LMFDB - Embedded newform 804.2.y.b.73.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(49,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 0, 46]))

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

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

chi := DirichletCharacter("804.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.y (of order $33$, degree $20$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$6$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			73.2
Character	$\chi$	$=$	804.73
Dual form			804.2.y.b.793.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415415 + 0.909632i) q^{3} +(-1.98933 - 0.584119i) q^{5} +(1.45645 - 0.280708i) q^{7} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.415415 + 0.909632i) q^{3} +(-1.98933 - 0.584119i) q^{5} +(1.45645 - 0.280708i) q^{7} +(-0.654861 - 0.755750i) q^{9} +(-0.875823 + 0.835095i) q^{11} +(0.0865958 - 1.81787i) q^{13} +(1.35773 - 1.56690i) q^{15} +(-4.57862 + 3.60066i) q^{17} +(-1.94659 - 0.375175i) q^{19} +(-0.349691 + 1.44145i) q^{21} +(-3.82426 + 0.365173i) q^{23} +(-0.590046 - 0.379199i) q^{25} +(0.959493 - 0.281733i) q^{27} +(1.66371 - 2.88163i) q^{29} +(-0.106537 - 2.23649i) q^{31} +(-0.395799 - 1.14359i) q^{33} +(-3.06133 - 0.292321i) q^{35} +(-3.40770 - 5.90231i) q^{37} +(1.61762 + 0.833941i) q^{39} +(-11.1387 - 4.45926i) q^{41} +(-1.31227 - 9.12705i) q^{43} +(0.861284 + 1.88595i) q^{45} +(1.50381 + 2.11180i) q^{47} +(-4.45612 + 1.78396i) q^{49} +(-1.37325 - 5.66063i) q^{51} +(-0.940432 + 6.54085i) q^{53} +(2.23009 - 1.14969i) q^{55} +(1.14991 - 1.61483i) q^{57} +(5.71618 - 3.67357i) q^{59} +(5.70773 + 5.44231i) q^{61} +(-1.16592 - 0.916889i) q^{63} +(-1.23412 + 3.56575i) q^{65} +(-5.94150 - 5.63015i) q^{67} +(1.25648 - 3.63037i) q^{69} +(-9.08998 - 7.14844i) q^{71} +(8.69359 + 8.28933i) q^{73} +(0.590046 - 0.379199i) q^{75} +(-1.04118 + 1.46213i) q^{77} +(-3.62828 + 1.87051i) q^{79} +(-0.142315 + 0.989821i) q^{81} +(-1.16023 - 4.78254i) q^{83} +(11.2116 - 4.48844i) q^{85} +(1.93009 + 2.71043i) q^{87} +(-0.134913 - 0.295419i) q^{89} +(-0.384169 - 2.67195i) q^{91} +(2.07864 + 0.832163i) q^{93} +(3.65326 + 1.88338i) q^{95} +(-0.558643 - 0.967597i) q^{97} +(1.20466 + 0.115032i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9}+O(q^{10}) $ 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9	$ 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9} + 11 q^{11} + 2 q^{13} - 9 q^{15} + 48 q^{17} - 4 q^{19} - q^{21} + 22 q^{23} - 42 q^{25} + 12 q^{27} - q^{29} + 27 q^{31} + 17 q^{35} - 8 q^{37} - 2 q^{39} - 58 q^{41} - 17 q^{43} - 2 q^{45} - 84 q^{47} + 101 q^{49} - 26 q^{51} + 28 q^{53} - 9 q^{55} + 26 q^{57} + 34 q^{59} + 16 q^{61} + 12 q^{63} + 144 q^{65} + 23 q^{67} + 11 q^{69} + 173 q^{71} - 2 q^{73} + 42 q^{75} + 128 q^{77} + 31 q^{79} - 12 q^{81} + 47 q^{83} - 75 q^{85} - 10 q^{87} - 67 q^{89} + 16 q^{91} + 6 q^{93} - 79 q^{95} + 10 q^{97}+O(q^{100}) $ 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9 + 11 * q^11 + 2 * q^13 - 9 * q^15 + 48 * q^17 - 4 * q^19 - q^21 + 22 * q^23 - 42 * q^25 + 12 * q^27 - q^29 + 27 * q^31 + 17 * q^35 - 8 * q^37 - 2 * q^39 - 58 * q^41 - 17 * q^43 - 2 * q^45 - 84 * q^47 + 101 * q^49 - 26 * q^51 + 28 * q^53 - 9 * q^55 + 26 * q^57 + 34 * q^59 + 16 * q^61 + 12 * q^63 + 144 * q^65 + 23 * q^67 + 11 * q^69 + 173 * q^71 - 2 * q^73 + 42 * q^75 + 128 * q^77 + 31 * q^79 - 12 * q^81 + 47 * q^83 - 75 * q^85 - 10 * q^87 - 67 * q^89 + 16 * q^91 + 6 * q^93 - 79 * q^95 + 10 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{20}{33}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.415415	+	0.909632i	−0.239840	+	0.525176i
$3$	−0.415415	+	0.909632i	−0.239840	+	0.525176i
$4$		0			0
$5$	−1.98933	−	0.584119i	−0.889653	−	0.261226i	−0.195200	−	0.980763i	$-0.562536\pi$
$5$	−1.98933	−	0.584119i	−0.889653	−	0.261226i	−0.694453	+	0.719538i	$0.744354\pi$
$6$		0			0
$7$	1.45645	−	0.280708i	0.550487	−	0.106098i	0.0935796	−	0.995612i	$-0.470169\pi$
$7$	1.45645	−	0.280708i	0.550487	−	0.106098i	0.456908	+	0.889514i	$0.348957\pi$
$8$		0			0
$9$	−0.654861	−	0.755750i	−0.218287	−	0.251917i
$10$		0			0
$11$	−0.875823	+	0.835095i	−0.264070	+	0.251791i	−0.810533	−	0.585693i	$-0.800823\pi$
$11$	−0.875823	+	0.835095i	−0.264070	+	0.251791i	0.546463	+	0.837483i	$0.315974\pi$
$12$		0			0
$13$	0.0865958	−	1.81787i	0.0240174	−	0.504187i	−0.954524	−	0.298135i	$-0.903635\pi$
$13$	0.0865958	−	1.81787i	0.0240174	−	0.504187i	0.978541	−	0.206052i	$-0.0660615\pi$
$14$		0			0
$15$	1.35773	−	1.56690i	0.350564	−	0.404573i
$16$		0			0
$17$	−4.57862	+	3.60066i	−1.11048	+	0.873289i	−0.992803	−	0.119763i	$-0.961787\pi$
$17$	−4.57862	+	3.60066i	−1.11048	+	0.873289i	−0.117675	+	0.993052i	$0.537544\pi$
$18$		0			0
$19$	−1.94659	−	0.375175i	−0.446578	−	0.0860709i	−0.0389960	−	0.999239i	$-0.512416\pi$
$19$	−1.94659	−	0.375175i	−0.446578	−	0.0860709i	−0.407582	+	0.913168i	$0.633628\pi$
$20$		0			0
$21$	−0.349691	+	1.44145i	−0.0763089	+	0.314549i
$22$		0			0
$23$	−3.82426	+	0.365173i	−0.797414	+	0.0761438i	−0.485806	−	0.874067i	$-0.661474\pi$
$23$	−3.82426	+	0.365173i	−0.797414	+	0.0761438i	−0.311608	+	0.950211i	$0.600868\pi$
$24$		0			0
$25$	−0.590046	−	0.379199i	−0.118009	−	0.0758399i
$26$		0			0
$27$	0.959493	−	0.281733i	0.184655	−	0.0542195i
$28$		0			0
$29$	1.66371	−	2.88163i	0.308943	−	0.535105i	−0.669188	−	0.743093i	$-0.733358\pi$
$29$	1.66371	−	2.88163i	0.308943	−	0.535105i	0.978131	+	0.207988i	$0.0666914\pi$
$30$		0			0
$31$	−0.106537	−	2.23649i	−0.0191347	−	0.401686i	−0.988035	−	0.154233i	$-0.950709\pi$
$31$	−0.106537	−	2.23649i	−0.0191347	−	0.401686i	0.968900	−	0.247453i	$-0.0795936\pi$
$32$		0			0
$33$	−0.395799	−	1.14359i	−0.0688998	−	0.199073i
$34$		0			0
$35$	−3.06133	−	0.292321i	−0.517459	−	0.0494113i
$36$		0			0
$37$	−3.40770	−	5.90231i	−0.560222	−	0.970334i	−0.997477	−	0.0709956i	$-0.977382\pi$
$37$	−3.40770	−	5.90231i	−0.560222	−	0.970334i	0.437254	−	0.899338i	$-0.355951\pi$
$38$		0			0
$39$	1.61762	+	0.833941i	0.259027	+	0.133537i
$40$		0			0
$41$	−11.1387	−	4.45926i	−1.73957	−	0.696419i	−0.999720	−	0.0236464i	$-0.992472\pi$
$41$	−11.1387	−	4.45926i	−1.73957	−	0.696419i	−0.739850	−	0.672772i	$-0.765103\pi$
$42$		0			0
$43$	−1.31227	−	9.12705i	−0.200120	−	1.39186i	−0.803925	−	0.594730i	$-0.797259\pi$
$43$	−1.31227	−	9.12705i	−0.200120	−	1.39186i	0.603806	−	0.797131i	$-0.293650\pi$
$44$		0			0
$45$	0.861284	+	1.88595i	0.128393	+	0.281141i
$46$		0			0
$47$	1.50381	+	2.11180i	0.219353	+	0.308038i	0.909559	−	0.415575i	$-0.136420\pi$
$47$	1.50381	+	2.11180i	0.219353	+	0.308038i	−0.690206	+	0.723613i	$0.742480\pi$
$48$		0			0
$49$	−4.45612	+	1.78396i	−0.636588	+	0.254851i
$50$		0			0
$51$	−1.37325	−	5.66063i	−0.192294	−	0.792646i
$52$		0			0
$53$	−0.940432	+	6.54085i	−0.129178	+	0.898454i	0.817421	+	0.576041i	$0.195403\pi$
$53$	−0.940432	+	6.54085i	−0.129178	+	0.898454i	−0.946599	+	0.322413i	$0.895506\pi$
$54$		0			0
$55$	2.23009	−	1.14969i	0.300705	−	0.155024i
$56$		0			0
$57$	1.14991	−	1.61483i	0.152310	−	0.213889i
$58$		0			0
$59$	5.71618	−	3.67357i	0.744183	−	0.478258i	−0.112790	−	0.993619i	$-0.535979\pi$
