	−	0.964394i
$595$		0			0
$596$	2.65675	−	1.96269i	0.108825	−	0.0803951i
$597$	0.705939			0.0288921
$598$	14.0166	−	4.61595i	0.573183	−	0.188760i
$599$			5.21309i			0.213001i	0.994313	+	0.106500i	$0.0339646\pi$
$599$			5.21309i			0.213001i	−0.994313	+	0.106500i	$0.966035\pi$
$600$	−1.47369	+	2.08006i	−0.0601631	+	0.0849182i
$601$			16.1103i			0.657154i	0.944477	+	0.328577i	$0.106569\pi$
$601$			16.1103i			0.657154i	−0.944477	+	0.328577i	$0.893431\pi$
$602$		0			0
$603$			21.5379i			0.877090i
$604$	−8.74198	−	11.8334i	−0.355706	−	0.481493i
$605$			3.00602i			0.122212i
$606$	−3.64576	−	11.0706i	−0.148099	−	0.449713i
$607$	9.65621			0.391933			0.195967	−	0.980611i	$-0.437216\pi$
$607$	9.65621			0.391933			0.195967	+	0.980611i	$0.437216\pi$
$608$	0.692317	+	34.8368i	0.0280772	+	1.41282i
$609$		0			0
$610$	13.9532	−	4.59506i	0.564949	−	0.186048i
$611$			28.0141i			1.13333i
$612$	−1.51758	−	2.05423i	−0.0613445	−	0.0830374i
$613$	7.84775			0.316968			0.158484	−	0.987362i	$-0.449339\pi$
$613$	7.84775			0.316968			0.158484	+	0.987362i	$0.449339\pi$
$614$	−14.0061	+	4.61249i	−0.565242	+	0.186145i
$615$	6.62501			0.267146
$616$		0			0
$617$	−28.8434			−1.16119			−0.580597	−	0.814191i	$-0.697181\pi$
$617$	−28.8434			−1.16119			−0.580597	+	0.814191i	$0.697181\pi$
$618$	12.3872	−	4.07935i	0.498287	−	0.164095i
$619$	2.48557			0.0999034			0.0499517	−	0.998752i	$-0.484093\pi$
$619$	2.48557			0.0999034			0.0499517	+	0.998752i	$0.484093\pi$
$620$	−3.01692	−	4.08377i	−0.121162	−	0.164008i
$621$		−	20.1615i		−	0.809052i
$622$	−10.6465	+	3.50609i	−0.426885	+	0.140581i
$623$		0			0
$624$	8.33885	+	2.56364i	0.333821	+	0.102628i
$625$	1.00000			0.0400000
$626$	−6.39943	−	19.4323i	−0.255773	−	0.776672i
$627$		−	20.7762i		−	0.829720i
$628$	3.66323	+	4.95864i	0.146179	+	0.197871i
$629$		−	6.59647i		−	0.263019i
$630$		0			0
$631$			8.90728i			0.354593i	0.984157	+	0.177297i	$0.0567352\pi$
$631$			8.90728i			0.354593i	−0.984157	+	0.177297i	$0.943265\pi$
$632$	1.05944	+	0.750598i	0.0421424	+	0.0298572i
$633$		−	8.31460i		−	0.330476i
$634$	−4.75115	+	1.56465i	−0.188692	+	0.0621400i
$635$	−4.91036			−0.194862
$636$	4.51609	−	3.33630i	0.179075	−	0.132293i
$637$		0			0
$638$	0.720911	+	2.18910i	0.0285412	+	0.0866672i
$639$		−	21.8063i		−	0.862645i
$640$	8.96447	−	6.90205i	0.354352	−	0.272827i
$641$	14.6330			0.577970			0.288985	−	0.957334i	$-0.406682\pi$
$641$	14.6330			0.577970			0.288985	+	0.957334i	$0.406682\pi$
$642$	−2.52449	−	7.66580i	−0.0996338	−	0.302545i
$643$	−24.2513			−0.956380			−0.478190	−	0.878256i	$-0.658707\pi$
$643$	−24.2513			−0.956380			−0.478190	+	0.878256i	$0.658707\pi$
$644$		0			0
$645$	5.22827			0.205863
$646$	−1.59047	−	4.82958i	−0.0625763	−	0.190017i
$647$	29.9156			1.17611			0.588053	−	0.808823i	$-0.299895\pi$
$647$	29.9156			1.17611			0.588053	+	0.808823i	$0.299895\pi$
$648$	−3.84106	+	5.42153i	−0.150891	+	0.212978i
$649$			12.9889i			0.509858i
$650$	−1.07046	−	3.25054i	−0.0419870	−	0.127496i
$651$		0			0
$652$	5.36935	+	7.26808i	0.210280	+	0.284640i
$653$	−15.5631			−0.609031			−0.304516	−	0.952507i	$-0.598495\pi$
$653$	−15.5631			−0.609031			−0.304516	+	0.952507i	$0.598495\pi$
