LMFDB - Embedded newform 378.2.z.a.83.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(41,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([17, 9]))

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

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

chi := DirichletCharacter("378.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.z (of order $18$, degree $6$, 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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			83.2
Character	$\chi$	$=$	378.83
Dual form			378.2.z.a.41.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.984808 - 0.173648i) q^{2} +(-1.56441 + 0.743380i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-0.941136 + 0.789707i) q^{5} +(1.66973 - 0.460429i) q^{6} +(2.62387 - 0.339554i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(1.89477 - 2.32590i) q^{9} +O(q^{10})$	\(q+(-0.984808 - 0.173648i) q^{2} +(-1.56441 + 0.743380i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-0.941136 + 0.789707i) q^{5} +(1.66973 - 0.460429i) q^{6} +(2.62387 - 0.339554i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(1.89477 - 2.32590i) q^{9} +(1.06397 - 0.614283i) q^{10} +(-1.50712 + 1.79612i) q^{11} +(-1.72432 + 0.163488i) q^{12} +(0.429778 - 0.0757815i) q^{13} +(-2.64297 - 0.121235i) q^{14} +(0.885273 - 1.93505i) q^{15} +(0.766044 + 0.642788i) q^{16} +(1.74272 + 3.01848i) q^{17} +(-2.26988 + 1.96155i) q^{18} +(-1.97392 - 1.13964i) q^{19} +(-1.15447 + 0.420194i) q^{20} +(-3.85240 + 2.48174i) q^{21} +(1.79612 - 1.50712i) q^{22} +(-1.85030 + 5.08367i) q^{23} +(1.72651 + 0.138421i) q^{24} +(-0.606141 + 3.43760i) q^{25} -0.436408 q^{26} +(-1.23518 + 5.04721i) q^{27} +(2.58177 + 0.578340i) q^{28} +(-2.08501 - 0.367644i) q^{29} +(-1.20784 + 1.75193i) q^{30} +(-2.87174 + 7.89005i) q^{31} +(-0.642788 - 0.766044i) q^{32} +(1.02256 - 3.93024i) q^{33} +(-1.19209 - 3.27524i) q^{34} +(-2.20127 + 2.39166i) q^{35} +(2.57601 - 1.53759i) q^{36} +(2.71169 + 4.69678i) q^{37} +(1.74604 + 1.46510i) q^{38} +(-0.616016 + 0.438042i) q^{39} +(1.20990 - 0.213338i) q^{40} +(0.273818 + 1.55290i) q^{41} +(4.22482 - 1.77507i) q^{42} +(-1.56927 - 1.31677i) q^{43} +(-2.03054 + 1.17233i) q^{44} +(0.0535437 + 3.68531i) q^{45} +(2.70496 - 4.68513i) q^{46} +(4.45922 - 1.62303i) q^{47} +(-1.67624 - 0.436123i) q^{48} +(6.76941 - 1.78189i) q^{49} +(1.19386 - 3.28012i) q^{50} +(-4.97020 - 3.42664i) q^{51} +(0.429778 + 0.0757815i) q^{52} +0.117957i q^{53} +(2.09285 - 4.75605i) q^{54} -2.88058i q^{55} +(-2.44212 - 1.01787i) q^{56} +(3.93522 + 0.315500i) q^{57} +(1.98950 + 0.724117i) q^{58} +(-9.22472 + 7.74046i) q^{59} +(1.49371 - 1.51557i) q^{60} +(-3.82461 - 10.5080i) q^{61} +(4.19821 - 7.27151i) q^{62} +(4.18187 - 6.74625i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-0.344635 + 0.410720i) q^{65} +(-1.68951 + 3.69296i) q^{66} +(1.46744 + 8.32229i) q^{67} +(0.605240 + 3.43248i) q^{68} +(-0.884457 - 9.32843i) q^{69} +(2.58314 - 1.97307i) q^{70} +(-1.77135 + 1.02269i) q^{71} +(-2.80387 + 1.06691i) q^{72} +(6.00651 + 3.46786i) q^{73} +(-1.85490 - 5.09631i) q^{74} +(-1.60718 - 5.82841i) q^{75} +(-1.46510 - 1.74604i) q^{76} +(-3.34462 + 5.22454i) q^{77} +(0.682723 - 0.324417i) q^{78} +(-0.916064 + 5.19526i) q^{79} -1.22857 q^{80} +(-1.81967 - 8.81413i) q^{81} -1.57686i q^{82} +(1.50719 - 8.54769i) q^{83} +(-4.46888 + 1.01447i) q^{84} +(-4.02385 - 1.46456i) q^{85} +(1.31677 + 1.56927i) q^{86} +(3.53512 - 0.974809i) q^{87} +(2.20327 - 0.801923i) q^{88} +(7.35317 - 12.7361i) q^{89} +(0.587217 - 3.63862i) q^{90} +(1.10195 - 0.344774i) q^{91} +(-3.47743 + 4.14424i) q^{92} +(-1.37271 - 14.4781i) q^{93} +(-4.67331 + 0.824031i) q^{94} +(2.75771 - 0.486259i) q^{95} +(1.57505 + 0.720574i) q^{96} +(9.82215 - 11.7056i) q^{97} +(-6.97599 + 0.579328i) q^{98} +(1.32195 + 6.90866i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 12 q^{9}+O(q^{10}) $ 144 * q - 12 * q^9	$ 144 q - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 24 q^{21} - 60 q^{23} + 12 q^{29} - 72 q^{30} + 54 q^{35} - 12 q^{36} + 48 q^{39} + 24 q^{42} + 18 q^{49} - 60 q^{50} - 36 q^{51} + 6 q^{56} - 60 q^{57} - 36 q^{60} - 78 q^{63} + 72 q^{64} - 120 q^{65} + 36 q^{70} - 72 q^{71} - 24 q^{72} - 36 q^{74} + 66 q^{77} - 60 q^{78} - 72 q^{79} + 12 q^{84} - 72 q^{85} - 48 q^{86} - 18 q^{91} + 12 q^{92} + 24 q^{93} - 120 q^{95} + 36 q^{98} + 144 q^{99}+O(q^{100}) $ 144 * q - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 24 * q^21 - 60 * q^23 + 12 * q^29 - 72 * q^30 + 54 * q^35 - 12 * q^36 + 48 * q^39 + 24 * q^42 + 18 * q^49 - 60 * q^50 - 36 * q^51 + 6 * q^56 - 60 * q^57 - 36 * q^60 - 78 * q^63 + 72 * q^64 - 120 * q^65 + 36 * q^70 - 72 * q^71 - 24 * q^72 - 36 * q^74 + 66 * q^77 - 60 * q^78 - 72 * q^79 + 12 * q^84 - 72 * q^85 - 48 * q^86 - 18 * q^91 + 12 * q^92 + 24 * q^93 - 120 * q^95 + 36 * q^98 + 144 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$-1$

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 $

$2$	−0.984808	−	0.173648i	−0.696364	−	0.122788i
$2$	−0.984808	−	0.173648i	−0.696364	−	0.122788i
$3$	−1.56441	+	0.743380i	−0.903214	+	0.429190i
$3$	−1.56441	+	0.743380i	−0.903214	+	0.429190i
$4$	0.939693	+	0.342020i	0.469846	+	0.171010i
$5$	−0.941136	+	0.789707i	−0.420889	+	0.353168i	−0.828501	−	0.559987i	$-0.810806\pi$
$5$	−0.941136	+	0.789707i	−0.420889	+	0.353168i	0.407612	+	0.913155i	$0.366362\pi$
$6$	1.66973	−	0.460429i	0.681665	−	0.187969i
$7$	2.62387	−	0.339554i	0.991730	−	0.128339i
$7$	2.62387	−	0.339554i	0.991730	−	0.128339i
$8$	−0.866025	−	0.500000i	−0.306186	−	0.176777i
$9$	1.89477	−	2.32590i	0.631591	−	0.775302i
$10$	1.06397	−	0.614283i	0.336457	−	0.194253i
$11$	−1.50712	+	1.79612i	−0.454415	+	0.541550i	−0.943800	−	0.330517i	$-0.892777\pi$
$11$	−1.50712	+	1.79612i	−0.454415	+	0.541550i	0.489385	+	0.872068i	$0.337221\pi$
$12$	−1.72432	+	0.163488i	−0.497768	+	0.0471949i
$13$	0.429778	−	0.0757815i	0.119199	−	0.0210180i	−0.113730	−	0.993512i	$-0.536280\pi$
$13$	0.429778	−	0.0757815i	0.119199	−	0.0210180i	0.232929	+	0.972494i	$0.425169\pi$
$14$	−2.64297	−	0.121235i	−0.706364	−	0.0324014i
$15$	0.885273	−	1.93505i	0.228577	−	0.499627i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	1.74272	+	3.01848i	0.422671	+	0.732088i	0.996200	−	0.0870975i	$-0.0277592\pi$
$17$	1.74272	+	3.01848i	0.422671	+	0.732088i	−0.573529	+	0.819186i	$0.694426\pi$
$18$	−2.26988	+	1.96155i	−0.535015	+	0.462341i
$19$	−1.97392	−	1.13964i	−0.452849	−	0.261452i	0.256184	−	0.966628i	$-0.417535\pi$
$19$	−1.97392	−	1.13964i	−0.452849	−	0.261452i	−0.709032	+	0.705176i	$0.750868\pi$
$20$	−1.15447	+	0.420194i	−0.258148	+	0.0939583i
$21$	−3.85240	+	2.48174i	−0.840663	+	0.541559i
$22$	1.79612	−	1.50712i	0.382934	−	0.321320i
$23$	−1.85030	+	5.08367i	−0.385815	+	1.06002i	0.583052	+	0.812435i	$0.301858\pi$
$23$	−1.85030	+	5.08367i	−0.385815	+	1.06002i	−0.968867	+	0.247583i	$0.920364\pi$
$24$	1.72651	+	0.138421i	0.352423	+	0.0282550i
$25$	−0.606141	+	3.43760i	−0.121228	+	0.687519i
$26$	−0.436408			−0.0855867
$27$	−1.23518	+	5.04721i	−0.237710	+	0.971336i
$28$	2.58177	+	0.578340i	0.487908	+	0.109296i
$29$	−2.08501	−	0.367644i	−0.387177	−	0.0682698i	−0.0233285	−	0.999728i	$-0.507426\pi$
$29$	−2.08501	−	0.367644i	−0.387177	−	0.0682698i	−0.363849	+	0.931458i	$0.618537\pi$
$30$	−1.20784	+	1.75193i	−0.220521	+	0.319856i
$31$	−2.87174	+	7.89005i	−0.515780	+	1.41709i	0.359348	+	0.933203i	$0.382999\pi$
$31$	−2.87174	+	7.89005i	−0.515780	+	1.41709i	−0.875129	+	0.483891i	$0.839223\pi$
$32$	−0.642788	−	0.766044i	−0.113630	−	0.135419i
$33$	1.02256	−	3.93024i	0.178005	−	0.684166i
$34$	−1.19209	−	3.27524i	−0.204442	−	0.561699i
$35$	−2.20127	+	2.39166i	−0.372083	+	0.404264i
$36$	2.57601	−	1.53759i	0.429335	−	0.256264i
$37$	2.71169	+	4.69678i	0.445799	+	0.772146i	0.998107	−	0.0614933i	$-0.0195863\pi$
$37$	2.71169	+	4.69678i	0.445799	+	0.772146i	−0.552309	+	0.833640i	$0.686253\pi$
$38$	1.74604	+	1.46510i	0.283244	+	0.237670i
$39$	−0.616016	+	0.438042i	−0.0986416	+	0.0701429i
$40$	1.20990	−	0.213338i	0.191302	−	0.0337317i
$41$	0.273818	+	1.55290i	0.0427632	+	0.242522i	0.998695	−	0.0510656i	$-0.0162618\pi$
$41$	0.273818	+	1.55290i	0.0427632	+	0.242522i	−0.955932	+	0.293588i	$0.905151\pi$
$42$	4.22482	−	1.77507i	0.651904	−	0.273899i
$43$	−1.56927	−	1.31677i	−0.239311	−	0.200806i	0.515242	−	0.857045i	$-0.327702\pi$
$43$	−1.56927	−	1.31677i	−0.239311	−	0.200806i	−0.754553	+	0.656239i	$0.772146\pi$
$44$	−2.03054	+	1.17233i	−0.306116	+	0.176736i
$45$	0.0535437	+	3.68531i	0.00798183	+	0.549373i
$46$	2.70496	−	4.68513i	0.398825	−	0.690785i
$47$	4.45922	−	1.62303i	0.650445	−	0.236743i	0.00433921	−	0.999991i	$-0.498619\pi$
$47$	4.45922	−	1.62303i	0.650445	−	0.236743i	0.646106	+	0.763248i	$0.276397\pi$
$48$	−1.67624	−	0.436123i	−0.241945	−	0.0629490i
$49$	6.76941	−	1.78189i	0.967058	−	0.254556i
$50$	1.19386	−	3.28012i	0.168838	−	0.463878i
$51$	−4.97020	−	3.42664i	−0.695968	−	0.479826i
$52$	0.429778	+	0.0757815i	0.0595995	+	0.0105090i
$53$			0.117957i			0.0162026i	0.999967	+	0.00810130i	$0.00257875\pi$
$53$			0.117957i			0.0162026i	−0.999967	+	0.00810130i	$0.997421\pi$
$54$	2.09285	−	4.75605i	0.284801	−	0.647216i
$55$		−	2.88058i		−	0.388417i
$56$	−2.44212	−	1.01787i	−0.326342	−	0.136019i
$57$	3.93522	+	0.315500i	0.521232	+	0.0417890i
$58$	1.98950	+	0.724117i	0.261234	+	0.0950813i
$59$	−9.22472	+	7.74046i	−1.20096	+	1.00772i	−0.201354	+	0.979519i	$0.564534\pi$
$59$	−9.22472	+	7.74046i	−1.20096	+	1.00772i	−0.999602	+	0.0282033i	$0.991021\pi$
$60$	1.49371	−	1.51557i	0.192837	−	0.195659i