$59$	5.71618	−	3.67357i	0.744183	−	0.478258i	0.856973	+	0.515361i	$0.172342\pi$
$60$		0			0
$61$	5.70773	+	5.44231i	0.730800	+	0.696817i	0.961068	−	0.276310i	$-0.0891118\pi$
$61$	5.70773	+	5.44231i	0.730800	+	0.696817i	−0.230268	+	0.973127i	$0.573960\pi$
$62$		0			0
$63$	−1.16592	−	0.916889i	−0.146892	−	0.115517i
$64$		0			0
$65$	−1.23412	+	3.56575i	−0.153074	+	0.442277i
$66$		0			0
$67$	−5.94150	−	5.63015i	−0.725870	−	0.687832i
$67$	−5.94150	−	5.63015i	−0.725870	−	0.687832i
$68$		0			0
$69$	1.25648	−	3.63037i	0.151263	−	0.437045i
$70$		0			0
$71$	−9.08998	−	7.14844i	−1.07878	−	0.848364i	−0.0897357	−	0.995966i	$-0.528602\pi$
$71$	−9.08998	−	7.14844i	−1.07878	−	0.848364i	−0.989047	+	0.147602i	$0.952845\pi$
$72$		0			0
$73$	8.69359	+	8.28933i	1.01751	+	0.970192i	0.999560	−	0.0296468i	$-0.00943824\pi$
$73$	8.69359	+	8.28933i	1.01751	+	0.970192i	0.0179478	+	0.999839i	$0.494287\pi$
$74$		0			0
$75$	0.590046	−	0.379199i	0.0681326	−	0.0437862i
$76$		0			0
$77$	−1.04118	+	1.46213i	−0.118653	+	0.166625i
$78$		0			0
$79$	−3.62828	+	1.87051i	−0.408214	+	0.210449i	−0.650088	−	0.759859i	$-0.725268\pi$
$79$	−3.62828	+	1.87051i	−0.408214	+	0.210449i	0.241875	+	0.970308i	$0.422238\pi$
$80$		0			0
$81$	−0.142315	+	0.989821i	−0.0158128	+	0.109980i
$82$		0			0
$83$	−1.16023	−	4.78254i	−0.127352	−	0.524952i	−0.999370	−	0.0354788i	$-0.988704\pi$
$83$	−1.16023	−	4.78254i	−0.127352	−	0.524952i	0.872019	−	0.489473i	$-0.162811\pi$
$84$		0			0
$85$	11.2116	−	4.48844i	1.21607	−	0.486839i
$86$		0			0
$87$	1.93009	+	2.71043i	0.206928	+	0.290589i
$88$		0			0
$89$	−0.134913	−	0.295419i	−0.0143008	−	0.0313144i	0.902347	−	0.431011i	$-0.141843\pi$
$89$	−0.134913	−	0.295419i	−0.0143008	−	0.0313144i	−0.916648	+	0.399696i	$0.869116\pi$
$90$		0			0
$91$	−0.384169	−	2.67195i	−0.0402718	−	0.280097i
$92$		0			0
$93$	2.07864	+	0.832163i	0.215545	+	0.0862912i
$94$		0			0
$95$	3.65326	+	1.88338i	0.374816	+	0.193231i
$96$		0			0
$97$	−0.558643	−	0.967597i	−0.0567216	−	0.0982446i	0.836270	−	0.548317i	$-0.184731\pi$
$97$	−0.558643	−	0.967597i	−0.0567216	−	0.0982446i	−0.892992	+	0.450073i	$0.851398\pi$
$98$		0			0
$99$	1.20466	+	0.115032i	0.121073	+	0.0115611i
$100$		0			0
$101$	0.820341	+	2.37022i	0.0816270	+	0.235846i	0.978428	−	0.206589i	$-0.0662362\pi$
$101$	0.820341	+	2.37022i	0.0816270	+	0.235846i	−0.896801	+	0.442434i	$0.854115\pi$
$102$		0			0
$103$	0.397650	+	8.34771i	0.0391817	+	0.822524i	0.929865	+	0.367900i	$0.119923\pi$
$103$	0.397650	+	8.34771i	0.0391817	+	0.822524i	−0.890684	+	0.454624i	$0.849774\pi$
$104$		0			0
$105$	1.53763	−	2.66325i	0.150057	−	0.259906i
$106$		0			0
$107$	−1.42680	+	0.418946i	−0.137934	+	0.0405010i	−0.349971	−	0.936761i	$-0.613808\pi$
$107$	−1.42680	+	0.418946i	−0.137934	+	0.0405010i	0.212037	+	0.977262i	$0.431990\pi$
$108$		0			0
$109$	4.65922	+	2.99430i	0.446272	+	0.286802i	0.744412	−	0.667721i	$-0.232730\pi$
$109$	4.65922	+	2.99430i	0.446272	+	0.286802i	−0.298140	+	0.954522i	$0.596366\pi$
$110$		0			0
$111$	6.78454	−	0.647845i	0.643960	−	0.0614907i
$112$		0			0
$113$	−3.33489	+	13.7466i	−0.313720	+	1.29317i	0.568635	+	0.822590i	$0.307472\pi$
$113$	−3.33489	+	13.7466i	−0.313720	+	1.29317i	−0.882356	+	0.470583i	$0.844044\pi$
$114$		0			0
$115$	7.82101	+	1.50738i	0.729313	+	0.140564i
$116$		0			0
$117$	−1.43056	+	1.12501i	−0.132256	+	0.104007i
$118$		0			0
$119$	−5.65780	+	6.52945i	−0.518650	+	0.598554i
$120$		0			0
$121$	−0.453720	+	9.52475i	−0.0412473	+	0.865886i
$122$		0			0
$123$	8.68346	−	8.27966i	0.782961	−	0.746552i
$124$		0			0
$125$	7.74094	+	8.93352i	0.692371	+	0.799038i
$126$		0			0
$127$	−19.9697	+	3.84884i	−1.77202	+	0.341529i	−0.967592	−	0.252518i	$-0.918741\pi$
$127$	−19.9697	+	3.84884i	−1.77202	+	0.341529i	−0.804430	+	0.594047i	$0.797529\pi$
$128$		0			0
$129$	8.84739	+	2.59783i	0.778969	+	0.228726i
$130$		0			0
$131$	3.70092	−	8.10389i	0.323351	−	0.708040i	−0.676239	−	0.736683i	$-0.736391\pi$
$131$	3.70092	−	8.10389i	0.323351	−	0.708040i	0.999590	+	0.0286426i	$0.00911846\pi$
$132$		0			0
$133$	−2.94043			−0.254968
$134$		0			0
$135$	−2.07331			−0.178442
$136$		0			0
$137$	0.136365	−	0.298599i	0.0116505	−	0.0255110i	−0.903717	−	0.428130i	$-0.859173\pi$
$137$	0.136365	−	0.298599i	0.0116505	−	0.0255110i	0.915368	+	0.402619i	$0.131900\pi$
$138$		0			0
$139$	4.41133	+	1.29528i	0.374164	+	0.109865i	0.463407	−	0.886145i	$-0.346627\pi$
$139$	4.41133	+	1.29528i	0.374164	+	0.109865i	−0.0892431	+	0.996010i	$0.528445\pi$
$140$		0			0
$141$	−2.54566	+	0.490636i	−0.214384	+	0.0413190i
$142$		0			0
$143$	1.44225	+	1.66445i	0.120607	+	0.139188i
$144$		0			0
$145$	−4.99287	+	4.76069i	−0.414635	+	0.395354i
$146$		0			0
$147$	0.228391	−	4.79451i	0.0188373	−	0.395445i
$148$		0			0
$149$	−10.3702	+	11.9679i	−0.849564	+	0.980449i	−0.999967	−	0.00817582i	$-0.997398\pi$
$149$	−10.3702	+	11.9679i	−0.849564	+	0.980449i	0.150403	+	0.988625i	$0.451943\pi$
$150$		0			0
$151$	10.4807	−	8.24210i	0.852906	−	0.670733i	−0.0928253	−	0.995682i	$-0.529590\pi$
$151$	10.4807	−	8.24210i	0.852906	−	0.670733i	0.945731	+	0.324950i	$0.105347\pi$
$152$		0			0
$153$	5.71956	+	1.10235i	0.462399	+	0.0891201i
$154$		0			0
$155$	−1.09444	+	4.51134i	−0.0879075	+	0.362360i
$156$		0			0
$157$	10.9904	−	1.04946i	0.877131	−	0.0837558i	0.353231	−	0.935536i	$-0.385083\pi$
$157$	10.9904	−	1.04946i	0.877131	−	0.0837558i	0.523899	+	0.851780i	$0.324477\pi$
$158$		0			0
$159$	−5.55909	−	3.57261i	−0.440865	−	0.283327i
$160$		0			0
$161$	−5.46735	+	1.60536i	−0.430888	+	0.126520i
$162$		0			0
$163$	2.78055	−	4.81606i	0.217790	−	0.377223i	−0.736342	−	0.676609i	$-0.763449\pi$
$163$	2.78055	−	4.81606i	0.217790	−	0.377223i	0.954132	+	0.299386i	$0.0967820\pi$
$164$		0			0
$165$	0.119383	+	2.50616i	0.00929397	+	0.195104i
$166$		0			0
$167$	0.362187	+	1.04647i	0.0280269	+	0.0809784i	0.958146	−	0.286278i	$-0.0924182\pi$
$167$	0.362187	+	1.04647i	0.0280269	+	0.0809784i	−0.930120	+	0.367257i	$0.880297\pi$
$168$		0			0
$169$	9.64398	+	0.920888i	0.741845	+	0.0708376i
$170$		0			0
$171$	0.991208	+	1.71682i	0.0757995	+	0.131289i
$172$		0			0
$173$	−5.65149	−	2.91354i	−0.429675	−	0.221513i	0.229802	−	0.973237i	$-0.426192\pi$
$173$	−5.65149	−	2.91354i	−0.429675	−	0.221513i	−0.659477	+	0.751725i	$0.729222\pi$
$174$		0			0
$175$	−0.965818	−	0.386655i	−0.0730090	−	0.0292284i
$176$		0			0
$177$	0.967006	+	6.72568i	0.0726846	+	0.505533i
$178$		0			0
$179$	−1.44208	−	3.15772i	−0.107786	−	0.236019i	0.848051	−	0.529914i	$-0.177776\pi$
$179$	−1.44208	−	3.15772i	−0.107786	−	0.236019i	−0.955838	+	0.293895i	$0.905049\pi$
$180$		0			0
$181$	−2.97164	−	4.17308i	−0.220880	−	0.310183i	0.689235	−	0.724538i	$-0.257947\pi$
$181$	−2.97164	−	4.17308i	−0.220880	−	0.310183i	−0.910115	+	0.414355i	$0.864007\pi$
$182$		0			0
$183$	−7.32158	+	2.93112i	−0.541227	+	0.216675i
$184$		0			0
$185$	3.33137	+	13.7321i	0.244928	+	1.00961i
$186$		0			0
$187$	1.00316	−	6.97713i	0.0733583	−	0.510218i
$188$		0			0
$189$	1.31837	−	0.679668i	0.0958974	−	0.0494386i
$190$		0			0
$191$	4.84737	−	6.80718i	0.350744	−	0.492550i	−0.601083	−	0.799186i	$-0.705264\pi$
$191$	4.84737	−	6.80718i	0.350744	−	0.492550i	0.951827	+	0.306636i	$0.0992034\pi$
$192$		0			0