$654$	−22.7123	+	7.47959i	−0.888121	+	0.292475i
$655$		−	15.8745i		−	0.620267i
$656$	−28.1046	−	8.64029i	−1.09730	−	0.337347i
$657$			21.4371i			0.836340i
$658$		0			0
$659$		−	30.2702i		−	1.17916i	−0.807710	−	0.589580i	$-0.799293\pi$
$659$		−	30.2702i		−	1.17916i	0.807710	−	0.589580i	$-0.200707\pi$
$660$	−5.42594	+	4.00845i	−0.211204	+	0.156029i
$661$		−	17.9220i		−	0.697084i	−0.937293	−	0.348542i	$-0.886677\pi$
$661$		−	17.9220i		−	0.697084i	0.937293	−	0.348542i	$-0.113323\pi$
$662$	10.4086	+	31.6063i	0.404540	+	1.22841i
$663$	−1.27309			−0.0494429
$664$	4.24714	−	5.99470i	0.164821	−	0.232640i
$665$		0			0
$666$	−33.2087	+	10.9363i	−1.28681	+	0.423772i
$667$			1.87776i			0.0727071i
$668$	−27.2436	+	20.1264i	−1.05409	+	0.778714i
$669$	−21.8452			−0.844585
$670$	13.2243	−	4.35501i	0.510899	−	0.168249i
$671$	38.8754			1.50077
$672$		0			0
$673$	21.1876			0.816723			0.408362	−	0.912820i	$-0.366100\pi$
$673$	21.1876			0.816723			0.408362	+	0.912820i	$0.366100\pi$
$674$	−6.85134	+	2.25628i	−0.263904	+	0.0869085i
$675$	−4.67556			−0.179962
$676$	11.4922	−	8.48996i	0.442009	−	0.326537i
$677$		−	25.2570i		−	0.970707i	−0.874318	−	0.485353i	$-0.838691\pi$
$677$		−	25.2570i		−	0.970707i	0.874318	−	0.485353i	$-0.161309\pi$
$678$	5.05863	−	1.66590i	0.194275	−	0.0639786i
$679$		0			0
$680$	−0.954444	+	1.34717i	−0.0366012	+	0.0516615i
$681$	9.58280			0.367214
$682$	−4.20275	−	12.7620i	−0.160932	−	0.488680i
$683$		−	22.0999i		−	0.845628i	−0.906216	−	0.422814i	$-0.861042\pi$
$683$		−	22.0999i		−	0.845628i	0.906216	−	0.422814i	$-0.138958\pi$
$684$	−21.6768	+	16.0139i	−0.828833	+	0.612306i
$685$			7.84221i			0.299635i
$686$		0			0
$687$			26.5993i			1.01483i
$688$	−22.1793	−	6.81868i	−0.845579	−	0.259960i
$689$			7.53778i			0.287167i
$690$	−5.22041	+	1.71918i	−0.198738	+	0.0654481i
$691$	−18.1102			−0.688943			−0.344471	−	0.938797i	$-0.611942\pi$
$691$	−18.1102			−0.688943			−0.344471	+	0.938797i	$0.611942\pi$
$692$	0.157697	+	0.213462i	0.00599473	+	0.00811461i
$693$		0			0
$694$	−0.737153	−	2.23841i	−0.0279819	−	0.0849691i
$695$			17.4044i			0.660188i
$696$	−0.641736	+	0.905790i	−0.0243249	+	0.0343339i
$697$	4.29073			0.162523
$698$	−12.2126	−	37.0845i	−0.462255	−	1.40367i
$699$	−25.2991			−0.956901
$700$		0			0
$701$	14.4315			0.545070			0.272535	−	0.962146i	$-0.412138\pi$
$701$	14.4315			0.545070			0.272535	+	0.962146i	$0.412138\pi$
$702$	5.00501	+	15.1981i	0.188902	+	0.573614i
$703$	−69.6077			−2.62530
$704$	28.2457	−	9.92814i	1.06455	−	0.374181i
$705$		−	10.4337i		−	0.392955i
$706$	12.0134	+	36.4796i	0.452131	+	1.37293i
$707$		0			0
$708$	−5.03189	+	3.71735i	−0.189110	+	0.139706i
$709$	−37.0262			−1.39055			−0.695275	−	0.718744i	$-0.744717\pi$
$709$	−37.0262			−1.39055			−0.695275	+	0.718744i	$0.744717\pi$
$710$	−13.3891	+	4.40929i	−0.502485	+	0.165478i
$711$			1.00426i			0.0376628i
$712$	22.8025	+	16.1551i	0.854559	+	0.605440i
$713$		−	10.9469i		−	0.409965i
$714$		0			0
$715$		−	9.05640i		−	0.338690i
$716$	−19.1320	−	25.8976i	−0.714997	−	0.967838i
$717$		−	12.2825i		−	0.458698i
$718$	−7.41168	−	22.5061i	−0.276601	−	0.839919i