$61$	−3.82461	−	10.5080i	−0.489691	−	1.34542i	−0.900960	−	0.433902i	$-0.857136\pi$
$61$	−3.82461	−	10.5080i	−0.489691	−	1.34542i	0.411269	−	0.911514i	$-0.365086\pi$
$62$	4.19821	−	7.27151i	0.533173	−	0.923482i
$63$	4.18187	−	6.74625i	0.526866	−	0.849948i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$	−0.344635	+	0.410720i	−0.0427467	+	0.0509435i
$66$	−1.68951	+	3.69296i	−0.207964	+	0.454572i
$67$	1.46744	+	8.32229i	0.179277	+	1.01673i	0.933091	+	0.359641i	$0.117101\pi$
$67$	1.46744	+	8.32229i	0.179277	+	1.01673i	−0.753814	+	0.657088i	$0.771788\pi$
$68$	0.605240	+	3.43248i	0.0733961	+	0.416250i
$69$	−0.884457	−	9.32843i	−0.106476	−	1.12301i
$70$	2.58314	−	1.97307i	0.308744	−	0.235828i
$71$	−1.77135	+	1.02269i	−0.210220	+	0.121371i	−0.601414	−	0.798938i	$-0.705396\pi$
$71$	−1.77135	+	1.02269i	−0.210220	+	0.121371i	0.391194	+	0.920308i	$0.372062\pi$
$72$	−2.80387	+	1.06691i	−0.330440	+	0.125736i
$73$	6.00651	+	3.46786i	0.703009	+	0.405882i	0.808467	−	0.588541i	$-0.200298\pi$
$73$	6.00651	+	3.46786i	0.703009	+	0.405882i	−0.105458	+	0.994424i	$0.533631\pi$
$74$	−1.85490	−	5.09631i	−0.215628	−	0.592434i
$75$	−1.60718	−	5.82841i	−0.185582	−	0.673007i
$76$	−1.46510	−	1.74604i	−0.168058	−	0.200284i
$77$	−3.34462	+	5.22454i	−0.381155	+	0.595391i
$78$	0.682723	−	0.324417i	0.0773031	−	0.0367330i
$79$	−0.916064	+	5.19526i	−0.103065	+	0.584512i	0.888910	+	0.458081i	$0.151463\pi$
$79$	−0.916064	+	5.19526i	−0.103065	+	0.584512i	−0.991975	+	0.126431i	$0.959648\pi$
$80$	−1.22857			−0.137358
$81$	−1.81967	−	8.81413i	−0.202185	−	0.979347i
$82$		−	1.57686i		−	0.174135i
$83$	1.50719	−	8.54769i	0.165435	−	0.938231i	−0.783179	−	0.621797i	$-0.786403\pi$
$83$	1.50719	−	8.54769i	0.165435	−	0.938231i	0.948614	−	0.316435i	$-0.102486\pi$
$84$	−4.46888	+	1.01447i	−0.487594	+	0.110688i
$85$	−4.02385	−	1.46456i	−0.436447	−	0.158854i
$86$	1.31677	+	1.56927i	0.141991	+	0.169219i
$87$	3.53512	−	0.974809i	0.379005	−	0.104511i
$88$	2.20327	−	0.801923i	0.234869	−	0.0854853i
$89$	7.35317	−	12.7361i	0.779434	−	1.35002i	−0.152834	−	0.988252i	$-0.548840\pi$
$89$	7.35317	−	12.7361i	0.779434	−	1.35002i	0.932268	−	0.361768i	$-0.117827\pi$
$90$	0.587217	−	3.63862i	0.0618981	−	0.383544i
$91$	1.10195	−	0.344774i	0.115516	−	0.0361422i
$92$	−3.47743	+	4.14424i	−0.362548	+	0.432067i
$93$	−1.37271	−	14.4781i	−0.142343	−	1.50131i
$94$	−4.67331	+	0.824031i	−0.482016	+	0.0849924i
$95$	2.75771	−	0.486259i	0.282935	−	0.0498891i
$96$	1.57505	+	0.720574i	0.160753	+	0.0735433i
$97$	9.82215	−	11.7056i	0.997288	−	1.18852i	0.0152411	−	0.999884i	$-0.495148\pi$
$97$	9.82215	−	11.7056i	0.997288	−	1.18852i	0.982047	−	0.188638i	$-0.0604071\pi$
$98$	−6.97599	+	0.579328i	−0.704681	+	0.0585210i
$99$	1.32195	+	6.90866i	0.132861	+	0.694347i
$100$	−1.74531	+	3.02297i	−0.174531	+	0.302297i
$101$	11.7582	−	4.27964i	1.16999	−	0.425840i	0.317331	−	0.948315i	$-0.397213\pi$
$101$	11.7582	−	4.27964i	1.16999	−	0.425840i	0.852654	+	0.522475i	$0.174991\pi$
$102$	4.29967	+	4.23765i	0.425730	+	0.419590i
$103$	4.48548	+	5.34559i	0.441967	+	0.526716i	0.940335	−	0.340249i	$-0.110511\pi$
$103$	4.48548	+	5.34559i	0.441967	+	0.526716i	−0.498368	+	0.866966i	$0.666067\pi$
$104$	−0.410090	−	0.149260i	−0.0402126	−	0.0146362i
$105$	1.66579	−	5.37792i	0.162564	−	0.524831i
$106$	0.0204830	−	0.116165i	0.00198948	−	0.0112829i
$107$			3.92045i			0.379004i	0.981880	+	0.189502i	$0.0606874\pi$
$107$			3.92045i			0.379004i	−0.981880	+	0.189502i	$0.939313\pi$
$108$	−2.88693	+	4.32037i	−0.277795	+	0.415728i
$109$	−14.6558			−1.40377			−0.701885	−	0.712290i	$-0.747658\pi$
$109$	−14.6558			−1.40377			−0.701885	+	0.712290i	$0.747658\pi$
$110$	−0.500207	+	2.83682i	−0.0476929	+	0.270480i
$111$	−7.73369	−	5.33189i	−0.734050	−	0.506081i
$112$	2.22826	+	1.42648i	0.210551	+	0.134790i
$113$	2.86487	+	3.41422i	0.269504	+	0.321183i	0.883775	−	0.467913i	$-0.154994\pi$
$113$	2.86487	+	3.41422i	0.269504	+	0.321183i	−0.614270	+	0.789096i	$0.710549\pi$
$114$	−3.82064	−	0.994050i	−0.357836	−	0.0931013i
$115$	−2.27322	−	6.24562i	−0.211979	−	0.582407i
$116$	−1.83353	−	1.05859i	−0.170239	−	0.0982875i
$117$	0.638072	−	1.14321i	0.0589898	−	0.105690i
$118$	10.4287	−	6.02101i	0.960039	−	0.554279i
$119$	5.59761	+	7.32835i	0.513132	+	0.671789i
$120$	−1.73419	+	1.23316i	−0.158309	+	0.112572i
$121$	0.955505	+	5.41894i	0.0868641	+	0.492631i
$122$	1.94181	+	11.0125i	0.175803	+	0.997028i
$123$	−1.58276	−	2.22583i	−0.142713	−	0.200696i
$124$	−5.39711	+	6.43202i	−0.484675	+	0.577613i
$125$	−5.21565	−	9.03376i	−0.466502	−	0.808004i
$126$	−5.28981	+	5.91759i	−0.471254	+	0.527181i
$127$	0.559717	−	0.969458i	0.0496668	−	0.0860255i	−0.840123	−	0.542396i	$-0.817517\pi$
$127$	0.559717	−	0.969458i	0.0496668	−	0.0860255i	0.889790	+	0.456370i	$0.150851\pi$
$128$	−0.342020	−	0.939693i	−0.0302306	−	0.0830579i
$129$	3.43385	+	0.893414i	0.302333	+	0.0786607i
$130$	0.410720	−	0.344635i	0.0360225	−	0.0302265i
$131$	−16.4598	−	5.99087i	−1.43810	−	0.523425i	−0.498857	−	0.866684i	$-0.666247\pi$
$131$	−16.4598	−	5.99087i	−1.43810	−	0.523425i	−0.939241	+	0.343260i	$0.888469\pi$
$132$	2.30512	−	3.34348i	0.200635	−	0.291012i
$133$	−5.56629	−	2.32003i	−0.482658	−	0.201172i
$134$		−	8.45068i		−	0.730027i
$135$	−2.82335	−	5.72554i	−0.242995	−	0.492776i
$136$		−	3.48544i		−	0.298874i
$137$	22.1177	+	3.89995i	1.88965	+	0.333196i	0.993801	−	0.111172i	$-0.0354605\pi$
$137$	22.1177	+	3.89995i	1.88965	+	0.333196i	0.895845	+	0.444368i	$0.146572\pi$
$138$	−0.748845	+	9.34030i	−0.0637459	+	0.795099i
$139$	−6.05302	+	16.6305i	−0.513411	+	1.41058i	0.364250	+	0.931301i	$0.381325\pi$
$139$	−6.05302	+	16.6305i	−0.513411	+	1.41058i	−0.877660	+	0.479283i	$0.840897\pi$
$140$	−2.88651	+	1.49454i	−0.243955	+	0.126312i
$141$	−5.76954	+	5.85398i	−0.485883	+	0.492994i
$142$	1.92202	−	0.699559i	0.161293	−	0.0587057i
$143$	−0.511616	+	0.886145i	−0.0427835	+	0.0741032i
$144$	2.94654	−	0.563810i	0.245545	−	0.0469841i
$145$	2.25261	−	1.30055i	0.187069	−	0.108004i
$146$	−5.31307	−	4.45820i	−0.439713	−	0.368963i
$147$	−9.26552	+	7.81986i	−0.764207	+	0.644971i
$148$	0.941760	+	5.34098i	0.0774122	+	0.439026i
$149$	11.4259	−	2.01470i	0.936049	−	0.165051i	0.315239	−	0.949012i	$-0.397915\pi$
$149$	11.4259	−	2.01470i	0.936049	−	0.165051i	0.620809	+	0.783962i	$0.286804\pi$
$150$	0.570675	+	6.01895i	0.0465954	+	0.491445i
$151$	−8.42543	−	7.06977i	−0.685652	−	0.575330i	0.232000	−	0.972716i	$-0.425473\pi$
$151$	−8.42543	−	7.06977i	−0.685652	−	0.575330i	−0.917652	+	0.397386i	$0.869918\pi$
$152$	1.13964	+	1.97392i	0.0924373	+	0.160106i
$153$	10.3227	+	1.66593i	0.834545	+	0.134683i
$154$	4.20104	−	4.56438i	0.338529	−	0.367808i
$155$	−3.52812	−	9.69344i	−0.283386	−	0.778596i
$156$	−0.728685	+	0.200935i	−0.0583415	+	0.0160877i
$157$	9.34321	+	11.1348i	0.745669	+	0.888654i	0.996852	−	0.0792859i	$-0.0252640\pi$
$157$	9.34321	+	11.1348i	0.745669	+	0.888654i	−0.251183	+	0.967940i	$0.580820\pi$
$158$	1.80429	−	4.95726i	0.143542	−	0.394378i
$159$	−0.0876867	−	0.184533i	−0.00695400	−	0.0146344i
$160$	1.20990	+	0.213338i	0.0956511	+	0.0168659i
$161$	−3.12878	+	13.9672i	−0.246582	+	1.10077i
$162$	0.261466	+	8.99620i	0.0205427	+	0.706808i
$163$	3.92430			0.307375			0.153687	−	0.988120i	$-0.450885\pi$
$163$	3.92430			0.307375			0.153687	+	0.988120i	$0.450885\pi$
$164$	−0.273818	+	1.55290i	−0.0213816	+	0.121261i
$165$	2.14136	+	4.50641i	0.166705	+	0.350824i
$166$	−2.96858	+	8.15611i	−0.230407	+	0.633037i
$167$	−4.67824	+	3.92551i	−0.362013	+	0.303765i	−0.805592	−	0.592470i	$-0.798153\pi$
$167$	−4.67824	+	3.92551i	−0.362013	+	0.303765i	0.443579	+	0.896235i	$0.353708\pi$
$168$	4.57714	−	0.223046i	0.353134	−	0.0172084i
$169$	−12.0370	+	4.38112i	−0.925926	+	0.337009i
$170$	3.70840	+	2.14104i	0.284421	+	0.164211i
$171$	−6.39084	+	2.43179i	−0.488719	+	0.185963i
$172$	−1.02427	−	1.77408i	−0.0780997	−	0.135273i
$173$	18.9535	+	15.9039i	1.44101	+	1.20915i	0.938829	+	0.344384i	$0.111912\pi$
$173$	18.9535	+	15.9039i	1.44101	+	1.20915i	0.502178	+	0.864764i	$0.332532\pi$
$174$	−3.65069	+	0.346133i	−0.276758	+	0.0262403i
$175$	−0.423185	+	9.22563i	−0.0319898	+	0.697392i
$176$	−2.30905	+	0.407147i	−0.174051	+	0.0306899i
$177$	8.67717	−	18.9667i	0.652216	−	1.42563i
$178$	−9.45305	+	11.2657i	−0.708536	+	0.844401i
$179$	15.9501	−	9.20879i	1.19217	−	0.688297i	0.233369	−	0.972388i	$-0.425025\pi$
$179$	15.9501	−	9.20879i	1.19217	−	0.688297i	0.958797	+	0.284091i	$0.0916918\pi$
$180$	−1.21014	+	3.48137i	−0.0901981	+	0.259486i
$181$	−4.81715	−	2.78118i	−0.358056	−	0.206724i	0.310172	−	0.950681i	$-0.399613\pi$
$181$	−4.81715	−	2.78118i	−0.358056	−	0.206724i	−0.668228	+	0.743957i	$0.732947\pi$
$182$	−1.14508	+	0.148184i	−0.0848790	+	0.0109842i
$183$	13.7947	+	13.5958i	1.01974	+	1.00503i
$184$	4.14424	−	3.47743i	0.305518	−	0.256360i
$185$	−6.26115	−	2.27887i	−0.460329	−	0.167546i
$186$	−1.16224	+	14.4965i	−0.0852193	+	1.06293i
$187$	−8.04804	−	1.41909i	−0.588531	−	0.103774i
$188$	4.74541			0.346094
$189$	−1.52714	+	13.6626i	−0.111083	+	0.993811i
$190$	−2.80026			−0.203152
$191$	9.01172	+	1.58901i	0.652065	+	0.114977i	0.489888	−	0.871785i	$-0.337038\pi$
$191$	9.01172	+	1.58901i	0.652065	+	0.114977i	0.162176	+	0.986762i	$0.448149\pi$
$192$	−1.42599	−	0.983131i	−0.102912	−	0.0709514i
$193$	−25.3984	−	9.24425i	−1.82821	−	0.665416i	−0.993374	−	0.114923i	$-0.963338\pi$
$193$	−25.3984	−	9.24425i	−1.82821	−	0.665416i	−0.834840	−	0.550492i	$-0.814440\pi$
$194$	−11.7056	+	9.82215i	−0.840412	+	0.705189i
$195$	0.233830	−	0.898730i	0.0167449	−	0.0643594i
$196$	6.97060	+	0.640840i	0.497900	+	0.0457743i