$193$	2.53306	−	1.62790i	0.182334	−	0.117179i	−0.446290	−	0.894889i	$-0.647255\pi$
$193$	2.53306	−	1.62790i	0.182334	−	0.117179i	0.628624	+	0.777710i	$0.283619\pi$
$194$		0			0
$195$	−2.73085	−	2.60386i	−0.195560	−	0.186466i
$196$		0			0
$197$	−6.16021	−	4.84444i	−0.438897	−	0.345152i	0.374132	−	0.927375i	$-0.377941\pi$
$197$	−6.16021	−	4.84444i	−0.438897	−	0.345152i	−0.813029	+	0.582223i	$0.802183\pi$
$198$		0			0
$199$	−0.740339	+	2.13907i	−0.0524812	+	0.151635i	−0.968195	−	0.250196i	$-0.919505\pi$
$199$	−0.740339	+	2.13907i	−0.0524812	+	0.151635i	0.915714	+	0.401831i	$0.131626\pi$
$200$		0			0
$201$	7.58955	−	3.06573i	0.535326	−	0.216240i
$202$		0			0
$203$	1.61422	−	4.66397i	0.113296	−	0.327347i
$204$		0			0
$205$	19.5537	+	15.3772i	1.36569	+	1.07399i
$206$		0			0
$207$	2.78034	+	2.65105i	0.193247	+	0.184261i
$208$		0			0
$209$	2.01817	−	1.29700i	0.139600	−	0.0897155i
$210$		0			0
$211$	7.23403	−	10.1588i	0.498011	−	0.699359i	−0.486697	−	0.873571i	$-0.661798\pi$
$211$	7.23403	−	10.1588i	0.498011	−	0.699359i	0.984708	+	0.174212i	$0.0557378\pi$
$212$		0			0
$213$	10.2786	−	5.29897i	0.704276	−	0.363079i
$214$		0			0
$215$	−2.72074	+	18.9232i	−0.185553	+	1.29055i
$216$		0			0
$217$	−0.782968	−	3.22744i	−0.0531513	−	0.219093i
$218$		0			0
$219$	−11.1517	+	4.46446i	−0.753561	+	0.301680i
$220$		0			0
$221$	6.14905	+	8.63514i	0.413630	+	0.580862i
$222$		0			0
$223$	7.25303	+	15.8819i	0.485699	+	1.06353i	0.980857	+	0.194729i	$0.0623829\pi$
$223$	7.25303	+	15.8819i	0.485699	+	1.06353i	−0.495158	+	0.868803i	$0.664890\pi$
$224$		0			0
$225$	0.0998180	+	0.694250i	0.00665453	+	0.0462833i
$226$		0			0
$227$	15.7351	+	6.29938i	1.04437	+	0.418105i	0.829482	−	0.558533i	$-0.188636\pi$
$227$	15.7351	+	6.29938i	1.04437	+	0.418105i	0.214892	+	0.976638i	$0.431060\pi$
$228$		0			0
$229$	11.1681	+	5.75757i	0.738010	+	0.380471i	0.785877	−	0.618383i	$-0.212212\pi$
$229$	11.1681	+	5.75757i	0.738010	+	0.380471i	−0.0478665	+	0.998854i	$0.515242\pi$
$230$		0			0
$231$	−0.897478	−	1.55448i	−0.0590497	−	0.102277i
$232$		0			0
$233$	−15.6855	−	1.49779i	−1.02759	−	0.0981233i	−0.432381	−	0.901691i	$-0.642326\pi$
$233$	−15.6855	−	1.49779i	−1.02759	−	0.0981233i	−0.595213	+	0.803568i	$0.702932\pi$
$234$		0			0
$235$	−1.75802	−	5.07946i	−0.114680	−	0.331347i
$236$		0			0
$237$	−0.194232	−	4.07744i	−0.0126167	−	0.264858i
$238$		0			0
$239$	−5.73555	+	9.93427i	−0.371002	+	0.642594i	−0.989720	−	0.143019i	$-0.954319\pi$
$239$	−5.73555	+	9.93427i	−0.371002	+	0.642594i	0.618718	+	0.785613i	$0.287652\pi$
$240$		0			0
$241$	−7.44401	+	2.18576i	−0.479511	+	0.140797i	−0.512551	−	0.858657i	$-0.671299\pi$
$241$	−7.44401	+	2.18576i	−0.479511	+	0.140797i	0.0330399	+	0.999454i	$0.489481\pi$
$242$		0			0
$243$	−0.841254	−	0.540641i	−0.0539664	−	0.0346821i
$244$		0			0
$245$	9.90671	−	0.945976i	0.632917	−	0.0604362i
$246$		0			0
$247$	−0.850585	+	3.50616i	−0.0541215	+	0.223092i
$248$		0			0
$249$	4.83233	+	0.931354i	0.306236	+	0.0590222i
$250$		0			0
$251$	11.4445	−	9.00008i	0.722373	−	0.568080i	−0.187851	−	0.982198i	$-0.560152\pi$
$251$	11.4445	−	9.00008i	0.722373	−	0.568080i	0.910223	+	0.414117i	$0.135910\pi$
$252$		0			0
$253$	3.04442	−	3.51345i	0.191401	−	0.220889i
$254$		0			0
$255$	−0.574630	+	12.0630i	−0.0359847	+	0.755413i
$256$		0			0
$257$	12.7263	−	12.1345i	0.793847	−	0.756932i	−0.180114	−	0.983646i	$-0.557647\pi$
$257$	12.7263	−	12.1345i	0.793847	−	0.756932i	0.973961	+	0.226714i	$0.0727983\pi$
$258$		0			0
$259$	−6.61998	−	7.63986i	−0.411346	−	0.474718i
$260$		0			0
$261$	−3.26729	+	0.629718i	−0.202240	+	0.0389786i
$262$		0			0
$263$	17.5286	+	5.14686i	1.08086	+	0.317369i	0.773223	−	0.634134i	$-0.218643\pi$
$263$	17.5286	+	5.14686i	1.08086	+	0.317369i	0.307638	+	0.951504i	$0.400462\pi$
$264$		0			0
$265$	5.69146	−	12.4625i	0.349623	−	0.765568i
$266$		0			0
$267$	0.324768			0.0198755
$268$		0			0
$269$	−13.2788			−0.809625			−0.404813	−	0.914400i	$-0.632663\pi$
$269$	−13.2788			−0.809625			−0.404813	+	0.914400i	$0.632663\pi$
$270$		0			0
$271$	5.20421	−	11.3956i	0.316133	−	0.692235i	−0.683143	−	0.730285i	$-0.739387\pi$
$271$	5.20421	−	11.3956i	0.316133	−	0.692235i	0.999276	+	0.0380496i	$0.0121145\pi$
$272$		0			0
$273$	2.59008	+	0.760517i	0.156759	+	0.0460286i
$274$		0			0
$275$	0.833443	−	0.160633i	0.0502585	−	0.00968653i
$276$		0			0
$277$	12.1064	+	13.9715i	0.727400	+	0.839465i	0.992176	−	0.124845i	$-0.0398435\pi$
$277$	12.1064	+	13.9715i	0.727400	+	0.839465i	−0.264776	+	0.964310i	$0.585298\pi$
$278$		0			0
$279$	−1.62046	+	1.54511i	−0.0970144	+	0.0925031i
$280$		0			0
$281$	0.938955	−	19.7111i	0.0560133	−	1.17586i	−0.779503	−	0.626399i	$-0.784528\pi$
$281$	0.938955	−	19.7111i	0.0560133	−	1.17586i	0.835516	−	0.549466i	$-0.185169\pi$
$282$		0			0
$283$	−2.91512	+	3.36422i	−0.173286	+	0.199982i	−0.835748	−	0.549113i	$-0.814966\pi$
$283$	−2.91512	+	3.36422i	−0.173286	+	0.199982i	0.662463	+	0.749095i	$0.269511\pi$
$284$		0			0
$285$	−3.23080	+	2.54073i	−0.191376	+	0.150500i
$286$		0			0
$287$	−17.4747	−	3.36798i	−1.03150	−	0.198805i
$288$		0			0
$289$	3.99105	−	16.4513i	0.234768	−	0.967726i
$290$		0			0
$291$	1.11223	−	0.106205i	0.0651998	−	0.00622583i
$292$		0			0
$293$	−10.5441	−	6.77630i	−0.615995	−	0.395876i	0.195106	−	0.980782i	$-0.437495\pi$
$293$	−10.5441	−	6.77630i	−0.615995	−	0.395876i	−0.811101	+	0.584906i	$0.801131\pi$
$294$		0			0
$295$	−13.5171	+	3.96899i	−0.786999	+	0.231084i
$296$		0			0
$297$	−0.605072	+	1.04802i	−0.0351099	+	0.0608120i
$298$		0			0
$299$	0.332672	+	6.98364i	0.0192389	+	0.403874i
$300$		0			0
$301$	−4.47330	−	12.9247i	−0.257837	−	0.744970i
$302$		0			0
$303$	−2.49681	−	0.238416i	−0.143438	−	0.0136967i
$304$		0			0
$305$	−8.17558	−	14.1605i	−0.468133	−	0.810829i
$306$		0			0
$307$	−14.9294	−	7.69665i	−0.852067	−	0.439271i	−0.0238745	−	0.999715i	$-0.507600\pi$
$307$	−14.9294	−	7.69665i	−0.852067	−	0.439271i	−0.828192	+	0.560444i	$0.810631\pi$
$308$		0			0
$309$	−7.75853	−	3.10605i	−0.441368	−	0.176697i
$310$		0			0
$311$	−0.158335	−	1.10125i	−0.00897837	−	0.0624459i	0.984840	−	0.173467i	$-0.0554970\pi$
$311$	−0.158335	−	1.10125i	−0.00897837	−	0.0624459i	−0.993818	+	0.111021i	$0.964588\pi$
$312$		0			0
$313$	−3.92565	−	8.59598i	−0.221891	−	0.485873i	0.765646	−	0.643262i	$-0.222420\pi$
$313$	−3.92565	−	8.59598i	−0.221891	−	0.485873i	−0.987537	+	0.157389i	$0.949692\pi$
$314$		0			0
$315$	1.78382	+	2.50503i	0.100507	+	0.141142i
$316$		0			0
$317$	0.319012	−	0.127713i	0.0179175	−	0.00717308i	−0.362686	−	0.931911i	$-0.618140\pi$
$317$	0.319012	−	0.127713i	0.0179175	−	0.00717308i	0.380604	+	0.924738i	$0.375716\pi$
$318$		0			0
$319$	0.949320	+	3.91315i	0.0531517	+	0.219094i
$320$		0			0
$321$	0.211627	−	1.47190i	0.0118119	−	0.0821533i
$322$		0			0
$323$	10.2636	−	5.29124i	0.571080	−	0.294412i
$324$		0			0
$325$	−0.740431	+	1.03979i	−0.0410717	+	0.0576771i
$326$		0			0
$327$	−4.65922	+	2.99430i	−0.257655	+	0.165585i
$328$		0			0
$329$	2.78302	+	2.65361i	0.153433	+	0.146298i
$330$		0			0
$331$	−14.8168	−	11.6521i	−0.814405	−	0.640455i	0.121546	−	0.992586i	$-0.461215\pi$
$331$	−14.8168	−	11.6521i	−0.814405	−	0.640455i	−0.935951	+	0.352131i	$0.885457\pi$