$719$	20.1950			0.753145			0.376573	−	0.926387i	$-0.377103\pi$
$719$	20.1950			0.753145			0.376573	+	0.926387i	$0.377103\pi$
$720$	8.36443	+	2.57151i	0.311724	+	0.0958345i
$721$		0			0
$722$	−25.4412	+	8.37828i	−0.946824	+	0.311807i
$723$		−	3.79204i		−	0.141028i
$724$	−4.74545	−	6.42357i	−0.176363	−	0.238730i
$725$	0.435463			0.0161727
$726$	−3.63921	+	1.19846i	−0.135064	+	0.0444791i
$727$	10.7925			0.400272			0.200136	−	0.979768i	$-0.435862\pi$
$727$	10.7925			0.400272			0.200136	+	0.979768i	$0.435862\pi$
$728$		0			0
$729$	7.50278			0.277881
$730$	13.1624	−	4.33463i	0.487162	−	0.160432i
$731$	3.38613			0.125240
$732$	11.1259	+	15.0603i	0.411226	+	0.556646i
$733$			7.23222i			0.267128i	0.991040	+	0.133564i	$0.0426422\pi$
$733$			7.23222i			0.267128i	−0.991040	+	0.133564i	$0.957358\pi$
$734$	11.3427	−	3.73538i	0.418668	−	0.137875i
$735$		0			0
$736$	24.3881	−	0.484669i	0.898958	−	0.0178651i
$737$	36.8445			1.35719
$738$	−7.11359	−	21.6009i	−0.261855	−	0.795140i
$739$		−	1.98524i		−	0.0730284i	−0.999333	−	0.0365142i	$-0.988375\pi$
$739$		−	1.98524i		−	0.0730284i	0.999333	−	0.0365142i	$-0.0116254\pi$
$740$	13.4298	+	18.1789i	0.493688	+	0.668269i
$741$			13.4340i			0.493511i
$742$		0			0
$743$			19.8225i			0.727216i	0.931552	+	0.363608i	$0.118455\pi$
$743$			19.8225i			0.727216i	−0.931552	+	0.363608i	$0.881545\pi$
$744$	3.74118	−	5.28055i	0.137158	−	0.193595i
$745$		−	1.65155i		−	0.0605082i
$746$	13.9392	−	4.59045i	0.510351	−	0.168068i
$747$	5.68247			0.207911
$748$	−3.51414	+	2.59610i	−0.128490	+	0.0949228i
$749$		0			0
$750$	0.398687	+	1.21064i	0.0145580	+	0.0442064i
$751$		−	24.1007i		−	0.879448i	−0.898133	−	0.439724i	$-0.855076\pi$
$751$		−	24.1007i		−	0.879448i	0.898133	−	0.439724i	$-0.144924\pi$
$752$	−13.6075	+	44.2616i	−0.496215	+	1.61406i
$753$	17.0184			0.620186
$754$	−0.466147	−	1.41549i	−0.0169761	−	0.0515490i
$755$	−7.35613			−0.267717
$756$		0			0
$757$	34.8711			1.26741			0.633706	−	0.773574i	$-0.281533\pi$
$757$	34.8711			1.26741			0.633706	+	0.773574i	$0.281533\pi$
$758$	−5.21876	−	15.8471i	−0.189554	−	0.575594i
$759$	−14.5447			−0.527940
$760$	14.2156	+	10.0715i	0.515656	+	0.365333i
$761$			8.96763i			0.325076i	0.986702	+	0.162538i	$0.0519681\pi$
$761$			8.96763i			0.325076i	−0.986702	+	0.162538i	$0.948032\pi$
$762$	−1.95770	−	5.94469i	−0.0709200	−	0.215353i
$763$		0			0
$764$	23.8273	+	32.2533i	0.862043	+	1.16688i
$765$	−1.27700			−0.0461700
$766$	−1.28555	+	0.423356i	−0.0464488	+	0.0152965i
$767$		−	8.39870i		−	0.303260i
$768$	11.9299	+	8.10100i	0.430484	+	0.292320i
$769$			0.573577i			0.0206837i	0.999947	+	0.0103419i	$0.00329197\pi$
$769$			0.573577i			0.0206837i	−0.999947	+	0.0103419i	$0.996708\pi$
$770$		0			0
$771$		−	23.2841i		−	0.838556i
$772$	31.1098	−	22.9826i	1.11966	−	0.827160i
$773$			4.34850i			0.156405i	0.996938	+	0.0782023i	$0.0249180\pi$
$773$			4.34850i			0.156405i	−0.996938	+	0.0782023i	$0.975082\pi$
$774$	−5.61385	−	17.0468i	−0.201786	−	0.612736i
$775$	−2.53865			−0.0911910
$776$	10.4789	+	7.42411i	0.376170	+	0.266510i
$777$		0			0
$778$	40.5179	−	13.3433i	1.45264	−	0.478381i
$779$		−	45.2769i		−	1.62221i