$197$	−9.39441	−	5.42386i	−0.669324	−	0.386434i	0.126497	−	0.991967i	$-0.459627\pi$
$197$	−9.39441	−	5.42386i	−0.669324	−	0.386434i	−0.795820	+	0.605533i	$0.792960\pi$
$198$	−0.102186	−	7.03326i	−0.00726204	−	0.499832i
$199$	4.71281	−	2.72094i	0.334082	−	0.192882i	−0.323570	−	0.946204i	$-0.604883\pi$
$199$	4.71281	−	2.72094i	0.334082	−	0.192882i	0.657652	+	0.753322i	$0.271550\pi$
$200$	2.24373	−	2.67397i	0.158656	−	0.189079i
$201$	−8.48231	−	11.9286i	−0.598296	−	0.841381i
$202$	−12.3227	+	2.17283i	−0.867024	+	0.152880i
$203$	−5.59564	−	0.256676i	−0.392737	−	0.0180151i
$204$	−3.49848	−	4.91990i	−0.244943	−	0.344462i
$205$	−1.48404	−	1.24525i	−0.103650	−	0.0869724i
$206$	−3.48908	−	6.04327i	−0.243096	−	0.421055i
$207$	8.31822	+	13.9360i	0.578156	+	0.968621i
$208$	0.377941	+	0.218204i	0.0262055	+	0.0151297i
$209$	5.02188	−	1.82781i	0.347371	−	0.126433i
$210$	−2.57435	+	5.00695i	−0.177647	+	0.345513i
$211$	17.8538	−	14.9811i	1.22911	−	1.03134i	0.230809	−	0.972999i	$-0.425863\pi$
$211$	17.8538	−	14.9811i	1.22911	−	1.03134i	0.998297	−	0.0583429i	$-0.0185817\pi$
$212$	−0.0403436	+	0.110843i	−0.00277081	+	0.00761273i
$213$	2.01087	−	2.91669i	0.137783	−	0.199848i
$214$	0.680779	−	3.86089i	0.0465371	−	0.263925i
$215$	2.51676			0.171642
$216$	3.59330	−	3.75342i	0.244493	−	0.255388i
$217$	−4.85598	+	21.6776i	−0.329646	+	1.47157i
$218$	14.4331	+	2.54495i	0.977536	+	0.172366i
$219$	−11.9746	−	0.960047i	−0.809168	−	0.0648739i
$220$	0.985216	−	2.70686i	0.0664232	−	0.182496i
$221$	0.977727	+	1.16521i	0.0657691	+	0.0783805i
$222$	6.69033	+	6.59383i	0.449025	+	0.442549i
$223$	−2.24207	−	6.16004i	−0.150140	−	0.412507i	0.841708	−	0.539933i	$-0.181551\pi$
$223$	−2.24207	−	6.16004i	−0.150140	−	0.412507i	−0.991848	+	0.127426i	$0.959328\pi$
$224$	−1.94671	−	1.79174i	−0.130070	−	0.119716i
$225$	6.84702	+	7.92329i	0.456468	+	0.528219i
$226$	−2.22847	−	3.85983i	−0.148236	−	0.256752i
$227$	4.62522	+	3.88102i	0.306986	+	0.257592i	0.783245	−	0.621713i	$-0.213563\pi$
$227$	4.62522	+	3.88102i	0.306986	+	0.257592i	−0.476259	+	0.879305i	$0.658007\pi$
$228$	3.58999	+	1.64240i	0.237753	+	0.108770i
$229$	19.5706	−	3.45082i	1.29326	−	0.228037i	0.515659	−	0.856794i	$-0.327547\pi$
$229$	19.5706	−	3.45082i	1.29326	−	0.228037i	0.777602	+	0.628757i	$0.216436\pi$
$230$	1.15414	+	6.54548i	0.0761020	+	0.431596i
$231$	1.34855	−	10.6597i	0.0887279	−	0.701354i
$232$	1.62185	+	1.36090i	0.106480	+	0.0893472i
$233$	3.33964	−	1.92814i	0.218787	−	0.126317i	−0.386601	−	0.922247i	$-0.626351\pi$
$233$	3.33964	−	1.92814i	0.218787	−	0.126317i	0.605389	+	0.795930i	$0.293018\pi$
$234$	−0.826895	+	1.01504i	−0.0540558	+	0.0663555i
$235$	−2.91502	+	5.04897i	−0.190155	+	0.329358i
$236$	−11.3158	+	4.11861i	−0.736595	+	0.268099i
$237$	−2.42895	−	8.80851i	−0.157777	−	0.572174i
$238$	−4.24001	−	8.18903i	−0.274839	−	0.530816i
$239$	3.12052	−	8.57356i	0.201850	−	0.554578i	−0.796924	−	0.604079i	$-0.793541\pi$
$239$	3.12052	−	8.57356i	0.201850	−	0.554578i	0.998774	+	0.0495016i	$0.0157633\pi$
$240$	1.92198	−	0.913291i	0.124064	−	0.0589527i
$241$	−27.7998	−	4.90186i	−1.79074	−	0.315757i	−0.823066	−	0.567945i	$-0.807739\pi$
$241$	−27.7998	−	4.90186i	−1.79074	−	0.315757i	−0.967678	+	0.252188i	$0.918850\pi$
$242$		−	5.50254i		−	0.353716i
$243$	9.39895	+	12.4362i	0.602943	+	0.797784i
$244$		−	11.1824i		−	0.715881i
$245$	−4.96376	+	7.02285i	−0.317123	+	0.448673i
$246$	1.17220	+	2.46685i	0.0747369	+	0.157281i
$247$	−0.934713	−	0.340208i	−0.0594743	−	0.0216469i
$248$	6.43202	−	5.39711i	0.408434	−	0.342717i
$249$	3.99632	+	14.4925i	0.253256	+	0.918427i
$250$	3.56771	+	9.80221i	0.225642	+	0.619946i
$251$	−5.07709	+	8.79378i	−0.320463	+	0.555058i	−0.980584	−	0.196101i	$-0.937172\pi$
$251$	−5.07709	+	8.79378i	−0.320463	+	0.555058i	0.660121	+	0.751160i	$0.270505\pi$
$252$	6.23703	−	4.90912i	0.392896	−	0.309246i
$253$	−6.34224	−	10.9851i	−0.398733	−	0.690626i
$254$	−0.719558	+	0.857536i	−0.0451491	+	0.0538066i
$255$	7.38368	−	0.700069i	0.462384	−	0.0438400i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−2.19809	−	12.4660i	−0.137113	−	0.777607i	−0.973365	−	0.229261i	$-0.926369\pi$
$257$	−2.19809	−	12.4660i	−0.137113	−	0.777607i	0.836252	−	0.548346i	$-0.184742\pi$
$258$	−3.22654	−	1.47612i	−0.200876	−	0.0918994i
$259$	8.70994	+	11.4030i	0.541209	+	0.708547i
$260$	−0.464325	+	0.268078i	−0.0287962	+	0.0166255i
$261$	−4.80573	+	4.15294i	−0.297467	+	0.257061i
$262$	15.1694	+	8.75806i	0.937169	+	0.541075i
$263$	−9.71268	−	26.6854i	−0.598909	−	1.64549i	−0.753451	−	0.657504i	$-0.771612\pi$
$263$	−9.71268	−	26.6854i	−0.598909	−	1.64549i	0.154542	−	0.987986i	$-0.450610\pi$
$264$	−2.85068	+	2.89240i	−0.175447	+	0.178015i
$265$	−0.0931513	−	0.111013i	−0.00572224	−	0.00681950i
$266$	5.07885	+	3.25136i	0.311405	+	0.199353i
$267$	−2.03566	+	25.3907i	−0.124580	+	1.55388i
$268$	−1.46744	+	8.32229i	−0.0896384	+	0.508365i
$269$	−12.8796			−0.785282			−0.392641	−	0.919692i	$-0.628438\pi$
$269$	−12.8796			−0.785282			−0.392641	+	0.919692i	$0.628438\pi$
$270$	1.78623	+	6.12883i	0.108706	+	0.372988i
$271$		−	23.3304i		−	1.41722i	−0.705601	−	0.708610i	$-0.749323\pi$
$271$		−	23.3304i		−	1.41722i	0.705601	−	0.708610i	$-0.250677\pi$
$272$	−0.605240	+	3.43248i	−0.0366980	+	0.208125i
$273$	−1.46761	+	1.35854i	−0.0888237	+	0.0822224i
$274$	−21.1045	−	7.68141i	−1.27497	−	0.464051i
$275$	−5.26080	−	6.26958i	−0.317238	−	0.378070i
$276$	2.35939	−	9.06836i	0.142019	−	0.545851i
$277$	−20.8905	+	7.60350i	−1.25519	+	0.456850i	−0.882151	−	0.470967i	$-0.843905\pi$
$277$	−20.8905	+	7.60350i	−1.25519	+	0.456850i	−0.373035	+	0.927817i	$0.621683\pi$
$278$	8.84893	−	15.3268i	0.530723	−	0.919240i
$279$	12.9102	+	21.6292i	0.772913	+	1.29491i
$280$	3.10219	−	0.970599i	0.185391	−	0.0580044i
$281$	−6.37582	+	7.59841i	−0.380350	+	0.453283i	−0.921925	−	0.387369i	$-0.873384\pi$
$281$	−6.37582	+	7.59841i	−0.380350	+	0.453283i	0.541575	+	0.840653i	$0.317828\pi$
$282$	6.69842	−	4.76317i	0.398885	−	0.283643i
$283$	7.82006	−	1.37889i	0.464855	−	0.0819664i	0.0636847	−	0.997970i	$-0.479715\pi$
$283$	7.82006	−	1.37889i	0.464855	−	0.0819664i	0.401170	+	0.916004i	$0.368604\pi$
$284$	−2.01430	+	0.355176i	−0.119527	+	0.0210758i
$285$	−3.95273	+	2.81074i	−0.234139	+	0.166494i
$286$	0.657721	−	0.783842i	0.0388919	−	0.0463495i
$287$	1.24576	+	3.98164i	0.0735348	+	0.235029i
$288$	−2.99968	+	0.0435823i	−0.176758	+	0.00256811i
$289$	2.42587	−	4.20172i	0.142698	−	0.247160i
$290$	−2.44423	+	0.889626i	−0.143530	+	0.0522406i
$291$	−6.66420	+	25.6139i	−0.390662	+	1.50152i
$292$	4.45820	+	5.31307i	0.260896	+	0.310924i
$293$	11.8053	+	4.29677i	0.689672	+	0.251020i	0.662995	−	0.748624i	$-0.269285\pi$
$293$	11.8053	+	4.29677i	0.689672	+	0.251020i	0.0266772	+	0.999644i	$0.491507\pi$
$294$	10.4827	−	6.09211i	0.611361	−	0.355299i
$295$	2.56902	−	14.5696i	0.149574	−	0.848278i
$296$		−	5.42338i		−	0.315227i
$297$	−7.20383	−	9.82529i	−0.418009	−	0.570121i
$298$	−11.6022			−0.672097
$299$	−0.409972	+	2.32507i	−0.0237093	+	0.134462i
$300$	0.483175	−	6.02660i	0.0278961	−	0.347946i
$301$	−4.56468	−	2.92219i	−0.263104	−	0.168432i
$302$	7.06977	+	8.42543i	0.406820	+	0.484829i
$303$	−15.2133	+	15.4359i	−0.873981	+	0.886771i
$304$	−0.779562	−	2.14183i	−0.0447110	−	0.122842i
$305$	11.8977	+	6.86917i	0.681263	+	0.393327i
$306$	−9.87663	−	3.43315i	−0.564610	−	0.196260i
$307$	−7.67098	+	4.42884i	−0.437806	+	0.252767i	−0.702667	−	0.711519i	$-0.748007\pi$
$307$	−7.67098	+	4.42884i	−0.437806	+	0.252767i	0.264861	+	0.964287i	$0.414674\pi$
$308$	−4.92981	+	3.76553i	−0.280902	+	0.214561i
$309$	−10.9909	−	5.02829i	−0.625253	−	0.286049i
$310$	1.79128	+	10.1588i	0.101738	+	0.576983i
$311$	−3.63244	−	20.6006i	−0.205977	−	1.16815i	−0.895895	−	0.444266i	$-0.853465\pi$
$311$	−3.63244	−	20.6006i	−0.205977	−	1.16815i	0.689918	−	0.723887i	$-0.257647\pi$
$312$	0.752507	−	0.0713474i	0.0426023	−	0.00403925i
$313$	−8.13089	+	9.69001i	−0.459585	+	0.547712i	−0.945213	−	0.326453i	$-0.894146\pi$
$313$	−8.13089	+	9.69001i	−0.459585	+	0.547712i	0.485628	+	0.874165i	$0.338591\pi$
$314$	−7.26772	−	12.5881i	−0.410141	−	0.710386i
$315$	1.39185	+	9.65160i	0.0784221	+	0.543806i
$316$	−2.63770	+	4.56863i	−0.148382	+	0.257006i
$317$	1.60647	+	4.41375i	0.0902285	+	0.247901i	0.976596	−	0.215081i	$-0.0690017\pi$
$317$	1.60647	+	4.41375i	0.0902285	+	0.247901i	−0.886368	+	0.462982i	$0.846779\pi$
$318$	0.0543107	+	0.196956i	0.00304559	+	0.0110448i
$319$	3.80270	−	3.19085i	0.212911	−	0.178653i
$320$	−1.15447	−	0.420194i	−0.0645371	−	0.0234896i
$321$	−2.91438	−	6.13320i	−0.162665	−	0.342322i
$322$	5.50662	−	13.2117i	0.306872	−	0.736258i
$323$		−	7.94431i		−	0.442033i
$324$	1.30468	−	8.90493i	0.0724822	−	0.494718i
$325$			1.52334i			0.0844996i
$326$	−3.86468	−	0.681447i	−0.214045	−	0.0377419i
$327$	22.9277	−	10.8948i	1.26791	−	0.602485i
$328$	0.539317	−	1.48176i	0.0297788	−	0.0818165i
$329$	11.1493	−	5.77276i	0.614682	−	0.318262i
$330$	−1.32630	−	4.80979i	−0.0730105	−	0.264770i
$331$	9.76080	−	3.55264i	0.536502	−	0.195271i	−0.0595370	−	0.998226i	$-0.518962\pi$
$331$	9.76080	−	3.55264i	0.536502	−	0.195271i	0.596039	+	0.802955i	$0.296740\pi$
$332$	4.33978	−	7.51671i	0.238176	−	0.412533i
$333$	16.0623	+	2.59221i	0.880209	+	0.142052i
$334$	5.28882	−	3.05350i	0.289392	−	0.167080i
$335$	−7.95324	−	6.67356i	−0.434532	−	0.364615i
$336$	−4.54634	−	0.575155i	−0.248023	−	0.0313773i
$337$	−0.683890	−	3.87853i	−0.0372538	−	0.211277i	0.960499	−	0.278285i	$-0.0897659\pi$
$337$	−0.683890	−	3.87853i	−0.0372538	−	0.211277i	−0.997752	+	0.0670077i	$0.978655\pi$
$338$	12.6149	−	2.22435i	0.686162	−	0.120989i