$332$		0			0
$333$	−2.22910	+	6.44056i	−0.122154	+	0.352940i
$334$		0			0
$335$	8.53091	+	14.6707i	0.466093	+	0.801548i
$336$		0			0
$337$	−2.16711	+	6.26145i	−0.118050	+	0.341083i	−0.988510	−	0.151157i	$-0.951700\pi$
$337$	−2.16711	+	6.26145i	−0.118050	+	0.341083i	0.870460	+	0.492239i	$0.163821\pi$
$338$		0			0
$339$	−11.1190	−	8.74408i	−0.603901	−	0.474913i
$340$		0			0
$341$	1.96099	+	1.86980i	0.106194	+	0.101255i
$342$		0			0
$343$	−14.7239	+	9.46249i	−0.795017	+	0.510926i
$344$		0			0
$345$	−4.62012	+	6.48805i	−0.248739	+	0.349305i
$346$		0			0
$347$	9.21913	−	4.75279i	0.494909	−	0.255143i	−0.192656	−	0.981266i	$-0.561710\pi$
$347$	9.21913	−	4.75279i	0.494909	−	0.255143i	0.687565	+	0.726123i	$0.258680\pi$
$348$		0			0
$349$	−3.03558	+	21.1129i	−0.162491	+	1.13015i	0.731428	+	0.681919i	$0.238854\pi$
$349$	−3.03558	+	21.1129i	−0.162491	+	1.13015i	−0.893918	+	0.448230i	$0.852055\pi$
$350$		0			0
$351$	−0.429065	−	1.76863i	−0.0229018	−	0.0944025i
$352$		0			0
$353$	−7.26908	+	2.91010i	−0.386894	+	0.154889i	−0.556951	−	0.830545i	$-0.688029\pi$
$353$	−7.26908	+	2.91010i	−0.386894	+	0.154889i	0.170057	+	0.985434i	$0.445605\pi$
$354$		0			0
$355$	13.9074	+	19.5302i	0.738128	+	1.03656i
$356$		0			0
$357$	−3.58906	−	7.85895i	−0.189953	−	0.415940i
$358$		0			0
$359$	−2.89114	−	20.1083i	−0.152588	−	1.06128i	−0.911860	−	0.410502i	$-0.865353\pi$
$359$	−2.89114	−	20.1083i	−0.152588	−	1.06128i	0.759271	−	0.650774i	$-0.225556\pi$
$360$		0			0
$361$	−13.9905	−	5.60096i	−0.736344	−	0.294788i
$362$		0			0
$363$	−8.47554	−	4.36944i	−0.444850	−	0.229336i
$364$		0			0
$365$	−12.4524	−	21.5683i	−0.651791	−	1.12893i
$366$		0			0
$367$	−21.4427	−	2.04753i	−1.11930	−	0.106880i	−0.481039	−	0.876699i	$-0.659741\pi$
$367$	−21.4427	−	2.04753i	−1.11930	−	0.106880i	−0.638263	+	0.769819i	$0.720347\pi$
$368$		0			0
$369$	3.92421	+	11.3382i	0.204286	+	0.590246i
$370$		0			0
$371$	0.466375	+	9.79042i	0.0242130	+	0.508293i
$372$		0			0
$373$	−6.52602	+	11.3034i	−0.337904	+	0.585268i	−0.984038	−	0.177956i	$-0.943051\pi$
$373$	−6.52602	+	11.3034i	−0.337904	+	0.585268i	0.646134	+	0.763224i	$0.276385\pi$
$374$		0			0
$375$	−11.3419	+	3.33029i	−0.585694	+	0.171975i
$376$		0			0
$377$	−5.09436	−	3.27394i	−0.262373	−	0.168617i
$378$		0			0
$379$	−10.9758	+	1.04806i	−0.563788	+	0.0538352i	−0.373059	−	0.927808i	$-0.621691\pi$
$379$	−10.9758	+	1.04806i	−0.563788	+	0.0538352i	−0.190729	+	0.981643i	$0.561085\pi$
$380$		0			0
$381$	4.79468	−	19.7639i	0.245639	−	1.01254i
$382$		0			0
$383$	8.93409	+	1.72190i	0.456511	+	0.0879852i	0.412322	−	0.911038i	$-0.364718\pi$
$383$	8.93409	+	1.72190i	0.456511	+	0.0879852i	0.0441882	+	0.999023i	$0.485930\pi$
$384$		0			0
$385$	2.92530	−	2.30048i	0.149087	−	0.117243i
$386$		0			0
$387$	−6.03841	+	6.96869i	−0.306949	+	0.354239i
$388$		0			0
$389$	0.284617	−	5.97484i	0.0144306	−	0.302936i	−0.980101	−	0.198500i	$-0.936393\pi$
$389$	0.284617	−	5.97484i	0.0144306	−	0.302936i	0.994532	−	0.104436i	$-0.0333039\pi$
$390$		0			0
$391$	16.1950	−	15.4419i	0.819015	−	0.780929i
$392$		0			0
$393$	5.83414	+	6.73295i	0.294293	+	0.339633i
$394$		0			0
$395$	8.31043	−	1.60170i	0.418143	−	0.0805905i
$396$		0			0
$397$	−35.2096	−	10.3385i	−1.76712	−	0.518873i	−0.773714	−	0.633535i	$-0.781603\pi$
$397$	−35.2096	−	10.3385i	−1.76712	−	0.518873i	−0.993405	+	0.114662i	$0.963422\pi$
$398$		0			0
$399$	1.22150	−	2.67471i	0.0611515	−	0.133903i
$400$		0			0
$401$	−26.3343			−1.31507			−0.657537	−	0.753422i	$-0.728402\pi$
$401$	−26.3343			−1.31507			−0.657537	+	0.753422i	$0.728402\pi$
$402$		0			0
$403$	−4.07488			−0.202984
$404$		0			0
$405$	0.861284	−	1.88595i	0.0427975	−	0.0937135i
$406$		0			0
$407$	7.91353	+	2.32362i	0.392259	+	0.115178i
$408$		0			0
$409$	−17.8356	+	3.43752i	−0.881911	+	0.169974i	−0.610051	−	0.792362i	$-0.708851\pi$
$409$	−17.8356	+	3.43752i	−0.881911	+	0.169974i	−0.271860	+	0.962337i	$0.587639\pi$
$410$		0			0
$411$	0.214967	+	0.248085i	0.0106035	+	0.0122371i
$412$		0			0
$413$	7.29415	−	6.95496i	0.358922	−	0.342231i
$414$		0			0
$415$	−0.485492	+	10.1917i	−0.0238319	+	0.500293i
$416$		0			0
$417$	−3.01077	+	3.47461i	−0.147438	+	0.170152i
$418$		0			0
$419$	10.4367	−	8.20751i	0.509866	−	0.400963i	−0.329813	−	0.944046i	$-0.606986\pi$
$419$	10.4367	−	8.20751i	0.509866	−	0.400963i	0.839679	+	0.543083i	$0.182743\pi$
$420$		0			0
$421$	−8.83433	−	1.70268i	−0.430559	−	0.0829835i	−0.0306326	−	0.999531i	$-0.509752\pi$
$421$	−8.83433	−	1.70268i	−0.430559	−	0.0829835i	−0.399926	+	0.916547i	$0.630964\pi$
$422$		0			0
$423$	0.611208	−	2.51943i	0.0297180	−	0.122499i
$424$		0			0
$425$	4.06696	−	0.388348i	0.197277	−	0.0188376i
$426$		0			0
$427$	9.84075	+	6.32426i	0.476227	+	0.306053i
$428$		0			0
$429$	−2.11317	+	0.620482i	−0.102025	+	0.0299572i
$430$		0			0
$431$	12.7657	−	22.1109i	0.614904	−	1.06505i	−0.375497	−	0.926824i	$-0.622528\pi$
$431$	12.7657	−	22.1109i	0.614904	−	1.06505i	0.990401	−	0.138222i	$-0.0441387\pi$
$432$		0			0
$433$	0.966549	+	20.2904i	0.0464494	+	0.975093i	0.895024	+	0.446017i	$0.147158\pi$
$433$	0.966549	+	20.2904i	0.0464494	+	0.975093i	−0.848575	+	0.529075i	$0.822539\pi$
$434$		0			0
$435$	−2.25637	−	6.51934i	−0.108184	−	0.312578i
$436$		0			0
$437$	7.58128	+	0.723924i	0.362662	+	0.0346300i
$438$		0			0
$439$	−17.5605	−	30.4157i	−0.838117	−	1.45166i	−0.891467	−	0.453086i	$-0.850323\pi$
$439$	−17.5605	−	30.4157i	−0.838117	−	1.45166i	0.0533496	−	0.998576i	$-0.483010\pi$
$440$		0			0
$441$	4.26636	+	2.19946i	0.203160	+	0.104736i
$442$		0			0
$443$	−3.63720	−	1.45611i	−0.172808	−	0.0691821i	0.283645	−	0.958929i	$-0.408456\pi$
$443$	−3.63720	−	1.45611i	−0.172808	−	0.0691821i	−0.456453	+	0.889747i	$0.650881\pi$
$444$		0			0
$445$	0.0958269	+	0.666491i	0.00454263	+	0.0315947i
$446$		0			0
$447$	−6.57843	−	14.4048i	−0.311149	−	0.681322i
$448$		0			0
$449$	5.66581	+	7.95651i	0.267386	+	0.375491i	0.926338	−	0.376694i	$-0.122939\pi$
$449$	5.66581	+	7.95651i	0.267386	+	0.375491i	−0.658952	+	0.752185i	$0.729000\pi$
$450$		0			0
$451$	13.4794	−	5.39634i	0.634721	−	0.254104i
$452$		0			0
$453$	3.14345	+	12.9575i	0.147692	+	0.608794i
$454$		0			0
$455$	−0.796500	+	5.53978i	−0.0373405	+	0.259709i
$456$		0			0
$457$	19.4058	−	10.0044i	0.907767	−	0.467986i	0.0599052	−	0.998204i	$-0.480920\pi$
$457$	19.4058	−	10.0044i	0.907767	−	0.467986i	0.847861	+	0.530218i	$0.177890\pi$
$458$		0			0
$459$	−3.37873	+	4.74476i	−0.157705	+	0.221466i
$460$		0			0
$461$	1.67364	−	1.07558i	0.0779493	−	0.0500950i	−0.501086	−	0.865398i	$-0.667066\pi$
$461$	1.67364	−	1.07558i	0.0779493	−	0.0500950i	0.579035	+	0.815303i	$0.303429\pi$
$462$		0			0
$463$	29.2039	+	27.8459i	1.35722	+	1.29411i	0.918464	+	0.395504i	$0.129430\pi$
$463$	29.2039	+	27.8459i	1.35722	+	1.29411i	0.438758	+	0.898605i	$0.355418\pi$
$464$		0			0
$465$	−3.64901	−	2.86962i	−0.169219	−	0.133075i
$466$		0			0
$467$	−5.41635	+	15.6495i	−0.250639	+	0.724173i	0.747561	+	0.664193i	$0.231225\pi$
$467$	−5.41635	+	15.6495i	−0.250639	+	0.724173i	−0.998200	+	0.0599799i	$0.980896\pi$
$468$		0			0
$469$	−10.2339	−	6.53222i	−0.472560	−	0.301630i
$470$		0			0
$471$	−3.61096	+	10.4332i	−0.166384	+	0.480736i