$780$	3.50845	−	2.59189i	0.125623	−	0.0928047i
$781$	−37.3038			−1.33483
$782$	−3.38103	+	1.11344i	−0.120905	+	0.0398165i
$783$	−2.03603			−0.0727618
$784$		0			0
$785$	3.08251			0.110019
$786$	19.2183	−	6.32895i	0.685493	−	0.225746i
$787$	21.0496			0.750337			0.375168	−	0.926957i	$-0.377585\pi$
$787$	21.0496			0.750337			0.375168	+	0.926957i	$0.377585\pi$
$788$	−2.63396	+	1.94585i	−0.0938308	+	0.0693181i
$789$		−	9.64110i		−	0.343232i
$790$	0.616619	−	0.203065i	0.0219383	−	0.00722471i
$791$		0			0
$792$	18.8957	+	13.3873i	0.671428	+	0.475695i
$793$	−25.1371			−0.892645
$794$	2.74570	+	8.33752i	0.0974414	+	0.295887i
$795$		−	2.80740i		−	0.0995682i
$796$	−1.25999	+	0.930826i	−0.0446591	+	0.0329922i
$797$			14.7349i			0.521938i	0.965347	+	0.260969i	$0.0840420\pi$
$797$			14.7349i			0.521938i	−0.965347	+	0.260969i	$0.915958\pi$
$798$		0			0
$799$		−	6.75744i		−	0.239061i
$800$	−0.112397	−	5.65574i	−0.00397385	−	0.199961i
$801$			21.6148i			0.763722i
$802$	−35.3449	+	11.6397i	−1.24807	+	0.411014i
$803$	36.6721			1.29413
$804$	10.5447	+	14.2736i	0.371883	+	0.503390i
$805$		0			0
$806$	2.71753	+	8.25198i	0.0957210	+	0.290663i
$807$		−	7.53930i		−	0.265396i
$808$	21.1044	+	14.9521i	0.742451	+	0.526014i
$809$	−14.4762			−0.508955			−0.254477	−	0.967079i	$-0.581903\pi$
$809$	−14.4762			−0.508955			−0.254477	+	0.967079i	$0.581903\pi$
$810$	1.03915	+	3.15545i	0.0365120	+	0.110871i
$811$	−18.5825			−0.652521			−0.326260	−	0.945280i	$-0.605789\pi$
$811$	−18.5825			−0.652521			−0.326260	+	0.945280i	$0.605789\pi$
$812$		0			0
$813$	24.4348			0.856967
$814$	18.7085	+	56.8097i	0.655733	+	1.99118i
$815$	4.51816			0.158264
$816$	−2.01146	−	0.618391i	−0.0704152	−	0.0216480i
$817$		−	35.7313i		−	1.25008i
$818$	−8.14069	−	24.7198i	−0.284633	−	0.864306i
$819$		0			0
$820$	−11.8246	+	8.73551i	−0.412933	+	0.305057i
$821$	−16.4055			−0.572556			−0.286278	−	0.958147i	$-0.592418\pi$
$821$	−16.4055			−0.572556			−0.286278	+	0.958147i	$0.592418\pi$
$822$	−9.49410	+	3.12659i	−0.331145	+	0.109052i
$823$			43.8972i			1.53016i	0.643934	+	0.765081i	$0.277301\pi$
$823$			43.8972i			1.53016i	−0.643934	+	0.765081i	$0.722699\pi$
$824$	−16.7303	+	23.6143i	−0.582829	+	0.822645i
$825$			3.37300i			0.117433i
$826$		0			0
$827$		−	8.10796i		−	0.281941i	−0.990014	−	0.140971i	$-0.954978\pi$
$827$		−	8.10796i		−	0.281941i	0.990014	−	0.140971i	$-0.0450224\pi$
$828$	11.2108	+	15.1752i	0.389602	+	0.527375i
$829$			42.2224i			1.46645i	0.679989	+	0.733223i	$0.261985\pi$
$829$			42.2224i			1.46645i	−0.679989	+	0.733223i	$0.738015\pi$
$830$	−1.14901	−	3.48905i	−0.0398827	−	0.121107i
$831$	−3.02814			−0.105045
$832$	−18.2639	+	6.41961i	−0.633185	+	0.222560i
$833$		0			0
$834$	−21.0705	+	6.93893i	−0.729613	+	0.240275i
$835$			16.9358i			0.586088i
$836$	27.3947	+	37.0822i	0.947466	+	1.28251i
$837$	11.8696			0.410274
$838$	−47.3396	+	15.5898i	−1.63532	+	0.538542i
$839$	−31.8404			−1.09925			−0.549627	−	0.835410i	$-0.685230\pi$
$839$	−31.8404			−1.09925			−0.549627	+	0.835410i	$0.685230\pi$
$840$		0			0
$841$	−28.8104			−0.993461
$842$	21.0446	−	6.93037i	0.725243	−	0.238836i
$843$	6.61491			0.227829