$339$	−7.01990	−	3.21156i	−0.381269	−	0.174428i
$340$	−3.28027	−	2.75247i	−0.177898	−	0.149274i
$341$	−9.84340	−	17.0493i	−0.533050	−	0.923269i
$342$	6.71602	−	1.28508i	0.363161	−	0.0694894i
$343$	17.1570	−	6.97404i	0.926391	−	0.376563i
$344$	0.700641	+	1.92499i	0.0377760	+	0.103789i
$345$	8.19912	+	8.08086i	0.441426	+	0.435059i
$346$	−15.9039	−	18.9535i	−0.854997	−	1.01895i
$347$	9.50367	−	26.1111i	0.510184	−	1.40172i	−0.370862	−	0.928688i	$-0.620938\pi$
$347$	9.50367	−	26.1111i	0.510184	−	1.40172i	0.881046	−	0.473030i	$-0.156840\pi$
$348$	3.65533	+	0.293061i	0.195946	+	0.0157097i
$349$	16.5657	+	2.92098i	0.886740	+	0.156356i	0.598425	−	0.801179i	$-0.295794\pi$
$349$	16.5657	+	2.92098i	0.886740	+	0.156356i	0.288316	+	0.957535i	$0.406905\pi$
$350$	2.01877	−	9.01198i	0.107908	−	0.481711i
$351$	−0.148367	+	2.26279i	−0.00791924	+	0.120779i
$352$	2.34467			0.124971
$353$	−0.293221	+	1.66294i	−0.0156066	+	0.0885094i	−0.991616	−	0.129218i	$-0.958753\pi$
$353$	−0.293221	+	1.66294i	−0.0156066	+	0.0885094i	0.976010	+	0.217727i	$0.0698644\pi$
$354$	−11.8389	+	17.1718i	−0.629229	+	0.912672i
$355$	0.859455	−	2.36133i	0.0456151	−	0.125327i
$356$	11.2657	−	9.45305i	0.597081	−	0.501011i
$357$	−14.2047	−	7.30341i	−0.751793	−	0.386538i
$358$	−17.3069	+	6.29918i	−0.914696	+	0.332922i
$359$	−10.5518	−	6.09211i	−0.556905	−	0.321529i	0.194997	−	0.980804i	$-0.437530\pi$
$359$	−10.5518	−	6.09211i	−0.556905	−	0.321529i	−0.751902	+	0.659274i	$0.770864\pi$
$360$	1.79628	−	3.21834i	0.0946725	−	0.169622i
$361$	−6.90242	−	11.9553i	−0.363285	−	0.629229i
$362$	4.26102	+	3.57542i	0.223954	+	0.187920i
$363$	−5.52313	−	7.76715i	−0.289889	−	0.407670i
$364$	1.15342	+	0.0529079i	0.0604554	+	0.00277313i
$365$	−8.39154	+	1.47965i	−0.439233	+	0.0774486i
$366$	−11.2243	−	15.7846i	−0.586702	−	0.825076i
$367$	13.7838	−	16.4269i	0.719507	−	0.857475i	−0.275076	−	0.961423i	$-0.588703\pi$
$367$	13.7838	−	16.4269i	0.719507	−	0.857475i	0.994583	+	0.103948i	$0.0331474\pi$
$368$	−4.68513	+	2.70496i	−0.244229	+	0.141006i
$369$	4.13072	+	2.30552i	0.215037	+	0.120021i
$370$	5.77031	+	3.33149i	0.299984	+	0.173196i
$371$	0.0400527	+	0.309503i	0.00207943	+	0.0160686i
$372$	3.66187	−	14.0744i	0.189859	−	0.729726i
$373$	15.0931	−	12.6646i	0.781491	−	0.655749i	−0.162133	−	0.986769i	$-0.551837\pi$
$373$	15.0931	−	12.6646i	0.781491	−	0.655749i	0.943624	+	0.331020i	$0.107393\pi$
$374$	7.67935	+	2.79505i	0.397090	+	0.144529i
$375$	14.8749	+	10.2553i	0.768139	+	0.529583i
$376$	−4.67331	−	0.824031i	−0.241008	−	0.0424962i
$377$	−0.923954			−0.0475861
$378$	3.87644	−	13.1899i	0.199382	−	0.678415i
$379$	24.8328			1.27558			0.637788	−	0.770212i	$-0.279849\pi$
$379$	24.8328			1.27558			0.637788	+	0.770212i	$0.279849\pi$
$380$	2.75771	+	0.486259i	0.141468	+	0.0249446i
$381$	−0.154953	+	1.93271i	−0.00793847	+	0.0990160i
$382$	−8.59888	−	3.12974i	−0.439957	−	0.160131i
$383$	−7.41782	+	6.22429i	−0.379033	+	0.318047i	−0.812323	−	0.583208i	$-0.801797\pi$
$383$	−7.41782	+	6.22429i	−0.379033	+	0.318047i	0.433290	+	0.901255i	$0.357353\pi$
$384$	1.23361	+	1.21582i	0.0629523	+	0.0620444i
$385$	−0.978113	−	7.55827i	−0.0498492	−	0.385205i
$386$	23.4073	+	13.5142i	1.19140	+	0.687854i
$387$	−6.03610	+	1.15498i	−0.306832	+	0.0587112i
$388$	13.2333	−	7.64027i	0.671821	−	0.387876i
$389$	19.7679	−	23.5584i	1.00227	−	1.19446i	0.0214059	−	0.999771i	$-0.493186\pi$
$389$	19.7679	−	23.5584i	1.00227	−	1.19446i	0.980865	−	0.194689i	$-0.0623698\pi$
$390$	−0.386341	+	0.844472i	−0.0195631	+	0.0427615i
$391$	−18.5695	+	3.27430i	−0.939099	+	0.165589i
$392$	−6.75342	−	1.84154i	−0.341099	−	0.0930117i
$393$	30.2034	−	2.86367i	1.52356	−	0.144453i
$394$	8.30984	+	6.97278i	0.418644	+	0.351284i
$395$	−3.24059	−	5.61286i	−0.163052	−	0.282414i
$396$	−1.12068	+	6.94415i	−0.0563162	+	0.348957i
$397$	−7.92617	−	4.57618i	−0.397803	−	0.229672i	0.287732	−	0.957711i	$-0.407099\pi$
$397$	−7.92617	−	4.57618i	−0.397803	−	0.229672i	−0.685536	+	0.728039i	$0.740432\pi$
$398$	−5.11369	+	1.86123i	−0.256326	+	0.0932952i
$399$	10.4326	−	0.508387i	0.522285	−	0.0254512i
$400$	−2.67397	+	2.24373i	−0.133699	+	0.112187i
$401$	−11.1932	+	30.7530i	−0.558961	+	1.53573i	0.262187	+	0.965017i	$0.415556\pi$
$401$	−11.1932	+	30.7530i	−0.558961	+	1.53573i	−0.821148	+	0.570715i	$0.806666\pi$
$402$	6.28206	+	13.2203i	0.313321	+	0.659371i
$403$	−0.636293	+	3.60860i	−0.0316960	+	0.179757i
$404$	12.5128			0.622536
$405$	8.67313	+	6.85829i	0.430971	+	0.340791i
$406$	5.46606	+	1.22445i	0.271276	+	0.0607684i
$407$	−12.5228	−	2.20811i	−0.620734	−	0.109452i
$408$	2.59100	+	5.45266i	0.128274	+	0.269947i
$409$	2.40239	−	6.60050i	0.118790	−	0.326374i	−0.866020	−	0.500010i	$-0.833330\pi$
$409$	2.40239	−	6.60050i	0.118790	−	0.326374i	0.984810	+	0.173637i	$0.0555518\pi$
$410$	1.24525	+	1.48404i	0.0614987	+	0.0732913i
$411$	−37.5004	+	10.3407i	−1.84976	+	0.510071i
$412$	2.38667	+	6.55733i	0.117583	+	0.323057i
$413$	−21.5762	+	23.4423i	−1.06169	+	1.15352i
$414$	−5.77188	−	15.1688i	−0.283673	−	0.745504i
$415$	5.33170	+	9.23478i	0.261723	+	0.453317i
$416$	−0.334308	−	0.280518i	−0.0163908	−	0.0137535i
$417$	−2.89338	−	30.5167i	−0.141690	−	1.49441i
$418$	−5.26298	+	0.928006i	−0.257421	+	0.0453902i
$419$	5.62520	+	31.9021i	0.274809	+	1.55852i	0.739568	+	0.673082i	$0.235030\pi$
$419$	5.62520	+	31.9021i	0.274809	+	1.55852i	−0.464759	+	0.885437i	$0.653859\pi$
$420$	3.40469	−	4.48386i	0.166132	−	0.218790i
$421$	7.36408	+	6.17920i	0.358903	+	0.301156i	0.804353	−	0.594151i	$-0.202512\pi$
$421$	7.36408	+	6.17920i	0.358903	+	0.301156i	−0.445450	+	0.895307i	$0.646956\pi$
$422$	−20.1840	+	11.6532i	−0.982541	+	0.567271i
$423$	4.67422	−	13.4470i	0.227268	−	0.653815i
$424$	0.0589784	−	0.102154i	0.00286424	−	0.00496101i
$425$	−11.4326	+	4.16114i	−0.554564	+	0.201845i
$426$	−2.48680	+	2.52319i	−0.120486	+	0.122249i
$427$	−13.6033	−	26.2731i	−0.658312	−	1.27144i
$428$	−1.34087	+	3.68402i	−0.0648135	+	0.178074i
$429$	0.141636	−	1.76662i	0.00683827	−	0.0852933i
$430$	−2.47853	−	0.437031i	−0.119525	−	0.0210755i
$431$		−	1.82273i		−	0.0877979i	−0.999036	−	0.0438989i	$-0.986022\pi$
$431$		−	1.82273i		−	0.0877979i	0.999036	−	0.0438989i	$-0.0139780\pi$
$432$	−4.19048	+	3.07243i	−0.201615	+	0.147822i
$433$			32.5239i			1.56300i	0.623906	+	0.781499i	$0.285545\pi$
$433$			32.5239i			1.56300i	−0.623906	+	0.781499i	$0.714455\pi$
$434$	8.54648	−	20.5050i	0.410244	−	0.984272i
$435$	−2.55722	+	3.70914i	−0.122609	+	0.177840i
$436$	−13.7719	−	5.01258i	−0.659556	−	0.240059i
$437$	9.44592	−	7.92607i	0.451860	−	0.379155i
$438$	11.6260	+	3.02483i	0.555510	+	0.144532i
$439$	10.8479	+	29.8044i	0.517743	+	1.42249i	0.873001	+	0.487719i	$0.162171\pi$
$439$	10.8479	+	29.8044i	0.517743	+	1.42249i	−0.355257	+	0.934768i	$0.615607\pi$
$440$	−1.44029	+	2.49465i	−0.0686631	+	0.118928i
$441$	8.68197	−	19.1213i	0.413427	−	0.910537i
$442$	−0.760537	−	1.31729i	−0.0361751	−	0.0626570i
$443$	−22.8370	+	27.2161i	−1.08502	+	1.29307i	−0.131640	+	0.991298i	$0.542024\pi$
$443$	−22.8370	+	27.2161i	−1.08502	+	1.29307i	−0.953379	+	0.301777i	$0.902420\pi$
$444$	−5.44368	−	7.65542i	−0.258346	−	0.363310i
$445$	3.13742	+	17.7932i	0.148728	+	0.843479i
$446$	1.13833	+	6.45579i	0.0539015	+	0.305690i
$447$	−16.3772	+	11.6456i	−0.774614	+	0.550819i
$448$	1.60600	+	2.10256i	0.0758763	+	0.0993367i
$449$	−5.81350	+	3.35643i	−0.274356	+	0.158400i	−0.630866	−	0.775892i	$-0.717300\pi$
$449$	−5.81350	+	3.35643i	−0.274356	+	0.158400i	0.356509	+	0.934292i	$0.383967\pi$
$450$	−5.36713	−	8.99189i	−0.253009	−	0.423882i
$451$	−3.20187	−	1.84860i	−0.150770	−	0.0870473i
$452$	1.52437	+	4.18816i	0.0717002	+	0.196995i
$453$	18.4364	+	4.79675i	0.866216	+	0.225371i
$454$	−3.88102	−	4.62522i	−0.182145	−	0.217072i
$455$	−0.764816	+	1.19470i	−0.0358551	+	0.0560083i
$456$	−3.25025	−	2.24084i	−0.152207	−	0.104937i
$457$	0.292432	−	1.65846i	0.0136794	−	0.0775796i	−0.977204	−	0.212303i	$-0.931904\pi$
$457$	0.292432	−	1.65846i	0.0136794	−	0.0775796i	0.990883	+	0.134724i	$0.0430147\pi$
$458$	−19.8725			−0.928580
$459$	−17.3875	+	5.06751i	−0.811577	+	0.236531i
$460$		−	6.64645i		−	0.309892i
$461$	0.201902	−	1.14505i	0.00940353	−	0.0533301i	−0.979745	−	0.200250i	$-0.935825\pi$
$461$	0.201902	−	1.14505i	0.00940353	−	0.0533301i	0.989148	+	0.146919i	$0.0469358\pi$
$462$	−3.17909	+	10.2635i	−0.147905	+	0.477503i
$463$	−0.00916975	−	0.00333751i	−0.000426154	−	0.000155107i	0.341807	−	0.939770i	$-0.388961\pi$
$463$	−0.00916975	−	0.00333751i	−0.000426154	−	0.000155107i	−0.342233	+	0.939615i	$0.611183\pi$
$464$	−1.36090	−	1.62185i	−0.0631780	−	0.0752926i
$465$	12.7253	+	12.5418i	0.590124	+	0.581612i
$466$	−3.62372	+	1.31893i	−0.167866	+	0.0610981i
$467$	4.32870	−	7.49752i	0.200308	−	0.346944i	−0.748320	−	0.663338i	$-0.769139\pi$
$467$	4.32870	−	7.49752i	0.200308	−	0.346944i	0.948628	+	0.316394i	$0.102472\pi$
$468$	0.990593	−	0.856035i	0.0457902	−	0.0395702i
$469$	6.67626	+	21.3383i	0.308281	+	0.985313i
$470$	3.74748	−	4.46607i	0.172858	−	0.206005i
$471$	−22.8940	−	10.4739i	−1.05490	−	0.482610i
$472$	11.8591	−	2.09107i	0.545858	−	0.0962495i
$473$	4.73017	−	0.834056i	0.217493	−	0.0383499i
$474$	0.862464	+	9.09647i	0.0396143	+	0.417815i
$475$	5.11411	−	6.09476i	0.234651	−	0.279647i
$476$	2.75359	+	8.80089i	0.126210	+	0.403388i
$477$	0.274356	+	0.223501i	0.0125619	+	0.0102334i
$478$	−4.56190	+	7.90144i	−0.208656	+	0.361403i
$479$	29.2874	−	10.6598i	1.33818	−	0.487056i	0.428939	−	0.903334i	$-0.358888\pi$
$479$	29.2874	−	10.6598i	1.33818	−	0.487056i	0.909238	+	0.416277i	$0.136665\pi$
$480$	−2.05138	+	0.565667i	−0.0936321	+	0.0258190i