$472$		0			0
$473$	8.77127	+	6.89780i	0.403304	+	0.317161i
$474$		0			0
$475$	1.00631	+	0.959516i	0.0461727	+	0.0440256i
$476$		0			0
$477$	5.55909	−	3.57261i	0.254533	−	0.163579i
$478$		0			0
$479$	9.58749	−	13.4637i	0.438064	−	0.615174i	−0.535239	−	0.844701i	$-0.679778\pi$
$479$	9.58749	−	13.4637i	0.438064	−	0.615174i	0.973302	+	0.229527i	$0.0737178\pi$
$480$		0			0
$481$	−11.0247	+	5.68364i	−0.502684	+	0.259152i
$482$		0			0
$483$	0.810934	−	5.64017i	0.0368988	−	0.256637i
$484$		0			0
$485$	0.546130	+	2.25118i	0.0247985	+	0.102221i
$486$		0			0
$487$	−29.1363	+	11.6644i	−1.32029	+	0.528566i	−0.921466	−	0.388460i	$-0.873007\pi$
$487$	−29.1363	+	11.6644i	−1.32029	+	0.528566i	−0.398828	+	0.917026i	$0.630583\pi$
$488$		0			0
$489$	3.22576	+	4.52994i	0.145874	+	0.204851i
$490$		0			0
$491$	−16.2252	−	35.5283i	−0.732234	−	1.60337i	−0.795922	−	0.605399i	$-0.793013\pi$
$491$	−16.2252	−	35.5283i	−0.732234	−	1.60337i	0.0636877	−	0.997970i	$-0.479714\pi$
$492$		0			0
$493$	2.75829	+	19.1843i	0.124227	+	0.864019i
$494$		0			0
$495$	−2.32928	−	0.932503i	−0.104693	−	0.0419129i
$496$		0			0
$497$	−15.2458	−	7.85974i	−0.683866	−	0.352557i
$498$		0			0
$499$	−6.32237	−	10.9507i	−0.283028	−	0.490219i	0.689101	−	0.724665i	$-0.258006\pi$
$499$	−6.32237	−	10.9507i	−0.283028	−	0.490219i	−0.972129	+	0.234446i	$0.924672\pi$
$500$		0			0
$501$	−1.10236	−	0.105263i	−0.0492499	−	0.00470280i
$502$		0			0
$503$	10.3218	+	29.8228i	0.460225	+	1.32973i	0.901662	+	0.432442i	$0.142348\pi$
$503$	10.3218	+	29.8228i	0.460225	+	1.32973i	−0.441436	+	0.897293i	$0.645531\pi$
$504$		0			0
$505$	−0.247436	−	5.19432i	−0.0110107	−	0.231144i
$506$		0			0
$507$	−4.84392	+	8.38992i	−0.215126	+	0.372610i
$508$		0			0
$509$	26.5837	−	7.80567i	1.17830	−	0.345980i	0.366782	−	0.930307i	$-0.380459\pi$
$509$	26.5837	−	7.80567i	1.17830	−	0.345980i	0.811519	+	0.584326i	$0.198641\pi$
$510$		0			0
$511$	14.9887	+	9.63265i	0.663061	+	0.426123i
$512$		0			0
$513$	−1.97344	+	0.188441i	−0.0871294	+	0.00831985i
$514$		0			0
$515$	4.08500	−	16.8386i	0.180006	−	0.741997i
$516$		0			0
$517$	−3.08062	−	0.593741i	−0.135486	−	0.0261127i
$518$		0			0
$519$	4.99797	−	3.93044i	0.219386	−	0.172527i
$520$		0			0
$521$	25.9289	−	29.9235i	1.13597	−	1.31097i	0.191826	−	0.981429i	$-0.438559\pi$
$521$	25.9289	−	29.9235i	1.13597	−	1.31097i	0.944140	−	0.329545i	$-0.106895\pi$
$522$		0			0
$523$	−0.435015	+	9.13209i	−0.0190219	+	0.399319i	0.969198	+	0.246281i	$0.0792086\pi$
$523$	−0.435015	+	9.13209i	−0.0190219	+	0.399319i	−0.988220	+	0.153038i	$0.951094\pi$
$524$		0			0
$525$	0.752929	−	0.717917i	0.0328605	−	0.0313325i
$526$		0			0
$527$	8.54065	+	9.85644i	0.372037	+	0.429353i
$528$		0			0
$529$	−8.09273	+	1.55975i	−0.351858	+	0.0678150i
$530$		0			0
$531$	−6.51960	−	1.91433i	−0.282926	−	0.0830747i
$532$		0			0
$533$	−9.07091	+	19.8625i	−0.392905	+	0.860342i
$534$		0			0
$535$	3.08308			0.133293
$536$		0			0
$537$	3.47143			0.149803
$538$		0			0
$539$	2.41299	−	5.28372i	0.103935	−	0.227586i
$540$		0			0
$541$	−36.6173	−	10.7518i	−1.57430	−	0.462257i	−0.626052	−	0.779781i	$-0.715330\pi$
$541$	−36.6173	−	10.7518i	−1.57430	−	0.462257i	−0.948250	+	0.317524i	$0.897149\pi$
$542$		0			0
$543$	5.03043	−	0.969536i	0.215876	−	0.0416068i
$544$		0			0
$545$	−7.51967	−	8.67817i	−0.322107	−	0.371732i
$546$		0			0
$547$	−4.44643	+	4.23966i	−0.190116	+	0.181275i	−0.779159	−	0.626827i	$-0.784353\pi$
$547$	−4.44643	+	4.23966i	−0.190116	+	0.181275i	0.589043	+	0.808102i	$0.299505\pi$
$548$		0			0
$549$	0.375255	−	7.87757i	0.0160155	−	0.336207i
$550$		0			0
$551$	−4.31967	+	4.98517i	−0.184024	+	0.212375i
$552$		0			0
$553$	−4.75935	+	3.74280i	−0.202388	+	0.159160i
$554$		0			0
$555$	−13.8751	−	2.67420i	−0.588964	−	0.113514i
$556$		0			0
$557$	1.34425	−	5.54106i	0.0569575	−	0.234782i	−0.936217	−	0.351424i	$-0.885698\pi$
$557$	1.34425	−	5.54106i	0.0569575	−	0.234782i	0.993174	+	0.116641i	$0.0372128\pi$
$558$		0			0
$559$	−16.7054	+	1.59518i	−0.706564	+	0.0674687i
$560$		0			0
$561$	5.92989	+	3.81091i	0.250360	+	0.160897i
$562$		0			0
$563$	−6.26471	+	1.83948i	−0.264026	+	0.0775250i	−0.411066	−	0.911606i	$-0.634843\pi$
$563$	−6.26471	+	1.83948i	−0.264026	+	0.0775250i	0.147040	+	0.989131i	$0.453025\pi$
$564$		0			0
$565$	14.6638	−	25.3985i	0.616913	−	1.06852i
$566$		0			0
$567$	0.0705762	+	1.48158i	0.00296392	+	0.0622204i
$568$		0			0
$569$	−8.23913	−	23.8054i	−0.345402	−	0.997975i	−0.975221	−	0.221233i	$-0.928992\pi$
$569$	−8.23913	−	23.8054i	−0.345402	−	0.997975i	0.629819	−	0.776742i	$-0.283129\pi$
$570$		0			0
$571$	−10.7299	−	1.02458i	−0.449032	−	0.0428773i	−0.131909	−	0.991262i	$-0.542111\pi$
$571$	−10.7299	−	1.02458i	−0.449032	−	0.0428773i	−0.317123	+	0.948385i	$0.602717\pi$
$572$		0			0
$573$	4.17836	+	7.23713i	0.174553	+	0.302336i
$574$		0			0
$575$	2.39496	+	1.23469i	0.0998769	+	0.0514901i
$576$		0			0
$577$	−27.6391	−	11.0650i	−1.15063	−	0.460643i	−0.283622	−	0.958936i	$-0.591536\pi$
$577$	−27.6391	−	11.0650i	−1.15063	−	0.460643i	−0.867009	+	0.498293i	$0.833960\pi$
$578$		0			0
$579$	0.428518	+	2.98041i	0.0178086	+	0.123862i
$580$		0			0
$581$	−3.03232	−	6.63985i	−0.125802	−	0.275468i
$582$		0			0
$583$	−4.63858	−	6.51397i	−0.192110	−	0.269781i
$584$		0			0
$585$	3.50299	−	1.40239i	0.144831	−	0.0579816i
$586$		0			0
$587$	−1.65795	−	6.83416i	−0.0684309	−	0.282076i	0.927307	−	0.374301i	$-0.122117\pi$
$587$	−1.65795	−	6.83416i	−0.0684309	−	0.282076i	−0.995738	+	0.0922249i	$0.970602\pi$
$588$		0			0
$589$	−0.631690	+	4.39350i	−0.0260283	+	0.181031i
$590$		0			0
$591$	6.96570	−	3.59107i	0.286531	−	0.147717i
$592$		0			0
$593$	−15.4682	+	21.7220i	−0.635202	+	0.892017i	−0.999225	−	0.0393733i	$-0.987464\pi$
$593$	−15.4682	+	21.7220i	−0.635202	+	0.892017i	0.364022	+	0.931390i	$0.381403\pi$
$594$		0			0
$595$	15.0692	−	9.68438i	0.617777	−	0.397021i
$596$		0			0
$597$	−1.63822	−	1.56204i	−0.0670478	−	0.0639299i
$598$		0			0
$599$	5.55558	+	4.36895i	0.226995	+	0.178511i	0.725179	−	0.688561i	$-0.241757\pi$
$599$	5.55558	+	4.36895i	0.226995	+	0.178511i	−0.498184	+	0.867071i	$0.666000\pi$
$600$		0			0
$601$	5.88377	−	17.0000i	0.240004	−	0.693446i	−0.759094	−	0.650981i	$-0.774358\pi$
$601$	5.88377	−	17.0000i	0.240004	−	0.693446i	0.999098	−	0.0424652i	$-0.0135212\pi$
$602$		0			0
$603$	−0.364127	+	8.17725i	−0.0148284	+	0.333003i
$604$		0			0
$605$	6.46618	−	18.6828i	0.262888	−	0.759564i
$606$		0			0
$607$	29.5713	+	23.2552i	1.20026	+	0.943898i	0.999362	−	0.0357135i	$-0.0113704\pi$
$607$	29.5713	+	23.2552i	1.20026	+	0.943898i	0.200902	+	0.979611i	$0.435613\pi$
$608$		0			0
$609$	3.57193	+	3.40583i	0.144742	+	0.138011i
$610$		0			0
$611$	3.96920	−	2.55085i	0.160577	−	0.103196i
$612$		0			0
$613$	25.8155	−	36.2527i	1.04268	−	1.46423i	0.164213	−	0.986425i	$-0.447492\pi$
$613$	25.8155	−	36.2527i	1.04268	−	1.46423i	0.878464	−	0.477809i	$-0.158569\pi$
$614$		0			0
$615$	−22.1105	+	11.3988i	−0.891583	+	0.459643i
$616$		0			0
$617$	6.29218	−	43.7631i	0.253314	−	1.76184i	−0.324709	−	0.945814i	$-0.605266\pi$
$617$	6.29218	−	43.7631i	0.253314	−	1.76184i	0.578022	−	0.816021i	$-0.303825\pi$
$618$		0			0