$844$	10.9633	+	14.8403i	0.377374	+	0.510823i
$845$		−	7.14406i		−	0.245763i
$846$	−34.0191	+	11.2031i	−1.16960	+	0.385171i
$847$		0			0
$848$	−3.66139	+	11.9095i	−0.125733	+	0.408975i
$849$	−6.49429			−0.222883
$850$	0.258212	+	0.784080i	0.00885662	+	0.0268937i
$851$			48.7301i			1.67045i
$852$	−10.6761	−	14.4515i	−0.365759	−	0.495100i
$853$		−	16.2023i		−	0.554755i	−0.960761	−	0.277378i	$-0.910535\pi$
$853$		−	16.2023i		−	0.554755i	0.960761	−	0.277378i	$-0.0894653\pi$
$854$		0			0
$855$			13.4752i			0.460843i
$856$	14.6137	+	10.3535i	0.499485	+	0.353876i
$857$		−	40.9525i		−	1.39891i	−0.714677	−	0.699455i	$-0.753426\pi$
$857$		−	40.9525i		−	1.39891i	0.714677	−	0.699455i	$-0.246574\pi$
$858$	10.9641	−	3.61067i	0.374307	−	0.123266i
$859$	12.0528			0.411236			0.205618	−	0.978632i	$-0.434080\pi$
$859$	12.0528			0.411236			0.205618	+	0.978632i	$0.434080\pi$
$860$	−9.33165	+	6.89382i	−0.318206	+	0.235077i
$861$		0			0
$862$	−0.887107	−	2.69376i	−0.0302150	−	0.0917499i
$863$		−	0.570852i		−	0.0194320i	−0.999953	−	0.00971602i	$-0.996907\pi$
$863$		−	0.570852i		−	0.0194320i	0.999953	−	0.00971602i	$-0.00309275\pi$
$864$	0.525521	+	26.4437i	0.0178786	+	0.899634i
$865$	0.132697			0.00451184
$866$	6.01509	+	18.2652i	0.204401	+	0.620678i
$867$	−15.0146			−0.509924
$868$		0			0
$869$	1.71798			0.0582784
$870$	0.173613	+	0.527189i	0.00588605	+	0.0178734i
$871$	−23.8239			−0.807243
$872$	30.6755	−	43.2975i	1.03880	−	1.46624i
$873$			9.93310i			0.336185i
$874$	11.7493	+	35.6775i	0.397426	+	1.20681i
$875$		0			0
$876$	10.4954	+	14.2068i	0.354605	+	0.480003i
$877$	18.9439			0.639689			0.319844	−	0.947470i	$-0.396369\pi$
$877$	18.9439			0.639689			0.319844	+	0.947470i	$0.396369\pi$
$878$	−39.0205	+	12.8502i	−1.31688	+	0.433673i
$879$			7.64174i			0.257750i
$880$	4.39904	−	14.3089i	0.148292	−	0.482353i
$881$		−	35.7695i		−	1.20511i	−0.798079	−	0.602553i	$-0.794150\pi$
$881$		−	35.7695i		−	1.20511i	0.798079	−	0.602553i	$-0.205850\pi$
$882$		0			0
$883$			25.4594i			0.856776i	0.903595	+	0.428388i	$0.140918\pi$
$883$			25.4594i			0.856776i	−0.903595	+	0.428388i	$0.859082\pi$
$884$	2.27227	−	1.67866i	0.0764248	−	0.0564594i
$885$			3.12804i			0.105148i
$886$	−6.47462	−	19.6606i	−0.217519	−	0.660512i
$887$	10.6049			0.356076			0.178038	−	0.984024i	$-0.443025\pi$
$887$	10.6049			0.356076			0.178038	+	0.984024i	$0.443025\pi$
$888$	−16.6538	+	23.5063i	−0.558865	+	0.788821i
$889$		0			0
$890$	13.2715	−	4.37057i	0.444863	−	0.146502i
$891$			8.79148i			0.294525i
$892$	38.9903	−	28.8043i	1.30549	−	0.964440i
$893$	−71.3062			−2.38617
$894$	1.99944	−	0.658453i	0.0668712	−	0.0220220i
$895$	−16.0991			−0.538132
$896$		0			0
$897$	9.40472			0.314014
$898$	36.3617	−	11.9746i	1.21340	−	0.399597i
$899$	−1.10549			−0.0368701
$900$	3.51922	−	2.59985i	0.117307	−	0.0866615i
$901$		−	1.81823i		−	0.0605741i
$902$	−36.9523	+	12.1691i	−1.23038	+	0.405187i
$903$		0			0
$904$	−6.83225	+	9.64350i	−0.227237	+	0.320738i
$905$	−3.99317			−0.132737
$906$	−2.93280	−	8.90564i	−0.0974356	−	0.295870i
$907$		−	15.3638i		−	0.510146i	−0.966922	−	0.255073i	$-0.917900\pi$
$907$		−	15.3638i		−	0.510146i	0.966922	−	0.255073i	$-0.0820996\pi$