$481$	1.52135	+	1.81308i	0.0693678	+	0.0826693i
$482$	26.5263	+	9.65478i	1.20824	+	0.439763i
$483$	−5.48821	−	24.1763i	−0.249722	−	1.10006i
$484$	−0.955505	+	5.41894i	−0.0434321	+	0.246315i
$485$			18.7732i			0.852445i
$486$	−7.09663	−	13.8794i	−0.321910	−	0.629582i
$487$	−1.34497			−0.0609466			−0.0304733	−	0.999536i	$-0.509701\pi$
$487$	−1.34497			−0.0609466			−0.0304733	+	0.999536i	$0.509701\pi$
$488$	−1.94181	+	11.0125i	−0.0879014	+	0.498514i
$489$	−6.13922	+	2.91724i	−0.277625	+	0.131922i
$490$	6.10785	−	6.05421i	0.275925	−	0.273501i
$491$	−4.22823	−	5.03901i	−0.190818	−	0.227407i	0.662150	−	0.749371i	$-0.269644\pi$
$491$	−4.22823	−	5.03901i	−0.190818	−	0.227407i	−0.852968	+	0.521964i	$0.825200\pi$
$492$	−0.726030	−	2.63293i	−0.0327320	−	0.118702i
$493$	−2.52387	−	6.93426i	−0.113669	−	0.312304i
$494$	0.861436	+	0.497350i	0.0387578	+	0.0223768i
$495$	−6.69995	−	5.45804i	−0.301140	−	0.245321i
$496$	−7.27151	+	4.19821i	−0.326500	+	0.188505i
$497$	−4.30053	+	3.28487i	−0.192905	+	0.147347i
$498$	−1.41900	−	14.9663i	−0.0635870	−	0.670656i
$499$	5.69767	+	32.3131i	0.255063	+	1.44653i	0.795911	+	0.605413i	$0.206992\pi$
$499$	5.69767	+	32.3131i	0.255063	+	1.44653i	−0.540848	+	0.841120i	$0.681897\pi$
$500$	−1.81138	−	10.2728i	−0.0810072	−	0.459414i
$501$	4.40055	−	9.61883i	0.196602	−	0.429737i
$502$	6.52698	−	7.77855i	0.291313	−	0.347174i
$503$	16.8167	+	29.1274i	0.749821	+	1.29873i	0.947908	+	0.318544i	$0.103194\pi$
$503$	16.8167	+	29.1274i	0.749821	+	1.29873i	−0.198087	+	0.980185i	$0.563473\pi$
$504$	−6.99473	+	3.75149i	−0.311570	+	0.167105i
$505$	−7.68641	+	13.3133i	−0.342041	+	0.592432i
$506$	4.33835	+	11.9195i	0.192863	+	0.529887i
$507$	15.5741	−	15.8020i	0.691668	−	0.701790i
$508$	0.857536	−	0.719558i	0.0380470	−	0.0319252i
$509$	−1.94816	−	0.709073i	−0.0863508	−	0.0314291i	0.298484	−	0.954415i	$-0.403519\pi$
$509$	−1.94816	−	0.709073i	−0.0863508	−	0.0314291i	−0.384834	+	0.922986i	$0.625741\pi$
$510$	−7.39307	−	0.592729i	−0.327371	−	0.0262465i
$511$	16.9378	+	7.05968i	0.749286	+	0.312302i
$512$		−	1.00000i		−	0.0441942i
$513$	8.19016	−	8.55513i	0.361605	−	0.377718i
$514$			12.6583i			0.558333i
$515$	−8.44289	−	1.48871i	−0.372038	−	0.0656004i
$516$	2.92120	+	2.01398i	0.128598	+	0.0886605i
$517$	−3.80545	+	10.4554i	−0.167364	+	0.459828i
$518$	−6.59751	−	12.7422i	−0.289878	−	0.559861i
$519$	−41.4737	−	10.7906i	−1.82049	−	0.473653i
$520$	0.503822	−	0.183376i	0.0220941	−	0.00804158i
$521$	−17.6685	+	30.6027i	−0.774069	+	1.34073i	0.161247	+	0.986914i	$0.448449\pi$
$521$	−17.6685	+	30.6027i	−0.774069	+	1.34073i	−0.935316	+	0.353813i	$0.884885\pi$
$522$	5.45387	−	3.25534i	0.238710	−	0.142482i
$523$	−0.666516	+	0.384813i	−0.0291447	+	0.0168267i	−0.514502	−	0.857489i	$-0.672023\pi$
$523$	−0.666516	+	0.384813i	−0.0291447	+	0.0168267i	0.485357	+	0.874316i	$0.338690\pi$
$524$	−13.4181	−	11.2592i	−0.586174	−	0.491858i
$525$	−6.19611	−	14.7473i	−0.270420	−	0.643624i
$526$	4.93126	+	27.9665i	0.215013	+	1.21940i
$527$	−28.8206	+	5.08184i	−1.25544	+	0.221368i
$528$	3.30964	−	2.35344i	0.144033	−	0.102421i
$529$	−4.80103	−	4.02854i	−0.208741	−	0.175154i
$530$	0.0724588	+	0.125502i	0.00314741	+	0.00545147i
$531$	0.524819	+	36.1222i	0.0227752	+	1.56757i
$532$	−4.43710	−	4.08389i	−0.192373	−	0.177059i
$533$	0.235362	+	0.646653i	0.0101947	+	0.0280096i
$534$	6.41378	−	24.6514i	0.277551	−	1.06677i
$535$	−3.09601	−	3.68968i	−0.133852	−	0.159519i
$536$	2.89030	−	7.94104i	0.124842	−	0.343001i
$537$	−18.1069	+	26.2633i	−0.781370	+	1.13335i
$538$	12.6839	+	2.23651i	0.546842	+	0.0964230i
$539$	−7.00183	+	14.8442i	−0.301590	+	0.639385i
$540$	−0.694829	−	6.34589i	−0.0299007	−	0.273084i
$541$	28.0848			1.20746			0.603731	−	0.797188i	$-0.293680\pi$
$541$	28.0848			1.20746			0.603731	+	0.797188i	$0.293680\pi$
$542$	−4.05128	+	22.9759i	−0.174017	+	0.986901i
$543$	9.60348	+	0.769946i	0.412125	+	0.0330415i
$544$	1.19209	−	3.27524i	0.0511104	−	0.140425i
$545$	13.7931	−	11.5738i	0.590831	−	0.495766i
$546$	1.68122	−	1.08305i	0.0719496	−	0.0463503i
$547$	30.8451	−	11.2267i	1.31884	−	0.480019i	0.415754	−	0.909477i	$-0.363518\pi$
$547$	30.8451	−	11.2267i	1.31884	−	0.480019i	0.903087	+	0.429458i	$0.141295\pi$
$548$	19.4500	+	11.2295i	0.830863	+	0.479699i
$549$	−31.6875	−	11.0147i	−1.35239	−	0.470094i
$550$	4.09218	+	7.08786i	0.174491	+	0.302227i
$551$	3.69667	+	3.10187i	0.157483	+	0.132144i
$552$	−3.89825	+	8.52089i	−0.165921	+	0.362673i
$553$	−0.639562	+	13.9427i	−0.0271970	+	0.592906i
$554$	21.8934	−	3.86040i	0.930162	−	0.164013i
$555$	11.4891	−	1.08932i	0.487685	−	0.0462389i
$556$	−11.3760	+	13.5573i	−0.482448	+	0.574959i
$557$	19.8930	−	11.4852i	0.842895	−	0.486645i	−0.0153525	−	0.999882i	$-0.504887\pi$
$557$	19.8930	−	11.4852i	0.842895	−	0.486645i	0.858247	+	0.513237i	$0.171554\pi$
$558$	−8.95818	−	23.5425i	−0.379230	−	0.996633i
$559$	−0.774225	−	0.446999i	−0.0327462	−	0.0189061i
$560$	−3.22360	+	0.417165i	−0.136222	+	0.0176284i
$561$	13.6454	−	3.76271i	0.576108	−	0.158862i
$562$	7.59841	−	6.37582i	0.320520	−	0.268948i
$563$	−18.1788	−	6.61655i	−0.766146	−	0.278854i	−0.0707626	−	0.997493i	$-0.522543\pi$
$563$	−18.1788	−	6.61655i	−0.766146	−	0.278854i	−0.695384	+	0.718639i	$0.744765\pi$
$564$	−7.42378	+	3.52764i	−0.312597	+	0.148540i
$565$	−5.39247	−	0.950837i	−0.226863	−	0.0400020i
$566$	−7.94070			−0.333773
$567$	−7.76745	−	22.5093i	−0.326202	−	0.945300i
$568$	2.04537			0.0858220
$569$	−13.7869	−	2.43100i	−0.577976	−	0.101913i	−0.122985	−	0.992409i	$-0.539247\pi$
$569$	−13.7869	−	2.43100i	−0.577976	−	0.101913i	−0.454992	+	0.890496i	$0.650358\pi$
$570$	4.38075	−	2.08165i	0.183490	−	0.0871908i
$571$	−25.4729	−	9.27136i	−1.06601	−	0.387994i	−0.251324	−	0.967903i	$-0.580866\pi$
$571$	−25.4729	−	9.27136i	−1.06601	−	0.387994i	−0.814682	+	0.579909i	$0.803088\pi$
$572$	−0.783842	+	0.657721i	−0.0327741	+	0.0275007i
$573$	−15.2793	+	4.21326i	−0.638301	+	0.176012i
$574$	−0.535429	−	4.13747i	−0.0223484	−	0.172695i
$575$	−16.3540	−	9.44201i	−0.682011	−	0.393759i
$576$	2.96168	+	0.477969i	0.123403	+	0.0199154i
$577$	−23.7587	+	13.7171i	−0.989089	+	0.571051i	−0.905002	−	0.425408i	$-0.860131\pi$
$577$	−23.7587	+	13.7171i	−0.989089	+	0.571051i	−0.0840869	+	0.996458i	$0.526797\pi$
$578$	−3.11863	+	3.71664i	−0.129718	+	0.154592i
$579$	46.6055	−	4.41881i	1.93686	−	0.183639i
$580$	2.56158	−	0.451675i	0.106364	−	0.0187548i
$581$	1.05226	−	22.9398i	0.0436553	−	0.951704i
$582$	11.0108	−	24.0676i	0.456411	−	0.997633i
$583$	−0.211864	−	0.177775i	−0.00877453	−	0.00736270i
$584$	−3.46786	−	6.00651i	−0.143501	−	0.248551i
$585$	0.302290	+	1.57981i	0.0124982	+	0.0653170i
$586$	−10.8798	−	6.28146i	−0.449441	−	0.259485i
$587$	−41.8734	+	15.2407i	−1.72830	+	0.629050i	−0.998507	−	0.0546196i	$-0.982605\pi$
$587$	−41.8734	+	15.2407i	−1.72830	+	0.629050i	−0.729792	+	0.683669i	$0.760383\pi$
$588$	−11.3813	+	4.17927i	−0.469356	+	0.172350i
$589$	14.6604	−	12.3016i	0.604073	−	0.506877i
$590$	−5.05999	+	13.9022i	−0.208316	+	0.572344i
$591$	18.7287	+	1.50155i	0.770397	+	0.0617655i
$592$	−0.941760	+	5.34098i	−0.0387061	+	0.219513i
$593$	15.7583			0.647115			0.323558	−	0.946209i	$-0.395121\pi$
$593$	15.7583			0.647115			0.323558	+	0.946209i	$0.395121\pi$
$594$	5.38824	+	10.9270i	0.221082	+	0.448338i
$595$	−11.0554	−	2.47650i	−0.453225	−	0.101527i
$596$	11.4259	+	2.01470i	0.468024	+	0.0825253i
$597$	−5.35008	+	7.76008i	−0.218964	+	0.317599i
$598$	0.807488	−	2.21856i	0.0330206	−	0.0907235i
$599$	13.2291	+	15.7658i	0.540525	+	0.644173i	0.965305	−	0.261124i	$-0.0840931\pi$
$599$	13.2291	+	15.7658i	0.540525	+	0.644173i	−0.424780	+	0.905296i	$0.639649\pi$
$600$	−1.52234	+	5.85114i	−0.0621494	+	0.238872i
$601$	−2.58497	−	7.10215i	−0.105443	−	0.289703i	0.875740	−	0.482784i	$-0.160374\pi$
$601$	−2.58497	−	7.10215i	−0.105443	−	0.289703i	−0.981183	+	0.193081i	$0.938152\pi$
$602$	3.98790	+	3.67045i	0.162535	+	0.149596i
$603$	22.1373	+	12.3557i	0.901502	+	0.503164i
$604$	−5.49931	−	9.52508i	−0.223764	−	0.387570i
$605$	−5.17863	−	4.34539i	−0.210541	−	0.176665i
$606$	17.6626	−	12.5597i	0.717493	−	0.510201i
$607$	25.2819	−	4.45788i	1.02616	−	0.180940i	0.364861	−	0.931062i	$-0.381116\pi$
$607$	25.2819	−	4.45788i	1.02616	−	0.180940i	0.661299	+	0.750122i	$0.270005\pi$
$608$	0.395794	+	2.24466i	0.0160516	+	0.0910330i
$609$	8.94470	−	3.75814i	0.362458	−	0.152288i
$610$	−10.5242	−	8.83083i	−0.426111	−	0.357550i
$611$	1.79348	−	1.03547i	0.0725566	−	0.0418906i
$612$	9.13043	+	5.09605i	0.369076	+	0.205996i
$613$	−10.0628	+	17.4293i	−0.406433	+	0.703962i	−0.994487	−	0.104859i	$-0.966561\pi$
$613$	−10.0628	+	17.4293i	−0.406433	+	0.703962i	0.588054	+	0.808821i	$0.299894\pi$
$614$	8.32350	−	3.02951i	0.335909	−	0.122261i
$615$	3.24734	+	0.844889i	0.130945	+	0.0340692i
$616$	5.50879	−	2.85227i	0.221956	−	0.114921i
$617$	3.08423	−	8.47385i	0.124166	−	0.341145i	−0.861999	−	0.506911i	$-0.830787\pi$
$617$	3.08423	−	8.47385i	0.124166	−	0.341145i	0.986165	+	0.165766i	$0.0530097\pi$
$618$	9.95081	+	6.86045i	0.400280	+	0.275968i
$619$	10.9095	+	1.92363i	0.438488	+	0.0773173i	0.388534	−	0.921434i	$-0.372981\pi$
$619$	10.9095	+	1.92363i	0.438488	+	0.0773173i	0.0499538	+	0.998752i	$0.484093\pi$
$620$		−	10.3155i		−	0.414282i
$621$	−23.3729	−	15.6181i	−0.937922	−	0.626733i
$622$			20.9184i			0.838752i
$623$	14.9692	−	35.9146i	0.599728	−	1.43889i
$624$	−0.753464	−	0.0604079i	−0.0301627	−	0.00241825i
$625$	−4.35792	−	1.58615i	−0.174317	−	0.0634461i
$626$	9.69001	−	8.13089i	0.387291	−	0.324976i
$627$	−6.49753	+	6.59262i	−0.259486	+	0.263284i