$619$	9.55701	+	39.3945i	0.384129	+	1.58340i	0.755650	+	0.654975i	$0.227321\pi$
$619$	9.55701	+	39.3945i	0.384129	+	1.58340i	−0.371522	+	0.928424i	$0.621164\pi$
$620$		0			0
$621$	−3.56647	+	1.42780i	−0.143118	+	0.0572956i
$622$		0			0
$623$	−0.279422	−	0.392393i	−0.0111948	−	0.0157209i
$624$		0			0
$625$	−8.72418	−	19.1033i	−0.348967	−	0.764131i
$626$		0			0
$627$	0.341415	+	2.37459i	0.0136348	+	0.0948320i
$628$		0			0
$629$	36.8548	+	14.7544i	1.46950	+	0.588298i
$630$		0			0
$631$	−27.1838	−	14.0142i	−1.08217	−	0.557897i	−0.177547	−	0.984112i	$-0.556816\pi$
$631$	−27.1838	−	14.0142i	−1.08217	−	0.557897i	−0.904622	+	0.426215i	$0.859847\pi$
$632$		0			0
$633$	6.23562	+	10.8004i	0.247844	+	0.429278i
$634$		0			0
$635$	41.9744	+	4.00807i	1.66570	+	0.159055i
$636$		0			0
$637$	2.85713	+	8.25513i	0.113204	+	0.327080i
$638$		0			0
$639$	0.550241	+	11.5510i	0.0217672	+	0.456950i
$640$		0			0
$641$	−16.3079	+	28.2461i	−0.644123	+	1.11565i	0.340380	+	0.940288i	$0.389444\pi$
$641$	−16.3079	+	28.2461i	−0.644123	+	1.11565i	−0.984503	+	0.175366i	$0.943889\pi$
$642$		0			0
$643$	29.2917	−	8.60083i	1.15515	−	0.339184i	0.352606	−	0.935772i	$-0.385296\pi$
$643$	29.2917	−	8.60083i	1.15515	−	0.339184i	0.802548	+	0.596588i	$0.203477\pi$
$644$		0			0
$645$	−16.0829	−	10.3359i	−0.633264	−	0.406974i
$646$		0			0
$647$	5.51082	−	0.526219i	0.216653	−	0.0206878i	0.0138347	−	0.999904i	$-0.495596\pi$
$647$	5.51082	−	0.526219i	0.216653	−	0.0206878i	0.202818	+	0.979216i	$0.434990\pi$
$648$		0			0
$649$	−1.93858	+	7.99095i	−0.0760961	+	0.313672i
$650$		0			0
$651$	3.26104	+	0.628514i	0.127810	+	0.0246334i
$652$		0			0
$653$	−30.2122	+	23.7591i	−1.18229	+	0.929766i	−0.998583	−	0.0532138i	$-0.983054\pi$
$653$	−30.2122	+	23.7591i	−1.18229	+	0.929766i	−0.183711	+	0.982980i	$0.558811\pi$
$654$		0			0
$655$	−12.0960	+	13.9595i	−0.472629	+	0.545443i
$656$		0			0
$657$	0.571561	−	11.9985i	0.0222987	−	0.468107i
$658$		0			0
$659$	18.3826	−	17.5278i	0.716086	−	0.682787i	−0.241673	−	0.970358i	$-0.577696\pi$
$659$	18.3826	−	17.5278i	0.716086	−	0.682787i	0.957759	+	0.287571i	$0.0928477\pi$
$660$		0			0
$661$	21.3585	+	24.6490i	0.830750	+	0.958736i	0.999638	−	0.0268988i	$-0.00856317\pi$
$661$	21.3585	+	24.6490i	0.830750	+	0.958736i	−0.168888	+	0.985635i	$0.554018\pi$
$662$		0			0
$663$	−10.4092	+	2.00621i	−0.404260	+	0.0779147i
$664$		0			0
$665$	5.84948	+	1.71756i	0.226833	+	0.0666042i
$666$		0			0
$667$	−5.31017	+	11.6276i	−0.205610	+	0.450224i
$668$		0			0
$669$	−17.4597			−0.675032
$670$		0			0
$671$	−9.54381			−0.368435
$672$		0			0
$673$	−18.7354	+	41.0248i	−0.722196	+	1.58139i	0.0886051	+	0.996067i	$0.471759\pi$
$673$	−18.7354	+	41.0248i	−0.722196	+	1.58139i	−0.810801	+	0.585322i	$0.800968\pi$
$674$		0			0
$675$	−0.672977	−	0.197604i	−0.0259029	−	0.00760578i
$676$		0			0
$677$	18.5643	−	3.57797i	0.713483	−	0.137513i	0.180422	−	0.983589i	$-0.442254\pi$
$677$	18.5643	−	3.57797i	0.713483	−	0.137513i	0.533061	+	0.846077i	$0.321041\pi$
$678$		0			0
$679$	−1.08525	−	1.25244i	−0.0416480	−	0.0480644i
$680$		0			0
$681$	−12.2667	+	11.6963i	−0.470061	+	0.448203i
$682$		0			0
$683$	−0.338595	+	7.10799i	−0.0129560	+	0.271980i	0.983089	+	0.183129i	$0.0586225\pi$
$683$	−0.338595	+	7.10799i	−0.0129560	+	0.271980i	−0.996045	+	0.0888509i	$0.971681\pi$
$684$		0			0
$685$	−0.445692	+	0.514356i	−0.0170290	+	0.0196525i
$686$		0			0
$687$	−9.87667	+	7.76710i	−0.376819	+	0.296333i
$688$		0			0
$689$	11.8090	+	2.27599i	0.449886	+	0.0867084i
$690$		0			0
$691$	0.121847	−	0.502261i	0.00463528	−	0.0191069i	−0.969447	−	0.245301i	$-0.921113\pi$
$691$	0.121847	−	0.502261i	0.00463528	−	0.0191069i	0.974082	+	0.226194i	$0.0726284\pi$
$692$		0			0
$693$	1.78683	−	0.170621i	0.0678760	−	0.00648137i
$694$		0			0
$695$	−8.01898	−	5.15348i	−0.304177	−	0.195483i
$696$		0			0
$697$	67.0561	−	19.6894i	2.53993	−	0.745790i
$698$		0			0
$699$	7.87845	−	13.6459i	0.297990	−	0.516134i
$700$		0			0
$701$	0.118521	+	2.48806i	0.00447647	+	0.0939727i	1.00000		0.000542904i	$-0.000172812\pi$
$701$	0.118521	+	2.48806i	0.00447647	+	0.0939727i	−0.995523	+	0.0945156i	$0.969870\pi$
$702$		0			0
$703$	4.41900	+	12.7679i	0.166666	+	0.481549i
$704$		0			0
$705$	5.35074	+	0.510934i	0.201521	+	0.0192429i
$706$		0			0
$707$	1.86013	+	3.22184i	0.0699573	+	0.121170i
$708$		0			0
$709$	−30.3153	−	15.6286i	−1.13851	−	0.586945i	−0.217340	−	0.976096i	$-0.569738\pi$
$709$	−30.3153	−	15.6286i	−1.13851	−	0.586945i	−0.921174	+	0.389151i	$0.872768\pi$
$710$		0			0
$711$	3.78966	+	1.51715i	0.142123	+	0.0568976i
$712$		0			0
$713$	1.22413	+	8.51403i	0.0458441	+	0.318853i
$714$		0			0
$715$	−1.89687	−	4.15358i	−0.0709391	−	0.155335i
$716$		0			0
$717$	−6.65389	−	9.34409i	−0.248494	−	0.348961i
$718$		0			0
$719$	14.4303	−	5.77702i	0.538159	−	0.215446i	−0.0866292	−	0.996241i	$-0.527610\pi$
$719$	14.4303	−	5.77702i	0.538159	−	0.215446i	0.624788	+	0.780794i	$0.285185\pi$
$720$		0			0
$721$	2.92243	+	12.0464i	0.108837	+	0.448632i
$722$		0			0
$723$	1.10412	−	7.67931i	0.0410626	−	0.285596i
$724$		0			0
$725$	−2.07438	+	1.06941i	−0.0770404	+	0.0397171i
$726$		0			0
$727$	15.6240	−	21.9408i	0.579461	−	0.813740i	−0.415954	−	0.909386i	$-0.636552\pi$
$727$	15.6240	−	21.9408i	0.579461	−	0.813740i	0.995415	+	0.0956459i	$0.0304916\pi$
$728$		0			0
$729$	0.841254	−	0.540641i	0.0311575	−	0.0200237i
$730$		0			0
$731$	38.8718	+	37.0642i	1.43773	+	1.37087i
$732$		0			0
$733$	2.46056	+	1.93501i	0.0908829	+	0.0714711i	0.662567	−	0.749003i	$-0.269467\pi$
$733$	2.46056	+	1.93501i	0.0908829	+	0.0714711i	−0.571684	+	0.820474i	$0.693710\pi$
$734$		0			0
$735$	−3.25491	+	9.40444i	−0.120059	+	0.346888i
$736$		0			0
$737$	9.90541	−	0.0307075i	0.364871	−	0.00113113i
$738$		0			0
$739$	10.2594	−	29.6426i	0.377398	−	1.09042i	−0.583164	−	0.812355i	$-0.698185\pi$
$739$	10.2594	−	29.6426i	0.377398	−	1.09042i	0.960562	−	0.278066i	$-0.0896934\pi$
$740$		0			0
$741$	−2.83597	−	2.23023i	−0.104182	−	0.0819296i
$742$		0			0
$743$	25.8736	+	24.6704i	0.949211	+	0.905070i	0.995586	−	0.0938537i	$-0.0299186\pi$
$743$	25.8736	+	24.6704i	0.949211	+	0.905070i	−0.0463755	+	0.998924i	$0.514767\pi$
$744$		0			0
$745$	27.6205	−	17.7506i	1.01194	−	0.650332i
$746$		0			0
$747$	−2.85461	+	4.00874i	−0.104445	+	0.146672i
$748$		0			0
$749$	−1.96046	+	1.01069i	−0.0716337	+	0.0369298i
$750$		0			0
$751$	−6.87031	+	47.7841i	−0.250701	+	1.74367i	0.343322	+	0.939218i	$0.388448\pi$
$751$	−6.87031	+	47.7841i	−0.250701	+	1.74367i	−0.594024	+	0.804448i	$0.702461\pi$
$752$		0			0
$753$	3.43253	+	14.1491i	0.125088	+	0.515621i
$754$		0			0
$755$	−25.6639	+	10.2743i	−0.934003	+	0.373919i
$756$		0			0
$757$	24.1544	+	33.9200i	0.877905	+	1.23284i	0.971453	+	0.237230i	$0.0762395\pi$
$757$	24.1544	+	33.9200i	0.877905	+	1.23284i	−0.0935487	+	0.995615i	$0.529821\pi$
$758$		0			0
$759$	1.93125	+	4.22884i	0.0700999	+	0.153497i
$760$		0			0
$761$	−4.89234	−	34.0269i	−0.177347	−	1.23348i	−0.862870	−	0.505425i	$-0.831336\pi$
$761$	−4.89234	−	34.0269i	−0.177347	−	1.23348i	0.685523	−	0.728051i	$-0.259573\pi$
$762$		0			0
$763$	7.62645	+	3.05317i	0.276096	+	0.110532i
$764$		0			0
$765$	−10.7342	−	5.53384i	−0.388094	−	0.200076i
$766$		0			0