$908$	−17.1038	+	12.6355i	−0.567609	+	0.419325i
$909$			20.0052i			0.663531i
$910$		0			0
$911$			22.0734i			0.731324i	0.930748	+	0.365662i	$0.119157\pi$
$911$			22.0734i			0.731324i	−0.930748	+	0.365662i	$0.880843\pi$
$912$	−6.52542	+	21.2254i	−0.216078	+	0.702845i
$913$		−	9.72092i		−	0.321715i
$914$	10.2169	−	3.36462i	0.337945	−	0.111292i
$915$	9.36216			0.309504
$916$	−35.0729	−	47.4755i	−1.15884	−	1.56864i
$917$		0			0
$918$	−1.20729	−	3.66601i	−0.0398464	−	0.120996i
$919$			52.1460i			1.72014i	0.510178	+	0.860069i	$0.329580\pi$
$919$			52.1460i			1.72014i	−0.510178	+	0.860069i	$0.670420\pi$
$920$	7.05076	−	9.95191i	0.232457	−	0.328105i
$921$	−9.39768			−0.309664
$922$	5.66010	+	17.1873i	0.186405	+	0.566033i
$923$	24.1209			0.793949
$924$		0			0
$925$	11.3008			0.371567
$926$	12.3496	+	37.5005i	0.405834	+	1.23234i
$927$	−22.3844			−0.735200
$928$	−0.0489449	−	2.46286i	−0.00160669	−	0.0808474i
$929$			28.7182i			0.942215i	0.882076	+	0.471107i	$0.156146\pi$
$929$			28.7182i			0.942215i	−0.882076	+	0.471107i	$0.843854\pi$
$930$	−1.01213	−	3.07340i	−0.0331890	−	0.100781i
$931$		0			0
$932$	45.1549	−	33.3585i	1.47910	−	1.09270i
$933$	−7.14345			−0.233866
$934$	30.3720	−	10.0021i	0.993801	−	0.327278i
$935$			2.18455i			0.0714423i
$936$	−12.2181	−	8.65630i	−0.399361	−	0.282940i
$937$			44.9045i			1.46697i	0.679707	+	0.733484i	$0.262107\pi$
$937$			44.9045i			1.46697i	−0.679707	+	0.733484i	$0.737893\pi$
$938$		0			0
$939$		−	13.0385i		−	0.425495i
$940$	13.7575	+	18.6225i	0.448719	+	0.607398i
$941$		−	17.7508i		−	0.578660i	−0.957229	−	0.289330i	$-0.906567\pi$
$941$		−	17.7508i		−	0.578660i	0.957229	−	0.289330i	$-0.0934325\pi$
$942$	1.22896	+	3.73181i	0.0400416	+	0.121589i
$943$	−31.6969			−1.03219
$944$	4.07957	−	13.2698i	0.132779	−	0.431894i
$945$		0			0
$946$	−29.1618	+	9.60352i	−0.948130	+	0.312237i
$947$			37.0775i			1.20486i	0.798173	+	0.602428i	$0.205800\pi$
$947$			37.0775i			1.20486i	−0.798173	+	0.602428i	$0.794200\pi$
$948$	0.491677	+	0.665546i	0.0159689	+	0.0216159i
$949$	−23.7125			−0.769739
$950$	8.27381	−	2.72472i	0.268438	−	0.0884017i
$951$	−3.18787			−0.103374
$952$		0			0
$953$	−28.5420			−0.924567			−0.462283	−	0.886732i	$-0.652970\pi$
$953$	−28.5420			−0.924567			−0.462283	+	0.886732i	$0.652970\pi$
$954$	−9.15355	+	3.01444i	−0.296357	+	0.0975961i
$955$	20.0500			0.648804
$956$	16.1953	+	21.9223i	0.523792	+	0.709018i
$957$			1.46882i			0.0474800i
$958$	29.5266	−	9.72368i	0.953962	−	0.314158i
$959$		0			0
$960$	6.80226	−	2.39094i	0.219542	−	0.0771674i
$961$	−24.5552			−0.792105
$962$	−12.0971	−	36.7336i	−0.390025	−	1.18434i
$963$			13.8525i			0.446391i
$964$	5.00006	+	6.76820i	0.161041	+	0.217989i
$965$		−	19.3392i		−	0.622550i
$966$		0			0
$967$			5.33936i			0.171702i	0.996308	+	0.0858510i	$0.0273609\pi$
$967$			5.33936i			0.171702i	−0.996308	+	0.0858510i	$0.972639\pi$
$968$	4.91517	−	6.93760i	0.157980	−	0.222983i
$969$		−	3.24050i		−	0.104100i
$970$	6.09894	−	2.00850i	0.195825	−	0.0644890i
$971$	10.9981			0.352946			0.176473	−	0.984305i	$-0.443531\pi$
$971$	10.9981			0.352946			0.176473	+	0.984305i	$0.443531\pi$