$628$	4.97142	+	13.6589i	0.198381	+	0.545048i
$629$	−9.45142	+	16.3703i	−0.376853	+	0.652728i
$630$	0.305273	−	9.74666i	0.0121624	−	0.388316i
$631$	−8.40768	−	14.5625i	−0.334704	−	0.579725i	0.648724	−	0.761024i	$-0.275303\pi$
$631$	−8.40768	−	14.5625i	−0.334704	−	0.579725i	−0.983428	+	0.181299i	$0.941970\pi$
$632$	3.39096	−	4.04119i	0.134885	−	0.160750i
$633$	−16.7940	+	36.7088i	−0.667503	+	1.45904i
$634$	−0.815627	−	4.62565i	−0.0323927	−	0.183708i
$635$	0.238818	+	1.35440i	0.00947720	+	0.0537479i
$636$	−0.0192845	−	0.203395i	−0.000764680	−	0.00806513i
$637$	2.77431	−	1.27882i	0.109922	−	0.0506685i
$638$	−4.29902	+	2.48204i	−0.170200	+	0.0982649i
$639$	−0.977626	+	6.05774i	−0.0386743	+	0.239641i
$640$	1.06397	+	0.614283i	0.0420571	+	0.0242817i
$641$	13.6635	+	37.5403i	0.539677	+	1.48275i	0.847233	+	0.531221i	$0.178267\pi$
$641$	13.6635	+	37.5403i	0.539677	+	1.48275i	−0.307556	+	0.951530i	$0.599511\pi$
$642$	1.80509	+	6.54610i	0.0712411	+	0.258354i
$643$	−9.74558	−	11.6143i	−0.384328	−	0.458025i	0.538847	−	0.842404i	$-0.318860\pi$
$643$	−9.74558	−	11.6143i	−0.384328	−	0.458025i	−0.923175	+	0.384379i	$0.874416\pi$
$644$	−7.71714	+	12.0547i	−0.304098	+	0.475023i
$645$	−3.93725	+	1.87091i	−0.155029	+	0.0736670i
$646$	−1.37952	+	7.82362i	−0.0542763	+	0.307816i
$647$	39.1958			1.54094			0.770472	−	0.637473i	$-0.220020\pi$
$647$	39.1958			1.54094			0.770472	+	0.637473i	$0.220020\pi$
$648$	−2.83118	+	8.54309i	−0.111219	+	0.335604i
$649$		−	28.2345i		−	1.10830i
$650$	0.264525	−	1.50020i	0.0103755	−	0.0588425i
$651$	−8.51791	−	37.5225i	−0.333843	−	1.47062i
$652$	3.68764	+	1.34219i	0.144419	+	0.0525642i
$653$	−25.1406	−	29.9614i	−0.983829	−	1.17248i	−0.985013	−	0.172482i	$-0.944821\pi$
$653$	−25.1406	−	29.9614i	−0.983829	−	1.17248i	0.00118396	−	0.999999i	$-0.499623\pi$
$654$	−24.4713	+	6.74795i	−0.956902	+	0.263866i
$655$	20.2219	−	7.36018i	0.790136	−	0.287586i
$656$	−0.788428	+	1.36560i	−0.0307830	+	0.0533176i
$657$	19.4469	−	7.39976i	0.758695	−	0.288692i
$658$	−11.9824	+	3.74900i	−0.467122	+	0.146151i
$659$	8.02297	−	9.56140i	0.312531	−	0.372459i	−0.586798	−	0.809734i	$-0.699612\pi$
$659$	8.02297	−	9.56140i	0.312531	−	0.372459i	0.899328	+	0.437274i	$0.144056\pi$
$660$	0.470939	+	4.96703i	0.0183313	+	0.193341i
$661$	27.8439	−	4.90963i	1.08300	−	0.190963i	0.396460	−	0.918052i	$-0.370239\pi$
$661$	27.8439	−	4.90963i	1.08300	−	0.190963i	0.686543	+	0.727090i	$0.259127\pi$
$662$	−10.2294	+	1.80372i	−0.397578	+	0.0701037i
$663$	−2.39576	−	1.09605i	−0.0930437	−	0.0425669i
$664$	−5.57911	+	6.64892i	−0.216511	+	0.258028i
$665$	7.07077	−	2.21228i	0.274193	−	0.0857883i
$666$	−15.3682	−	5.34202i	−0.595504	−	0.206999i
$667$	5.72689	−	9.91926i	0.221746	−	0.384075i
$668$	−5.73871	+	2.08872i	−0.222037	+	0.0808150i
$669$	8.08677	+	7.97013i	0.312653	+	0.308143i
$670$	6.67356	+	7.95324i	0.257822	+	0.307260i
$671$	24.6378	+	8.96744i	0.951133	+	0.346184i
$672$	4.37740	+	1.35588i	0.168862	+	0.0523042i
$673$	−1.02565	+	5.81673i	−0.0395358	+	0.224219i	−0.998174	−	0.0604101i	$-0.980759\pi$
$673$	−1.02565	+	5.81673i	−0.0395358	+	0.224219i	0.958638	+	0.284629i	$0.0918703\pi$
$674$			3.93836i			0.151700i
$675$	−16.6016	−	7.30536i	−0.638995	−	0.281183i
$676$	−12.8095			−0.492675
$677$	−6.20980	+	35.2175i	−0.238662	+	1.35352i	0.596101	+	0.802910i	$0.296716\pi$
$677$	−6.20980	+	35.2175i	−0.238662	+	1.35352i	−0.834763	+	0.550610i	$0.814395\pi$
$678$	6.35557	+	4.38177i	0.244084	+	0.168281i
$679$	21.7974	−	34.0491i	0.836506	−	1.30668i
$680$	2.75247	+	3.28027i	0.105553	+	0.125793i
$681$	−10.1208	−	2.63322i	−0.387831	−	0.100905i
$682$	6.73328	+	18.4995i	0.257831	+	0.708384i
$683$	−37.1567	−	21.4524i	−1.42176	−	0.820855i	−0.425313	−	0.905046i	$-0.639836\pi$
$683$	−37.1567	−	21.4524i	−1.42176	−	0.820855i	−0.996450	+	0.0841913i	$0.973169\pi$
$684$	−6.83714	+	0.0993366i	−0.261425	+	0.00379823i
$685$	−23.8956	+	13.7961i	−0.913005	+	0.527123i
$686$	−18.1074	+	3.88881i	−0.691343	+	0.148475i
$687$	−28.0512	+	19.9469i	−1.07022	+	0.761021i
$688$	−0.355725	−	2.01741i	−0.0135619	−	0.0769132i
$689$	0.00893894	+	0.0506953i	0.000340547	+	0.00193134i
$690$	−6.67133	−	9.38186i	−0.253973	−	0.357161i
$691$	−22.9322	+	27.3296i	−0.872383	+	1.03967i	0.126479	+	0.991969i	$0.459632\pi$
$691$	−22.9322	+	27.3296i	−0.872383	+	1.03967i	−0.998862	+	0.0476960i	$0.984812\pi$
$692$	12.3710	+	21.4272i	0.470275	+	0.814541i
$693$	5.81448	+	17.6786i	0.220874	+	0.671554i
$694$	−13.8934	+	24.0641i	−0.527388	+	0.913462i
$695$	−7.43654	−	20.4317i	−0.282084	−	0.775019i
$696$	−3.54891	−	0.923350i	−0.134521	−	0.0349995i
$697$	−4.21021	+	3.53278i	−0.159473	+	0.133814i
$698$	−15.8068	−	5.75320i	−0.598296	−	0.217762i
$699$	−3.79123	+	5.49903i	−0.143398	+	0.207992i
$700$	−3.55301	+	8.52452i	−0.134291	+	0.322196i
$701$			22.7597i			0.859624i	0.902918	+	0.429812i	$0.141420\pi$
$701$			22.7597i			0.859624i	−0.902918	+	0.429812i	$0.858580\pi$
$702$	0.539042	−	2.20265i	0.0203448	−	0.0831335i
$703$		−	12.3614i		−	0.466221i
$704$	−2.30905	−	0.407147i	−0.0870255	−	0.0153449i
$705$	0.806999	−	10.0656i	0.0303933	−	0.379094i
$706$	0.577533	−	1.58676i	0.0217358	−	0.0597185i
$707$	29.3989	−	15.2218i	1.10566	−	0.572473i
$708$	14.6409	−	14.8551i	0.550238	−	0.558290i
$709$	42.5614	−	15.4911i	1.59843	−	0.581780i	0.619323	−	0.785136i	$-0.287407\pi$
$709$	42.5614	−	15.4911i	1.59843	−	0.581780i	0.979105	+	0.203356i	$0.0651848\pi$
$710$	−1.25644	+	2.17622i	−0.0471533	+	0.0816719i
$711$	10.3479	+	11.9745i	0.388078	+	0.449079i
$712$	−12.7361	+	7.35317i	−0.477304	+	0.275572i
$713$	−34.7968	−	29.1980i	−1.30315	−	1.09347i
$714$	12.7207	+	9.65908i	0.476060	+	0.361482i
$715$	−0.218295	−	1.23801i	−0.00816376	−	0.0462990i
$716$	18.1378	−	3.19818i	0.677840	−	0.119522i
$717$	1.49163	+	15.7323i	0.0557059	+	0.587534i
$718$	9.33366	+	7.83187i	0.348329	+	0.292283i
$719$	0.807602	+	1.39881i	0.0301185	+	0.0521667i	0.880692	−	0.473690i	$-0.157078\pi$
$719$	0.807602	+	1.39881i	0.0301185	+	0.0521667i	−0.850573	+	0.525857i	$0.823745\pi$
$720$	−2.32785	+	2.85753i	−0.0867540	+	0.106494i
$721$	13.5844	+	12.5031i	0.505911	+	0.465639i
$722$	4.72154	+	12.9723i	0.175717	+	0.482780i
$723$	47.1344	−	12.9973i	1.75295	−	0.483375i
$724$	−3.57542	−	4.26102i	−0.132879	−	0.158359i
$725$	2.52762	−	6.94459i	0.0938736	−	0.257916i
$726$	4.09047	+	8.60824i	0.151812	+	0.319482i
$727$	48.1472	+	8.48966i	1.78568	+	0.314864i	0.966114	−	0.258117i	$-0.0831020\pi$
$727$	48.1472	+	8.48966i	1.78568	+	0.314864i	0.819569	+	0.572981i	$0.194213\pi$
$728$	−1.12671	−	0.252393i	−0.0417585	−	0.00935429i
$729$	−23.9487	−	12.4684i	−0.886988	−	0.461792i
$730$	8.52099			0.315376
$731$	1.23986	−	7.03157i	0.0458577	−	0.260072i
$732$	8.31278	+	17.4939i	0.307249	+	0.646594i
$733$	0.0218471	−	0.0600243i	0.000806939	−	0.00221705i	−0.939288	−	0.343128i	$-0.888513\pi$
$733$	0.0218471	−	0.0600243i	0.000806939	−	0.00221705i	0.940095	+	0.340911i	$0.110736\pi$
$734$	−16.4269	+	13.7838i	−0.606326	+	0.508768i
$735$	2.54472	−	14.6766i	0.0938634	−	0.541354i
$736$	5.08367	−	1.85030i	0.187386	−	0.0682031i
$737$	−17.1594	−	9.90701i	−0.632076	−	0.364929i
$738$	−3.66762	−	2.98779i	−0.135007	−	0.109982i
$739$	11.3282	+	19.6211i	0.416715	+	0.721772i	0.995607	−	0.0936324i	$-0.0298478\pi$
$739$	11.3282	+	19.6211i	0.416715	+	0.721772i	−0.578891	+	0.815405i	$0.696514\pi$
$740$	−5.10414	−	4.28288i	−0.187632	−	0.157442i
$741$	1.71518	−	0.162621i	0.0630087	−	0.00597405i
$742$	0.0143005	−	0.311756i	0.000524987	−	0.0114449i
$743$	−28.1945	+	4.97145i	−1.03436	+	0.182385i	−0.664954	−	0.746885i	$-0.731549\pi$
$743$	−28.1945	+	4.97145i	−1.03436	+	0.182385i	−0.369402	+	0.929270i	$0.620438\pi$
$744$	−6.05024	+	13.2247i	−0.221812	+	0.484843i
$745$	−9.16233	+	10.9192i	−0.335682	+	0.400050i
$746$	−17.0630	+	9.85132i	−0.624720	+	0.360682i
$747$	−17.0253	−	19.7015i	−0.622925	−	0.720841i
$748$	−7.07732	−	4.08609i	−0.258773	−	0.149402i
$749$	1.33121	+	10.2868i	0.0486412	+	0.375870i
$750$	−12.8681	−	12.6825i	−0.469878	−	0.463101i
$751$	33.1976	−	27.8561i	1.21140	−	1.01648i	0.212169	−	0.977233i	$-0.431947\pi$
$751$	33.1976	−	27.8561i	1.21140	−	1.01648i	0.999229	−	0.0392509i	$-0.0124972\pi$
$752$	4.45922	+	1.62303i	0.162611	+	0.0591856i
$753$	1.40555	−	17.5313i	0.0512210	−	0.638876i
$754$	0.909917	+	0.160443i	0.0331372	+	0.00584299i
$755$	13.5125			0.491771
$756$	−6.10794	+	12.3164i	−0.222144	+	0.447942i
$757$	24.6013			0.894149			0.447075	−	0.894497i	$-0.352466\pi$
$757$	24.6013			0.894149			0.447075	+	0.894497i	$0.352466\pi$
$758$	−24.4556	−	4.31218i	−0.888266	−	0.156625i
$759$	18.0880	+	12.4705i	0.656551	+	0.452651i
$760$	−2.63138	−	0.957744i	−0.0954501	−	0.0347410i
$761$	0.393164	−	0.329903i	0.0142522	−	0.0119590i	−0.635634	−	0.771991i	$-0.719261\pi$
$761$	0.393164	−	0.329903i	0.0142522	−	0.0119590i	0.649886	+	0.760032i	$0.274817\pi$
$762$	0.488211	−	1.87644i	0.0176860	−	0.0679764i
$763$	−38.4549	+	4.97644i	−1.39216	+	0.180159i
$764$	7.92477	+	4.57537i	0.286708	+	0.165531i
$765$	−11.0307	+	6.58408i	−0.398816	+	0.238048i
$766$	8.38597	−	4.84164i	0.302997	−	0.174936i
$767$	−3.37800	+	4.02575i	−0.121973	+	0.145361i
$768$	−1.00374	−	1.41156i	−0.0362195	−	0.0509353i
$769$	16.7334	−	2.95055i	0.603423	−	0.106400i	0.136413	−	0.990652i	$-0.456443\pi$
$769$	16.7334	−	2.95055i	0.603423	−	0.106400i	0.467009	+	0.884252i	$0.345331\pi$
$770$	−0.349226	+	7.61329i	−0.0125852	+	0.274364i
$771$	12.7057	+	17.8679i	0.457584	+	0.643498i
$772$	−20.7049	−	17.3735i	−0.745187	−	0.625286i
$773$	12.8605	+	22.2751i	0.462561	+	0.801179i	0.999088	−	0.0427040i	$-0.0135973\pi$