$767$	−6.18307	−	10.7094i	−0.223258	−	0.386694i
$768$		0			0
$769$	13.2626	+	1.26643i	0.478262	+	0.0456685i	0.331404	−	0.943489i	$-0.392478\pi$
$769$	13.2626	+	1.26643i	0.478262	+	0.0456685i	0.146858	+	0.989158i	$0.453084\pi$
$770$		0			0
$771$	5.75125	+	16.6172i	0.207126	+	0.598452i
$772$		0			0
$773$	2.22124	+	46.6295i	0.0798923	+	1.67715i	0.582653	+	0.812721i	$0.302014\pi$
$773$	2.22124	+	46.6295i	0.0798923	+	1.67715i	−0.502761	+	0.864425i	$0.667682\pi$
$774$		0			0
$775$	−0.785214	+	1.36003i	−0.0282057	+	0.0488538i
$776$		0			0
$777$	9.69950	−	2.84803i	0.347968	−	0.102173i
$778$		0			0
$779$	20.0095	+	12.8593i	0.716913	+	0.460732i
$780$		0			0
$781$	13.9308	−	1.33023i	0.498485	−	0.0475995i
$782$		0			0
$783$	0.784468	−	3.23362i	0.0280346	−	0.115560i
$784$		0			0
$785$	−22.4765	−	4.33200i	−0.802222	−	0.154616i
$786$		0			0
$787$	9.38207	−	7.37814i	0.334435	−	0.263002i	−0.436793	−	0.899562i	$-0.643886\pi$
$787$	9.38207	−	7.37814i	0.334435	−	0.263002i	0.771227	+	0.636560i	$0.219643\pi$
$788$		0			0
$789$	−11.9634	+	13.8065i	−0.425908	+	0.491524i
$790$		0			0
$791$	−0.998326	+	20.9574i	−0.0354964	+	0.745161i
$792$		0			0
$793$	10.3877	−	9.90464i	0.368878	−	0.351724i
$794$		0			0
$795$	8.97202	+	10.3543i	0.318205	+	0.367228i
$796$		0			0
$797$	−37.3955	+	7.20740i	−1.32462	+	0.255299i	−0.802029	−	0.597286i	$-0.796246\pi$
$797$	−37.3955	+	7.20740i	−1.32462	+	0.255299i	−0.522589	+	0.852585i	$0.675034\pi$
$798$		0			0
$799$	−14.4892	−	4.25442i	−0.512592	−	0.150511i
$800$		0			0
$801$	−0.134913	+	0.295419i	−0.00476693	+	0.0104381i
$802$		0			0
$803$	−14.5364			−0.512979
$804$		0			0
$805$	11.8141			0.416391
$806$		0			0
$807$	5.51623	−	12.0789i	0.194181	−	0.425196i
$808$		0			0
$809$	20.1008	+	5.90213i	0.706707	+	0.207508i	0.615285	−	0.788304i	$-0.289041\pi$
$809$	20.1008	+	5.90213i	0.706707	+	0.207508i	0.0914214	+	0.995812i	$0.470859\pi$
$810$		0			0
$811$	−27.4476	+	5.29009i	−0.963815	+	0.185760i	−0.646800	−	0.762660i	$-0.723893\pi$
$811$	−27.4476	+	5.29009i	−0.963815	+	0.185760i	−0.317016	+	0.948420i	$0.602681\pi$
$812$		0			0
$813$	8.20393	+	9.46783i	0.287724	+	0.332051i
$814$		0			0
$815$	−8.34457	+	7.95654i	−0.292298	+	0.278705i
$816$		0			0
$817$	−0.869781	+	18.2590i	−0.0304298	+	0.638800i
$818$		0			0
$819$	−1.76775	+	2.04009i	−0.0617701	+	0.0712866i
$820$		0			0
$821$	21.7453	−	17.1007i	0.758917	−	0.596819i	−0.161903	−	0.986807i	$-0.551763\pi$
$821$	21.7453	−	17.1007i	0.758917	−	0.596819i	0.920820	+	0.389988i	$0.127521\pi$
$822$		0			0
$823$	14.6055	+	2.81498i	0.509115	+	0.0981240i	0.437339	−	0.899297i	$-0.355921\pi$
$823$	14.6055	+	2.81498i	0.509115	+	0.0981240i	0.0717765	+	0.997421i	$0.477133\pi$
$824$		0			0
$825$	−0.200108	+	0.824856i	−0.00696686	+	0.0287178i
$826$		0			0
$827$	28.8268	−	2.75263i	1.00241	−	0.0957183i	0.419075	−	0.907952i	$-0.362355\pi$
$827$	28.8268	−	2.75263i	1.00241	−	0.0957183i	0.583333	+	0.812233i	$0.301748\pi$
$828$		0			0
$829$	−17.2781	−	11.1040i	−0.600094	−	0.385657i	0.205037	−	0.978754i	$-0.434269\pi$
$829$	−17.2781	−	11.1040i	−0.600094	−	0.385657i	−0.805131	+	0.593097i	$0.797905\pi$
$830$		0			0
$831$	−17.7381	+	5.20836i	−0.615326	+	0.180676i
$832$		0			0
$833$	13.9794	−	24.2131i	0.484358	−	0.838933i
$834$		0			0
$835$	−0.109245	−	2.29333i	−0.00378058	−	0.0793641i
$836$		0			0
$837$	−0.732314	−	2.11588i	−0.0253125	−	0.0731356i
$838$		0			0
$839$	−4.66375	−	0.445334i	−0.161010	−	0.0153746i	0.0142395	−	0.999899i	$-0.495467\pi$
$839$	−4.66375	−	0.445334i	−0.161010	−	0.0153746i	−0.175250	+	0.984524i	$0.556073\pi$
$840$		0			0
$841$	8.96415	+	15.5264i	0.309109	+	0.535392i
$842$		0			0
$843$	17.5398	+	9.04238i	0.604102	+	0.311436i
$844$		0			0
$845$	−18.6471	−	7.46518i	−0.641480	−	0.256810i
$846$		0			0
$847$	2.01285	+	13.9997i	0.0691625	+	0.481036i
$848$		0			0
$849$	−1.84922	−	4.04923i	−0.0634651	−	0.138969i
$850$		0			0
$851$	15.1873	+	21.3276i	0.520614	+	0.731100i
$852$		0			0
$853$	−0.870350	+	0.348435i	−0.0298002	+	0.0119302i	−0.386515	−	0.922283i	$-0.626321\pi$
$853$	−0.870350	+	0.348435i	−0.0298002	+	0.0119302i	0.356714	+	0.934213i	$0.383897\pi$
$854$		0			0
$855$	−0.969007	−	3.99430i	−0.0331393	−	0.136602i
$856$		0			0
$857$	−3.35687	+	23.3475i	−0.114668	+	0.797537i	0.848607	+	0.529023i	$0.177442\pi$
$857$	−3.35687	+	23.3475i	−0.114668	+	0.797537i	−0.963276	+	0.268514i	$0.913468\pi$
$858$		0			0
$859$	17.9149	−	9.23577i	0.611249	−	0.315121i	−0.124662	−	0.992199i	$-0.539785\pi$
$859$	17.9149	−	9.23577i	0.611249	−	0.315121i	0.735911	+	0.677079i	$0.236754\pi$
$860$		0			0
$861$	10.3229	−	14.4965i	0.351803	−	0.494038i
$862$		0			0
$863$	31.2952	−	20.1122i	1.06530	−	0.684628i	0.114185	−	0.993460i	$-0.463574\pi$
$863$	31.2952	−	20.1122i	1.06530	−	0.684628i	0.951117	+	0.308832i	$0.0999380\pi$
$864$		0			0
$865$	9.54080	+	9.09713i	0.324397	+	0.309312i
$866$		0			0
$867$	13.3067	+	10.4645i	0.451920	+	0.355394i
$868$		0			0
$869$	1.61568	−	4.66820i	0.0548081	−	0.158358i
$870$		0			0
$871$	−10.7494	+	10.3133i	−0.364229	+	0.349454i
$872$		0			0
$873$	−0.365428	+	1.05584i	−0.0123679	+	0.0357346i
$874$		0			0
$875$	13.7820	+	10.8383i	0.465918	+	0.366402i
$876$		0			0
$877$	−16.4454	−	15.6806i	−0.555321	−	0.529497i	0.359613	−	0.933102i	$-0.382909\pi$
$877$	−16.4454	−	15.6806i	−0.555321	−	0.529497i	−0.914934	+	0.403604i	$0.867757\pi$
$878$		0			0
$879$	10.5441	−	6.77630i	0.355645	−	0.228559i
$880$		0			0
$881$	8.88373	−	12.4755i	0.299300	−	0.420309i	−0.637350	−	0.770575i	$-0.719969\pi$
$881$	8.88373	−	12.4755i	0.299300	−	0.420309i	0.936650	+	0.350266i	$0.113909\pi$
$882$		0			0
$883$	−32.8270	+	16.9235i	−1.10472	+	0.569521i	−0.911361	−	0.411607i	$-0.864968\pi$
$883$	−32.8270	+	16.9235i	−1.10472	+	0.569521i	−0.193356	+	0.981129i	$0.561937\pi$
$884$		0			0
$885$	2.00490	−	13.9444i	0.0673941	−	0.468736i
$886$		0			0
$887$	10.7646	+	44.3721i	0.361439	+	1.48987i	0.804810	+	0.593532i	$0.202267\pi$
$887$	10.7646	+	44.3721i	0.361439	+	1.48987i	−0.443372	+	0.896338i	$0.646218\pi$
$888$		0			0
$889$	−28.0045	+	11.2113i	−0.939241	+	0.376015i
$890$		0			0
$891$	−0.701953	−	0.985755i	−0.0235163	−	0.0330240i
$892$		0			0
$893$	−2.13500	−	4.67500i	−0.0714450	−	0.156443i
$894$		0			0
$895$	1.02429	+	7.12409i	0.0342382	+	0.238132i
$896$		0			0
$897$	−6.49074	−	2.59850i	−0.216719	−	0.0867613i
$898$		0			0
$899$	−6.62198	−	3.41387i	−0.220856	−	0.113859i
$900$		0			0
$901$	−19.2455	−	33.3342i	−0.641161	−	1.11052i
$902$		0			0
$903$	13.6150	+	1.30008i	0.453080	+	0.0432639i
$904$		0			0
$905$	3.47398	+	10.0374i	0.115479	+	0.333655i
$906$		0			0
$907$	−2.49127	−	52.2981i	−0.0827211	−	1.73653i	−0.535174	−	0.844742i	$-0.679754\pi$
$907$	−2.49127	−	52.2981i	−0.0827211	−	1.73653i	0.452453	−	0.891788i	$-0.350549\pi$
$908$		0			0
$909$	1.25408	−	2.17214i	0.0415953	−	0.0720452i
$910$		0			0
$911$	−44.7887	+	13.1511i	−1.48391	+	0.435717i	−0.920594	−	0.390522i	$-0.872295\pi$
$911$	−44.7887	+	13.1511i	−1.48391	+	0.435717i	−0.563321	+	0.826238i	$0.690476\pi$
$912$		0			0
$913$	5.01003	+	3.21975i	0.165808	+	0.106558i
$914$		0			0
$915$	16.2771	−	1.55428i	0.538105	−	0.0513828i
$916$		0			0
$917$	3.11539	−	12.8418i	0.102879	−	0.424074i
$918$		0			0