$972$	−25.9697	+	19.1853i	−0.832978	+	0.615368i
$973$		0			0
$974$	−11.2283	−	34.0955i	−0.359778	−	1.09249i
$975$		−	2.18101i		−	0.0698481i
$976$	−39.7161	−	12.2101i	−1.27128	−	0.390835i
$977$	−31.4868			−1.00735			−0.503676	−	0.863893i	$-0.668019\pi$
$977$	−31.4868			−1.00735			−0.503676	+	0.863893i	$0.668019\pi$
$978$	1.80133	+	5.46987i	0.0576002	+	0.174907i
$979$	36.9761			1.18176
$980$		0			0
$981$	41.0424			1.31038
$982$	16.1299	+	48.9796i	0.514726	+	1.56300i
$983$	34.5524			1.10205			0.551025	−	0.834489i	$-0.314237\pi$
$983$	34.5524			1.10205			0.551025	+	0.834489i	$0.314237\pi$
$984$	−15.2899	−	10.8326i	−0.487424	−	0.345331i
$985$			1.63738i			0.0521713i
$986$	0.112442	+	0.341438i	0.00358088	+	0.0108736i
$987$		0			0
$988$	−17.7136	−	23.9776i	−0.563545	−	0.762829i
$989$	−25.0143			−0.795409
$990$	10.9977	−	3.62175i	0.349530	−	0.115107i
$991$		−	55.2718i		−	1.75577i	−0.478874	−	0.877884i	$-0.658955\pi$
$991$		−	55.2718i		−	1.75577i	0.478874	−	0.877884i	$-0.341045\pi$
$992$	0.285338	+	14.3579i	0.00905948	+	0.455865i
$993$			21.2068i			0.672978i
$994$		0			0
$995$			0.783264i			0.0248311i
$996$	3.76589	−	2.78208i	0.119327	−	0.0881535i
$997$		−	15.2817i		−	0.483978i	−0.970279	−	0.241989i	$-0.922200\pi$
$997$		−	15.2817i		−	0.483978i	0.970279	−	0.241989i	$-0.0777997\pi$
$998$	5.25472	+	15.9563i	0.166335	+	0.505089i
$999$	−52.8374			−1.67170

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.g.a.391.7		32
4.3	odd	2	inner	980.2.g.a.391.6		32
7.2	even	3		140.2.o.a.31.13	yes	32
7.3	odd	6		140.2.o.a.131.9	yes	32
7.4	even	3		980.2.o.f.411.9		32
7.5	odd	6		980.2.o.f.31.13		32
7.6	odd	2	inner	980.2.g.a.391.8		32
28.3	even	6		140.2.o.a.131.13	yes	32
28.11	odd	6		980.2.o.f.411.13		32
28.19	even	6		980.2.o.f.31.9		32
28.23	odd	6		140.2.o.a.31.9	✓	32
28.27	even	2	inner	980.2.g.a.391.5		32
35.2	odd	12		700.2.t.c.199.6		32
35.3	even	12		700.2.t.c.299.1		32
35.9	even	6		700.2.p.c.451.4		32
35.17	even	12		700.2.t.d.299.16		32
35.23	odd	12		700.2.t.d.199.11		32
35.24	odd	6		700.2.p.c.551.8		32
140.3	odd	12		700.2.t.c.299.6		32
140.23	even	12		700.2.t.d.199.16		32
140.59	even	6		700.2.p.c.551.4		32
140.79	odd	6		700.2.p.c.451.8		32
140.87	odd	12		700.2.t.d.299.11		32
140.107	even	12		700.2.t.c.199.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.o.a.31.9	✓	32	28.23	odd	6
140.2.o.a.31.13	yes	32	7.2	even	3
140.2.o.a.131.9	yes	32	7.3	odd	6
140.2.o.a.131.13	yes	32	28.3	even	6
700.2.p.c.451.4		32	35.9	even	6
700.2.p.c.451.8		32	140.79	odd	6
700.2.p.c.551.4		32	140.59	even	6
700.2.p.c.551.8		32	35.24	odd	6
700.2.t.c.199.1		32	140.107	even	12
700.2.t.c.199.6		32	35.2	odd	12
700.2.t.c.299.1		32	35.3	even	12
700.2.t.c.299.6		32	140.3	odd	12
700.2.t.d.199.11		32	35.23	odd	12
700.2.t.d.199.16		32	140.23	even	12
700.2.t.d.299.11		32	140.87	odd	12
700.2.t.d.299.16		32	35.17	even	12
980.2.g.a.391.5		32	28.27	even	2	inner
980.2.g.a.391.6		32	4.3	odd	2	inner
980.2.g.a.391.7		32	1.1	even	1	trivial
980.2.g.a.391.8		32	7.6	odd	2	inner
980.2.o.f.31.9		32	28.19	even	6
980.2.o.f.31.13		32	7.5	odd	6
980.2.o.f.411.9		32	7.4	even	3
980.2.o.f.411.13		32	28.11	odd	6