$773$	12.8605	+	22.2751i	0.462561	+	0.801179i	−0.536527	+	0.843883i	$0.680264\pi$
$774$	6.14496	−	0.0892799i	0.220876	−	0.00320910i
$775$	−25.3821	−	14.6544i	−0.911752	−	0.526400i
$776$	−14.3590	+	5.22626i	−0.515459	+	0.187612i
$777$	−22.1027	−	11.3642i	−0.792930	−	0.407688i
$778$	−23.5584	+	19.7679i	−0.844611	+	0.708713i
$779$	1.22926	−	3.37736i	0.0440427	−	0.121006i
$780$	0.527112	−	0.764555i	0.0188736	−	0.0273755i
$781$	0.832769	−	4.72287i	0.0297988	−	0.168997i
$782$	18.8560			0.674288
$783$	4.43094	−	10.0694i	0.158349	−	0.359851i
$784$	6.33105	+	2.98628i	0.226109	+	0.106653i
$785$	−17.5865	−	3.10097i	−0.627688	−	0.110678i
$786$	−30.2418	−	2.42459i	−1.07869	−	0.0864824i
$787$	7.98929	−	21.9504i	0.284788	−	0.782448i	−0.711987	−	0.702193i	$-0.752204\pi$
$787$	7.98929	−	21.9504i	0.284788	−	0.782448i	0.996774	−	0.0802546i	$-0.0255733\pi$
$788$	−6.97278	−	8.30984i	−0.248395	−	0.296026i
$789$	35.0320	+	34.5267i	1.24717	+	1.22918i
$790$	2.21669	+	6.09032i	0.0788664	+	0.216684i
$791$	8.67637	+	7.98570i	0.308496	+	0.283939i
$792$	2.30949	−	6.64405i	0.0820643	−	0.236086i
$793$	−2.44005	−	4.22629i	−0.0866487	−	0.150080i
$794$	7.01111	+	5.88302i	0.248815	+	0.208781i
$795$	0.228252	+	0.104424i	0.00809527	+	0.00370354i
$796$	5.35921	−	0.944973i	0.189952	−	0.0334937i
$797$	−3.92923	−	22.2838i	−0.139181	−	0.789332i	−0.971857	−	0.235572i	$-0.924304\pi$
$797$	−3.92923	−	22.2838i	−0.139181	−	0.789332i	0.832676	−	0.553760i	$-0.186808\pi$
$798$	−10.3624	−	1.31094i	−0.366825	−	0.0464069i
$799$	12.6702	+	10.6316i	0.448241	+	0.376119i
$800$	3.02297	−	1.74531i	0.106878	−	0.0617061i
$801$	−15.6903	−	41.2347i	−0.554389	−	1.45696i
$802$	16.3633	−	28.3421i	0.577810	−	1.00080i
$803$	−15.2812	+	5.56192i	−0.539263	+	0.196276i
$804$	−3.89093	−	14.1104i	−0.137223	−	0.497634i
$805$	−8.08537	−	15.6158i	−0.284972	−	0.550386i
$806$	1.25325	−	3.44328i	0.0441439	−	0.121284i
$807$	20.1490	−	9.57441i	0.709277	−	0.337035i
$808$	−12.3227	−	2.17283i	−0.433512	−	0.0764398i
$809$			11.9777i			0.421115i	0.977582	+	0.210557i	$0.0675279\pi$
$809$			11.9777i			0.421115i	−0.977582	+	0.210557i	$0.932472\pi$
$810$	−7.35044	−	8.26017i	−0.258268	−	0.290233i
$811$		−	7.72412i		−	0.271230i	−0.990762	−	0.135615i	$-0.956699\pi$
$811$		−	7.72412i		−	0.271230i	0.990762	−	0.135615i	$-0.0433011\pi$
$812$	−5.17040	−	2.15502i	−0.181445	−	0.0756263i
$813$	17.3433	+	36.4983i	0.608257	+	1.28005i
$814$	11.9491	+	4.34913i	0.418817	+	0.152437i
$815$	−3.69330	+	3.09905i	−0.129371	+	0.108555i
$816$	−1.60479	−	5.81975i	−0.0561791	−	0.203732i
$817$	1.59696	+	4.38762i	0.0558706	+	0.153503i
$818$	−3.51205	+	6.08305i	−0.122796	+	0.212689i
$819$	1.28604	−	3.21630i	0.0449378	−	0.112387i
$820$	−0.968636	−	1.67773i	−0.0338262	−	0.0585888i
$821$	−1.09508	+	1.30506i	−0.0382184	+	0.0455469i	−0.784815	−	0.619730i	$-0.787242\pi$
$821$	−1.09508	+	1.30506i	−0.0382184	+	0.0455469i	0.746597	+	0.665277i	$0.231687\pi$
$822$	38.7263	−	3.67176i	1.35074	−	0.128067i
$823$	1.25194	+	7.10010i	0.0436399	+	0.247494i	0.998822	−	0.0485248i	$-0.0154520\pi$
$823$	1.25194	+	7.10010i	0.0436399	+	0.247494i	−0.955182	+	0.296019i	$0.904341\pi$
$824$	−1.21175	−	6.87215i	−0.0422132	−	0.239403i
$825$	12.8907	+	5.89744i	0.448798	+	0.205322i
$826$	25.3191	−	19.3395i	0.880964	−	0.672906i
$827$	17.5393	−	10.1263i	0.609901	−	0.352126i	−0.163026	−	0.986622i	$-0.552125\pi$
$827$	17.5393	−	10.1263i	0.609901	−	0.352126i	0.772927	+	0.634495i	$0.218792\pi$
$828$	3.05017	+	15.9406i	0.106001	+	0.553974i
$829$	−40.7465	−	23.5250i	−1.41519	−	0.817058i	−0.419315	−	0.907841i	$-0.637730\pi$
$829$	−40.7465	−	23.5250i	−1.41519	−	0.817058i	−0.995871	+	0.0907826i	$0.971063\pi$
$830$	−3.64710	−	10.0203i	−0.126593	−	0.347810i
$831$	27.0290	−	27.4246i	0.937626	−	0.951347i
$832$	0.280518	+	0.334308i	0.00972521	+	0.0115901i
$833$	17.1758	+	17.3280i	0.595105	+	0.600378i
$834$	−2.44975	+	30.5555i	−0.0848278	+	1.05805i
$835$	1.30286	−	7.38888i	0.0450873	−	0.255703i
$836$	5.34417			0.184832
$837$	−36.2756	−	24.2399i	−1.25387	−	0.837853i
$838$		−	32.3942i		−	1.11904i
$839$	5.25636	−	29.8103i	0.181470	−	1.02917i	−0.748938	−	0.662640i	$-0.769436\pi$
$839$	5.25636	−	29.8103i	0.181470	−	1.02917i	0.930408	−	0.366526i	$-0.119453\pi$
$840$	−4.13157	+	3.82452i	−0.142553	+	0.131958i
$841$	−23.0390	−	8.38550i	−0.794447	−	0.289155i
$842$	−6.17920	−	7.36408i	−0.212949	−	0.253783i
$843$	4.32592	−	16.6267i	0.148992	−	0.572654i
$844$	21.9009	−	7.97128i	0.753861	−	0.274383i
$845$	7.86869	−	13.6290i	0.270691	−	0.468851i
$846$	−6.93825	+	12.4310i	−0.238542	+	0.427388i
$847$	4.34715	+	13.8942i	0.149370	+	0.477409i
$848$	−0.0758211	+	0.0903601i	−0.00260371	+	0.00310298i
$849$	−11.2088	+	7.97043i	−0.384684	+	0.273544i
$850$	11.9815	−	2.11267i	0.410963	−	0.0724638i
$851$	−28.8943	+	5.09485i	−0.990485	+	0.174649i
$852$	2.88717	−	2.05303i	0.0989127	−	0.0703357i
$853$	33.2273	−	39.5988i	1.13768	−	1.35584i	0.212120	−	0.977244i	$-0.431963\pi$
$853$	33.2273	−	39.5988i	1.13768	−	1.35584i	0.925563	−	0.378594i	$-0.123592\pi$
$854$	8.83440	+	28.2361i	0.302307	+	0.966220i
$855$	4.09425	−	7.33553i	0.140020	−	0.250870i
$856$	1.96023	−	3.39521i	0.0669991	−	0.116046i
$857$	2.22382	−	0.809405i	0.0759643	−	0.0276487i	−0.303758	−	0.952749i	$-0.598242\pi$
$857$	2.22382	−	0.809405i	0.0759643	−	0.0276487i	0.379723	+	0.925100i	$0.376019\pi$
$858$	−0.446255	+	1.71519i	−0.0152349	+	0.0585556i
$859$	13.6641	+	16.2842i	0.466212	+	0.555610i	0.947003	−	0.321225i	$-0.104095\pi$
$859$	13.6641	+	16.2842i	0.466212	+	0.555610i	−0.480791	+	0.876835i	$0.659650\pi$
$860$	2.36498	+	0.860783i	0.0806452	+	0.0293525i
$861$	−4.90875	−	5.30285i	−0.167290	−	0.180721i
$862$	−0.316514	+	1.79504i	−0.0107805	+	0.0611393i
$863$		−	13.3941i		−	0.455942i	−0.973668	−	0.227971i	$-0.926791\pi$
$863$		−	13.3941i		−	0.455942i	0.973668	−	0.227971i	$-0.0732092\pi$
$864$	4.66034	−	2.29808i	0.158548	−	0.0781824i
$865$	−30.3972			−1.03354
$866$	5.64771	−	32.0298i	0.191917	−	1.08842i
$867$	−0.671580	+	8.37657i	−0.0228080	+	0.284483i
$868$	−11.9773	+	18.7094i	−0.406536	+	0.635039i
$869$	−7.95068	−	9.47525i	−0.269708	−	0.321426i
$870$	3.16245	−	3.20873i	0.107217	−	0.108786i
$871$	1.26135	+	3.46554i	0.0427393	+	0.117425i
$872$	12.6923	+	7.32790i	0.429815	+	0.248154i
$873$	−8.61532	−	45.0248i	−0.291584	−	1.52386i
$874$	−10.6788	+	6.16539i	−0.361215	+	0.208547i
$875$	−16.7526	−	21.9324i	−0.566343	−	0.741452i
$876$	−10.9241	−	4.99770i	−0.369091	−	0.168857i
$877$	−3.38439	−	19.1938i	−0.114283	−	0.648129i	−0.987103	−	0.160087i	$-0.948822\pi$
$877$	−3.38439	−	19.1938i	−0.114283	−	0.648129i	0.872820	−	0.488042i	$-0.162289\pi$
$878$	−5.50764	−	31.2354i	−0.185874	−	1.05414i
$879$	−21.6625	+	2.05388i	−0.730657	+	0.0692758i
$880$	1.85160	−	2.20665i	0.0624174	−	0.0743862i
$881$	11.0298	+	19.1042i	0.371604	+	0.643637i	0.989812	−	0.142377i	$-0.0454745\pi$
$881$	11.0298	+	19.1042i	0.371604	+	0.643637i	−0.618208	+	0.786014i	$0.712141\pi$
$882$	−11.8705	+	17.3232i	−0.399699	+	0.583302i
$883$	−17.0509	+	29.5330i	−0.573808	+	0.993864i	0.422362	+	0.906427i	$0.361201\pi$
$883$	−17.0509	+	29.5330i	−0.573808	+	0.993864i	−0.996170	+	0.0874371i	$0.972132\pi$
$884$	0.520238	+	1.42934i	0.0174975	+	0.0480740i
$885$	6.81177	+	24.7027i	0.228975	+	0.830372i
$886$	27.2161	−	22.8370i	0.914342	−	0.767224i
$887$	−19.4112	−	7.06510i	−0.651765	−	0.237223i	−0.00508786	−	0.999987i	$-0.501620\pi$
$887$	−19.4112	−	7.06510i	−0.651765	−	0.237223i	−0.646677	+	0.762764i	$0.723842\pi$
$888$	4.03163	+	8.48440i	0.135293	+	0.284718i
$889$	1.13944	−	2.73379i	0.0382156	−	0.0916883i
$890$		−	18.0677i		−	0.605631i
$891$	18.5737	+	10.0156i	0.622242	+	0.335536i
$892$		−	6.55538i		−	0.219490i
$893$	−10.6518	−	1.87820i	−0.356450	−	0.0628517i
$894$	18.1506	−	8.62484i	0.607047	−	0.288458i
$895$	−7.73896	+	21.2626i	−0.258685	+	0.710731i
$896$	−1.21649	−	2.34950i	−0.0406402	−	0.0784912i
$897$	−1.08704	−	3.94213i	−0.0362953	−	0.131624i
$898$	6.30802	−	2.29593i	0.210501	−	0.0766162i
$899$	8.88835	−	15.3951i	0.296443	−	0.513454i
$900$	3.72417	+	9.78728i	0.124139	+	0.326243i
$901$	−0.356050	+	0.205565i	−0.0118617	+	0.00684838i
$902$	2.83222	+	2.37652i	0.0943027	+	0.0791294i
$903$	9.31334	+	1.17823i	0.309929	+	0.0392089i
$904$	−0.773941	−	4.38924i	−0.0257409	−	0.145984i
$905$	6.72991	−	1.18666i	0.223710	−	0.0394461i
$906$	−17.3233	−	7.92532i	−0.575529	−	0.263301i
$907$	−7.48056	−	6.27693i	−0.248388	−	0.208422i	0.510090	−	0.860121i	$-0.329612\pi$
$907$	−7.48056	−	6.27693i	−0.248388	−	0.208422i	−0.758478	+	0.651699i	$0.774057\pi$
$908$	3.01890	+	5.22888i	0.100186	+	0.173527i
$909$	12.3251	−	35.4574i	0.408798	−	1.17605i
$910$	0.960654	−	1.04374i	0.0318454	−	0.0345996i
$911$	1.54942	+	4.25699i	0.0513345	+	0.141040i	0.962710	−	0.270535i	$-0.0872007\pi$
$911$	1.54942	+	4.25699i	0.0513345	+	0.141040i	−0.911375	+	0.411576i	$0.864979\pi$
$912$	2.81175	+	2.77119i	0.0931063	+	0.0917634i
$913$	13.0812	+	15.5895i	0.432923	+	0.515938i
$914$	−0.575978	+	1.58249i	−0.0190517	+	0.0523440i
$915$	−23.7194	−	1.90167i	−0.784139	−	0.0628672i
$916$	19.5706	+	3.45082i	0.646630	+	0.114018i
$917$	−45.2226	−	10.1303i	−1.49338	−	0.334531i
$918$	18.0033	−	1.97123i	0.594196	−	0.0650602i
$919$	−6.66460			−0.219845			−0.109922	−	0.993940i	$-0.535060\pi$
$919$	−6.66460			−0.219845			−0.109922	+	0.993940i	$0.535060\pi$
$920$	−1.15414	+	6.54548i	−0.0380510	+	0.215798i
$921$	8.70827	−	12.6310i	0.286947	−	0.416205i
$922$	−0.397670	+	1.09259i	−0.0130966	+	0.0359825i
$923$	−0.683786	+	0.573764i	−0.0225071	+	0.0188857i
$924$	4.91304	−	9.55557i	0.161627	−	0.314355i
$925$	−17.7893	+	6.47478i	−0.584909	+	0.212889i