$919$	−33.4434	−	6.44568i	−1.10320	−	0.212623i	−0.395029	−	0.918669i	$-0.629265\pi$
$919$	−33.4434	−	6.44568i	−1.10320	−	0.212623i	−0.708167	+	0.706045i	$0.750477\pi$
$920$		0			0
$921$	13.2030	−	10.3830i	0.435054	−	0.342131i
$922$		0			0
$923$	−13.7821	+	15.9054i	−0.453643	+	0.523532i
$924$		0			0
$925$	−0.227453	+	4.77483i	−0.00747861	+	0.156995i
$926$		0			0
$927$	6.04837	−	5.76711i	0.198655	−	0.189417i
$928$		0			0
$929$	−25.7393	−	29.7047i	−0.844478	−	0.974580i	0.155434	−	0.987846i	$-0.450323\pi$
$929$	−25.7393	−	29.7047i	−0.844478	−	0.974580i	−0.999912	+	0.0132663i	$0.995777\pi$
$930$		0			0
$931$	9.34353	−	1.80082i	0.306222	−	0.0590194i
$932$		0			0
$933$	1.06750	+	0.313447i	0.0349485	+	0.0102618i
$934$		0			0
$935$	−6.07108	+	13.2938i	−0.198546	+	0.434754i
$936$		0			0
$937$	−32.5721			−1.06408			−0.532041	−	0.846718i	$-0.678575\pi$
$937$	−32.5721			−1.06408			−0.532041	+	0.846718i	$0.678575\pi$
$938$		0			0
$939$	9.44995			0.308387
$940$		0			0
$941$	4.40546	−	9.64662i	0.143614	−	0.314471i	−0.824132	−	0.566397i	$-0.808337\pi$
$941$	4.40546	−	9.64662i	0.143614	−	0.314471i	0.967746	+	0.251926i	$0.0810641\pi$
$942$		0			0
$943$	44.2256	+	12.9858i	1.44019	+	0.422877i
$944$		0			0
$945$	−3.01968	+	0.581995i	−0.0982301	+	0.0189323i
$946$		0			0
$947$	−10.3252	−	11.9159i	−0.335524	−	0.387215i	0.562768	−	0.826615i	$-0.309736\pi$
$947$	−10.3252	−	11.9159i	−0.335524	−	0.387215i	−0.898291	+	0.439400i	$0.855191\pi$
$948$		0			0
$949$	15.8217	−	15.0860i	0.513596	−	0.489713i
$950$		0			0
$951$	−0.0163504	+	0.343237i	−0.000530199	+	0.0111302i
$952$		0			0
$953$	25.4013	−	29.3147i	0.822830	−	0.949597i	−0.176568	−	0.984288i	$-0.556499\pi$
$953$	25.4013	−	29.3147i	0.822830	−	0.949597i	0.999398	+	0.0346917i	$0.0110449\pi$
$954$		0			0
$955$	−13.6192	+	10.7103i	−0.440707	+	0.346576i
$956$		0			0
$957$	−3.95389	−	0.762050i	−0.127811	−	0.0246336i
$958$		0			0
$959$	0.114791	−	0.473174i	0.00370679	−	0.0152796i
$960$		0			0
$961$	25.8691	−	2.47020i	0.834487	−	0.0796838i
$962$		0			0
$963$	1.25097	+	0.803951i	0.0403120	+	0.0259069i
$964$		0			0
$965$	−5.98998	+	1.75882i	−0.192824	+	0.0566183i
$966$		0			0
$967$	−18.4106	+	31.8880i	−0.592044	+	1.02545i	0.401913	+	0.915678i	$0.368345\pi$
$967$	−18.4106	+	31.8880i	−0.592044	+	1.02545i	−0.993957	+	0.109772i	$0.964988\pi$
$968$		0			0
$969$	0.549438	+	11.5341i	0.0176505	+	0.370530i
$970$		0			0
$971$	−19.8889	−	57.4653i	−0.638267	−	1.84415i	−0.526024	−	0.850470i	$-0.676318\pi$
$971$	−19.8889	−	57.4653i	−0.638267	−	1.84415i	−0.112243	−	0.993681i	$-0.535803\pi$
$972$		0			0
$973$	6.78850	+	0.648223i	0.217629	+	0.0207811i
$974$		0			0
$975$	−0.638240	−	1.10546i	−0.0204400	−	0.0354032i
$976$		0			0
$977$	−39.5716	−	20.4006i	−1.26601	−	0.652673i	−0.311327	−	0.950303i	$-0.600773\pi$
$977$	−39.5716	−	20.4006i	−1.26601	−	0.652673i	−0.954681	+	0.297630i	$0.903804\pi$
$978$		0			0
$979$	0.364864	+	0.146069i	0.0116611	+	0.00466840i
$980$		0			0
$981$	−0.788199	−	5.48205i	−0.0251653	−	0.175028i
$982$		0			0
$983$	−14.7451	−	32.2872i	−0.470295	−	1.02980i	−0.985019	−	0.172446i	$-0.944833\pi$
$983$	−14.7451	−	32.2872i	−0.470295	−	1.02980i	0.514724	−	0.857356i	$-0.327894\pi$
$984$		0			0
$985$	9.42493	+	13.2355i	0.300303	+	0.421717i
$986$		0			0
$987$	−3.56991	+	1.42918i	−0.113632	+	0.0454912i
$988$		0			0
$989$	8.35142	+	34.4250i	0.265560	+	1.09465i
$990$		0			0
$991$	4.71163	−	32.7701i	0.149670	−	1.04098i	−0.767091	−	0.641539i	$-0.778296\pi$
$991$	4.71163	−	32.7701i	0.149670	−	1.04098i	0.916761	−	0.399437i	$-0.130794\pi$
$992$		0			0
$993$	16.7542	−	8.63739i	0.531679	−	0.274099i
$994$		0			0
$995$	2.72225	−	3.82286i	0.0863010	−	0.121193i
$996$		0			0
$997$	11.8604	−	7.62224i	0.375624	−	0.241399i	−0.339183	−	0.940720i	$-0.610151\pi$
$997$	11.8604	−	7.62224i	0.375624	−	0.241399i	0.714807	+	0.699321i	$0.246514\pi$
$998$		0			0
$999$	−4.93254	−	4.70316i	−0.156059	−	0.148802i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.y.b.73.2	✓	120
67.56	even	33	inner	804.2.y.b.793.2	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.y.b.73.2	✓	120	1.1	even	1	trivial
804.2.y.b.793.2	yes	120	67.56	even	33	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.415415 + 0.909632i) q^{3} +(-1.98933 - 0.584119i) q^{5} +(1.45645 - 0.280708i) q^{7} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.415415 + 0.909632i) q^{3} +(-1.98933 - 0.584119i) q^{5} +(1.45645 - 0.280708i) q^{7} +(-0.654861 - 0.755750i) q^{9} +(-0.875823 + 0.835095i) q^{11} +(0.0865958 - 1.81787i) q^{13} +(1.35773 - 1.56690i) q^{15} +(-4.57862 + 3.60066i) q^{17} +(-1.94659 - 0.375175i) q^{19} +(-0.349691 + 1.44145i) q^{21} +(-3.82426 + 0.365173i) q^{23} +(-0.590046 - 0.379199i) q^{25} +(0.959493 - 0.281733i) q^{27} +(1.66371 - 2.88163i) q^{29} +(-0.106537 - 2.23649i) q^{31} +(-0.395799 - 1.14359i) q^{33} +(-3.06133 - 0.292321i) q^{35} +(-3.40770 - 5.90231i) q^{37} +(1.61762 + 0.833941i) q^{39} +(-11.1387 - 4.45926i) q^{41} +(-1.31227 - 9.12705i) q^{43} +(0.861284 + 1.88595i) q^{45} +(1.50381 + 2.11180i) q^{47} +(-4.45612 + 1.78396i) q^{49} +(-1.37325 - 5.66063i) q^{51} +(-0.940432 + 6.54085i) q^{53} +(2.23009 - 1.14969i) q^{55} +(1.14991 - 1.61483i) q^{57} +(5.71618 - 3.67357i) q^{59} +(5.70773 + 5.44231i) q^{61} +(-1.16592 - 0.916889i) q^{63} +(-1.23412 + 3.56575i) q^{65} +(-5.94150 - 5.63015i) q^{67} +(1.25648 - 3.63037i) q^{69} +(-9.08998 - 7.14844i) q^{71} +(8.69359 + 8.28933i) q^{73} +(0.590046 - 0.379199i) q^{75} +(-1.04118 + 1.46213i) q^{77} +(-3.62828 + 1.87051i) q^{79} +(-0.142315 + 0.989821i) q^{81} +(-1.16023 - 4.78254i) q^{83} +(11.2116 - 4.48844i) q^{85} +(1.93009 + 2.71043i) q^{87} +(-0.134913 - 0.295419i) q^{89} +(-0.384169 - 2.67195i) q^{91} +(2.07864 + 0.832163i) q^{93} +(3.65326 + 1.88338i) q^{95} +(-0.558643 - 0.967597i) q^{97} +(1.20466 + 0.115032i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9}+O(q^{10}) \) 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9	\( 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9} + 11 q^{11} + 2 q^{13} - 9 q^{15} + 48 q^{17} - 4 q^{19} - q^{21} + 22 q^{23} - 42 q^{25} + 12 q^{27} - q^{29} + 27 q^{31} + 17 q^{35} - 8 q^{37} - 2 q^{39} - 58 q^{41} - 17 q^{43} - 2 q^{45} - 84 q^{47} + 101 q^{49} - 26 q^{51} + 28 q^{53} - 9 q^{55} + 26 q^{57} + 34 q^{59} + 16 q^{61} + 12 q^{63} + 144 q^{65} + 23 q^{67} + 11 q^{69} + 173 q^{71} - 2 q^{73} + 42 q^{75} + 128 q^{77} + 31 q^{79} - 12 q^{81} + 47 q^{83} - 75 q^{85} - 10 q^{87} - 67 q^{89} + 16 q^{91} + 6 q^{93} - 79 q^{95} + 10 q^{97}+O(q^{100}) \) 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9 + 11 * q^11 + 2 * q^13 - 9 * q^15 + 48 * q^17 - 4 * q^19 - q^21 + 22 * q^23 - 42 * q^25 + 12 * q^27 - q^29 + 27 * q^31 + 17 * q^35 - 8 * q^37 - 2 * q^39 - 58 * q^41 - 17 * q^43 - 2 * q^45 - 84 * q^47 + 101 * q^49 - 26 * q^51 + 28 * q^53 - 9 * q^55 + 26 * q^57 + 34 * q^59 + 16 * q^61 + 12 * q^63 + 144 * q^65 + 23 * q^67 + 11 * q^69 + 173 * q^71 - 2 * q^73 + 42 * q^75 + 128 * q^77 + 31 * q^79 - 12 * q^81 + 47 * q^83 - 75 * q^85 - 10 * q^87 - 67 * q^89 + 16 * q^91 + 6 * q^93 - 79 * q^95 + 10 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more