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.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34325 + 0.442358i) q^{2} -0.901278 q^{3} +(1.60864 - 1.18839i) q^{4} -1.00000i q^{5} +(1.21064 - 0.398687i) q^{6} +(-1.63511 + 2.30790i) q^{8} -2.18770 q^{9} +O(q^{10})\)	\(q+(-1.34325 + 0.442358i) q^{2} -0.901278 q^{3} +(1.60864 - 1.18839i) q^{4} -1.00000i q^{5} +(1.21064 - 0.398687i) q^{6} +(-1.63511 + 2.30790i) q^{8} -2.18770 q^{9} +(0.442358 + 1.34325i) q^{10} +3.74246i q^{11} +(-1.44983 + 1.07107i) q^{12} -2.41990i q^{13} +0.901278i q^{15} +(1.17544 - 3.82339i) q^{16} +0.583719i q^{17} +(2.93862 - 0.967745i) q^{18} +6.15955 q^{19} +(-1.18839 - 1.60864i) q^{20} +(-1.65551 - 5.02706i) q^{22} -4.31210i q^{23} +(1.47369 - 2.08006i) q^{24} -1.00000 q^{25} +(1.07046 + 3.25054i) q^{26} +4.67556 q^{27} -0.435463 q^{29} +(-0.398687 - 1.21064i) q^{30} +2.53865 q^{31} +(0.112397 + 5.65574i) q^{32} -3.37300i q^{33} +(-0.258212 - 0.784080i) q^{34} +(-3.51922 + 2.59985i) q^{36} -11.3008 q^{37} +(-8.27381 + 2.72472i) q^{38} +2.18101i q^{39} +(2.30790 + 1.63511i) q^{40} -7.35068i q^{41} -5.80096i q^{43} +(4.44752 + 6.02027i) q^{44} +2.18770i q^{45} +(1.90749 + 5.79223i) q^{46} -11.5765 q^{47} +(-1.05940 + 3.44594i) q^{48} +(1.34325 - 0.442358i) q^{50} -0.526093i q^{51} +(-2.87580 - 3.89275i) q^{52} -3.11491 q^{53} +(-6.28044 + 2.06827i) q^{54} +3.74246 q^{55} -5.55147 q^{57} +(0.584935 - 0.192630i) q^{58} +3.47068 q^{59} +(1.07107 + 1.44983i) q^{60} -10.3877i q^{61} +(-3.41004 + 1.12299i) q^{62} +(-2.65284 - 7.54735i) q^{64} -2.41990 q^{65} +(1.49207 + 4.53078i) q^{66} -9.84499i q^{67} +(0.693688 + 0.938993i) q^{68} +3.88640i q^{69} +9.96771i q^{71} +(3.57712 - 5.04900i) q^{72} -9.79892i q^{73} +(15.1798 - 4.99899i) q^{74} +0.901278 q^{75} +(9.90849 - 7.31997i) q^{76} +(-0.964785 - 2.92964i) q^{78} -0.459050i q^{79} +(-3.82339 - 1.17544i) q^{80} +2.34912 q^{81} +(3.25163 + 9.87380i) q^{82} -2.59747 q^{83} +0.583719 q^{85} +(2.56610 + 7.79213i) q^{86} +0.392473 q^{87} +(-8.63724 - 6.11933i) q^{88} -9.88016i q^{89} +(-0.967745 - 2.93862i) q^{90} +(-5.12447 - 6.93662i) q^{92} -2.28803 q^{93} +(15.5502 - 5.12097i) q^{94} -6.15955i q^{95} +(-0.101301 - 5.09739i) q^{96} -4.54044i q^{97} -8.18738i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{2} + 4 q^{4} - 4 q^{8} + 32 q^{9}+O(q^{10}) \) 32 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 + 32 * q^9	\( 32 q - 4 q^{2} + 4 q^{4} - 4 q^{8} + 32 q^{9} + 28 q^{16} - 8 q^{22} - 32 q^{25} - 40 q^{29} - 4 q^{32} + 60 q^{36} - 16 q^{37} + 36 q^{44} - 4 q^{46} + 4 q^{50} + 16 q^{53} + 48 q^{57} - 4 q^{58} - 28 q^{60} + 4 q^{64} - 8 q^{65} - 8 q^{72} - 76 q^{74} + 120 q^{78} + 72 q^{81} - 56 q^{86} - 8 q^{88} - 4 q^{92} + 16 q^{93}+O(q^{100}) \) 32 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 + 32 * q^9 + 28 * q^16 - 8 * q^22 - 32 * q^25 - 40 * q^29 - 4 * q^32 + 60 * q^36 - 16 * q^37 + 36 * q^44 - 4 * q^46 + 4 * q^50 + 16 * q^53 + 48 * q^57 - 4 * q^58 - 28 * q^60 + 4 * q^64 - 8 * q^65 - 8 * q^72 - 76 * q^74 + 120 * q^78 + 72 * q^81 - 56 * q^86 - 8 * q^88 - 4 * q^92 + 16 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more