$926$	0.00845088	+	0.00487912i	0.000277713	+	0.000160338i
$927$	20.9323	−	0.304125i	0.687507	−	0.00998877i
$928$	1.05859	+	1.83353i	0.0347499	+	0.0601886i
$929$	40.4176	+	33.9144i	1.32606	+	1.11270i	0.984981	+	0.172662i	$0.0552367\pi$
$929$	40.4176	+	33.9144i	1.32606	+	1.11270i	0.341079	+	0.940035i	$0.389208\pi$
$930$	−10.3542	−	14.5610i	−0.339526	−	0.477474i
$931$	−15.3930	−	4.19739i	−0.504485	−	0.137564i
$932$	3.79770	−	0.669637i	0.124398	−	0.0219347i
$933$	20.9967	+	29.5276i	0.687401	+	0.966689i
$934$	−5.56487	+	6.63195i	−0.182088	+	0.217004i
$935$	8.69496	−	5.02004i	0.284356	−	0.164173i
$936$	−1.12419	+	0.671015i	−0.0367454	+	0.0219328i
$937$	−24.6944	−	14.2573i	−0.806732	−	0.465767i	0.0390877	−	0.999236i	$-0.487555\pi$
$937$	−24.6944	−	14.2573i	−0.806732	−	0.465767i	−0.845820	+	0.533469i	$0.820888\pi$
$938$	−2.86946	−	22.1735i	−0.0936913	−	0.723990i
$939$	5.51670	−	21.2035i	0.180031	−	0.691950i
$940$	−4.46607	+	3.74748i	−0.145667	+	0.122229i
$941$	−4.64598	−	1.69100i	−0.151455	−	0.0551250i	0.265180	−	0.964199i	$-0.414568\pi$
$941$	−4.64598	−	1.69100i	−0.151455	−	0.0551250i	−0.416635	+	0.909074i	$0.636791\pi$
$942$	20.7274	+	14.2903i	0.675336	+	0.465602i
$943$	−8.40108	−	1.48134i	−0.273577	−	0.0482390i
$944$	−12.0420			−0.391934
$945$	−9.35223	−	14.0644i	−0.304228	−	0.457515i
$946$	−4.80314			−0.156163
$947$	20.0258	+	3.53109i	0.650752	+	0.114745i	0.489273	−	0.872131i	$-0.337262\pi$
$947$	20.0258	+	3.53109i	0.650752	+	0.114745i	0.161480	+	0.986876i	$0.448373\pi$
$948$	0.730224	−	9.10804i	0.0237166	−	0.295815i
$949$	2.84427	+	1.03523i	0.0923289	+	0.0336050i
$950$	−6.09476	+	5.11411i	−0.197740	+	0.165924i
$951$	−5.79427	−	5.71070i	−0.187892	−	0.185182i
$952$	−1.18350	−	9.14534i	−0.0383573	−	0.296402i
$953$	21.1725	+	12.2240i	0.685846	+	0.395973i	0.802054	−	0.597252i	$-0.203741\pi$
$953$	21.1725	+	12.2240i	0.685846	+	0.395973i	−0.116208	+	0.993225i	$0.537074\pi$
$954$	−0.231378	−	0.267747i	−0.00749112	−	0.00866864i
$955$	−9.73610	+	5.62114i	−0.315053	+	0.181896i
$956$	5.86466	−	6.98923i	0.189677	−	0.226048i
$957$	−3.57699	+	7.81866i	−0.115628	+	0.252741i
$958$	−30.6935	+	5.41210i	−0.991663	+	0.174857i
$959$	59.3583	+	2.72281i	1.91678	+	0.0879240i
$960$	2.11844	−	0.200855i	0.0683723	−	0.00648258i
$961$	−30.2585	−	25.3899i	−0.976082	−	0.819030i
$962$	−1.18340	−	2.04972i	−0.0381545	−	0.0660855i
$963$	9.11859	+	7.42836i	0.293843	+	0.239376i
$964$	−24.4468	−	14.1143i	−0.787377	−	0.454592i
$965$	31.2036	−	11.3572i	1.00448	−	0.365600i
$966$	1.20666	+	24.7620i	0.0388238	+	0.796705i
$967$	−16.8178	+	14.1118i	−0.540823	+	0.453805i	−0.871819	−	0.489827i	$-0.837060\pi$
$967$	−16.8178	+	14.1118i	−0.540823	+	0.453805i	0.330996	+	0.943632i	$0.392615\pi$
$968$	1.88198	−	5.17069i	0.0604891	−	0.166192i
$969$	5.90564	+	12.4282i	0.189717	+	0.399251i
$970$	3.25992	−	18.4880i	0.104670	−	0.593612i
$971$	17.7138			0.568462			0.284231	−	0.958756i	$-0.408262\pi$
$971$	17.7138			0.568462			0.284231	+	0.958756i	$0.408262\pi$
$972$	4.57869	+	14.9009i	0.146861	+	0.477945i
$973$	−10.2354	+	45.6917i	−0.328131	+	1.46481i
$974$	1.32454	+	0.233552i	0.0424410	+	0.00748350i
$975$	−1.13242	−	2.38313i	−0.0362664	−	0.0763212i
$976$	3.82461	−	10.5080i	0.122423	−	0.336354i
$977$	28.9823	+	34.5397i	0.927225	+	1.10502i	0.994230	+	0.107271i	$0.0342112\pi$
$977$	28.9823	+	34.5397i	0.927225	+	1.10502i	−0.0670051	+	0.997753i	$0.521344\pi$
$978$	6.55253	−	1.80686i	0.209527	−	0.0577770i
$979$	11.7934	+	32.4020i	0.376917	+	1.03557i
$980$	−7.06636	+	4.90162i	−0.225727	+	0.156576i
$981$	−27.7694	+	34.0880i	−0.886609	+	1.08835i
$982$	3.28898	+	5.69668i	0.104956	+	0.181789i
$983$	−39.6733	−	33.2899i	−1.26538	−	1.06178i	−0.995087	−	0.0990054i	$-0.968434\pi$
$983$	−39.6733	−	33.2899i	−1.26538	−	1.06178i	−0.270296	−	0.962777i	$-0.587122\pi$
$984$	0.257797	+	2.71900i	0.00821826	+	0.0866786i
$985$	13.1247	−	2.31423i	0.418187	−	0.0737377i
$986$	1.28140	+	7.26718i	0.0408081	+	0.231434i
$987$	−13.1508	+	17.3192i	−0.418595	+	0.551275i
$988$	−0.761985	−	0.639381i	−0.0242420	−	0.0203414i
$989$	9.59767	−	5.54122i	0.305188	−	0.176200i
$990$	5.65038	+	6.53856i	0.179581	+	0.207809i
$991$	25.8908	−	44.8442i	0.822449	−	1.42452i	−0.0814048	−	0.996681i	$-0.525941\pi$
$991$	25.8908	−	44.8442i	0.822449	−	1.42452i	0.903854	−	0.427842i	$-0.140726\pi$
$992$	7.89005	−	2.87174i	0.250509	−	0.0911779i
$993$	−12.6290	+	12.8138i	−0.400768	+	0.406633i
$994$	4.80560	−	2.48819i	0.152425	−	0.0789204i
$995$	−2.28665	+	6.28251i	−0.0724916	+	0.199169i
$996$	−1.20143	+	14.9853i	−0.0380687	+	0.474829i
$997$	31.2822	+	5.51589i	0.990717	+	0.174690i	0.645440	−	0.763811i	$-0.276674\pi$
$997$	31.2822	+	5.51589i	0.990717	+	0.174690i	0.345277	+	0.938501i	$0.387785\pi$
$998$		−	32.8116i		−	1.03863i
$999$	−27.0551	+	7.88511i	−0.855985	+	0.249474i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.z.a.83.2	yes	144
7.6	odd	2	inner	378.2.z.a.83.11	yes	144
27.14	odd	18	inner	378.2.z.a.41.11	yes	144
189.41	even	18	inner	378.2.z.a.41.2	✓	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.z.a.41.2	✓	144	189.41	even	18	inner
378.2.z.a.41.11	yes	144	27.14	odd	18	inner
378.2.z.a.83.2	yes	144	1.1	even	1	trivial
378.2.z.a.83.11	yes	144	7.6	odd	2	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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.z (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.984808 - 0.173648i) q^{2} +(-1.56441 + 0.743380i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-0.941136 + 0.789707i) q^{5} +(1.66973 - 0.460429i) q^{6} +(2.62387 - 0.339554i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(1.89477 - 2.32590i) q^{9} +O(q^{10})\)	\(q+(-0.984808 - 0.173648i) q^{2} +(-1.56441 + 0.743380i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-0.941136 + 0.789707i) q^{5} +(1.66973 - 0.460429i) q^{6} +(2.62387 - 0.339554i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(1.89477 - 2.32590i) q^{9} +(1.06397 - 0.614283i) q^{10} +(-1.50712 + 1.79612i) q^{11} +(-1.72432 + 0.163488i) q^{12} +(0.429778 - 0.0757815i) q^{13} +(-2.64297 - 0.121235i) q^{14} +(0.885273 - 1.93505i) q^{15} +(0.766044 + 0.642788i) q^{16} +(1.74272 + 3.01848i) q^{17} +(-2.26988 + 1.96155i) q^{18} +(-1.97392 - 1.13964i) q^{19} +(-1.15447 + 0.420194i) q^{20} +(-3.85240 + 2.48174i) q^{21} +(1.79612 - 1.50712i) q^{22} +(-1.85030 + 5.08367i) q^{23} +(1.72651 + 0.138421i) q^{24} +(-0.606141 + 3.43760i) q^{25} -0.436408 q^{26} +(-1.23518 + 5.04721i) q^{27} +(2.58177 + 0.578340i) q^{28} +(-2.08501 - 0.367644i) q^{29} +(-1.20784 + 1.75193i) q^{30} +(-2.87174 + 7.89005i) q^{31} +(-0.642788 - 0.766044i) q^{32} +(1.02256 - 3.93024i) q^{33} +(-1.19209 - 3.27524i) q^{34} +(-2.20127 + 2.39166i) q^{35} +(2.57601 - 1.53759i) q^{36} +(2.71169 + 4.69678i) q^{37} +(1.74604 + 1.46510i) q^{38} +(-0.616016 + 0.438042i) q^{39} +(1.20990 - 0.213338i) q^{40} +(0.273818 + 1.55290i) q^{41} +(4.22482 - 1.77507i) q^{42} +(-1.56927 - 1.31677i) q^{43} +(-2.03054 + 1.17233i) q^{44} +(0.0535437 + 3.68531i) q^{45} +(2.70496 - 4.68513i) q^{46} +(4.45922 - 1.62303i) q^{47} +(-1.67624 - 0.436123i) q^{48} +(6.76941 - 1.78189i) q^{49} +(1.19386 - 3.28012i) q^{50} +(-4.97020 - 3.42664i) q^{51} +(0.429778 + 0.0757815i) q^{52} +0.117957i q^{53} +(2.09285 - 4.75605i) q^{54} -2.88058i q^{55} +(-2.44212 - 1.01787i) q^{56} +(3.93522 + 0.315500i) q^{57} +(1.98950 + 0.724117i) q^{58} +(-9.22472 + 7.74046i) q^{59} +(1.49371 - 1.51557i) q^{60} +(-3.82461 - 10.5080i) q^{61} +(4.19821 - 7.27151i) q^{62} +(4.18187 - 6.74625i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-0.344635 + 0.410720i) q^{65} +(-1.68951 + 3.69296i) q^{66} +(1.46744 + 8.32229i) q^{67} +(0.605240 + 3.43248i) q^{68} +(-0.884457 - 9.32843i) q^{69} +(2.58314 - 1.97307i) q^{70} +(-1.77135 + 1.02269i) q^{71} +(-2.80387 + 1.06691i) q^{72} +(6.00651 + 3.46786i) q^{73} +(-1.85490 - 5.09631i) q^{74} +(-1.60718 - 5.82841i) q^{75} +(-1.46510 - 1.74604i) q^{76} +(-3.34462 + 5.22454i) q^{77} +(0.682723 - 0.324417i) q^{78} +(-0.916064 + 5.19526i) q^{79} -1.22857 q^{80} +(-1.81967 - 8.81413i) q^{81} -1.57686i q^{82} +(1.50719 - 8.54769i) q^{83} +(-4.46888 + 1.01447i) q^{84} +(-4.02385 - 1.46456i) q^{85} +(1.31677 + 1.56927i) q^{86} +(3.53512 - 0.974809i) q^{87} +(2.20327 - 0.801923i) q^{88} +(7.35317 - 12.7361i) q^{89} +(0.587217 - 3.63862i) q^{90} +(1.10195 - 0.344774i) q^{91} +(-3.47743 + 4.14424i) q^{92} +(-1.37271 - 14.4781i) q^{93} +(-4.67331 + 0.824031i) q^{94} +(2.75771 - 0.486259i) q^{95} +(1.57505 + 0.720574i) q^{96} +(9.82215 - 11.7056i) q^{97} +(-6.97599 + 0.579328i) q^{98} +(1.32195 + 6.90866i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 12 q^{9}+O(q^{10}) \) 144 * q - 12 * q^9	\( 144 q - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 24 q^{21} - 60 q^{23} + 12 q^{29} - 72 q^{30} + 54 q^{35} - 12 q^{36} + 48 q^{39} + 24 q^{42} + 18 q^{49} - 60 q^{50} - 36 q^{51} + 6 q^{56} - 60 q^{57} - 36 q^{60} - 78 q^{63} + 72 q^{64} - 120 q^{65} + 36 q^{70} - 72 q^{71} - 24 q^{72} - 36 q^{74} + 66 q^{77} - 60 q^{78} - 72 q^{79} + 12 q^{84} - 72 q^{85} - 48 q^{86} - 18 q^{91} + 12 q^{92} + 24 q^{93} - 120 q^{95} + 36 q^{98} + 144 q^{99}+O(q^{100}) \) 144 * q - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 24 * q^21 - 60 * q^23 + 12 * q^29 - 72 * q^30 + 54 * q^35 - 12 * q^36 + 48 * q^39 + 24 * q^42 + 18 * q^49 - 60 * q^50 - 36 * q^51 + 6 * q^56 - 60 * q^57 - 36 * q^60 - 78 * q^63 + 72 * q^64 - 120 * q^65 + 36 * q^70 - 72 * q^71 - 24 * q^72 - 36 * q^74 + 66 * q^77 - 60 * q^78 - 72 * q^79 + 12 * q^84 - 72 * q^85 - 48 * q^86 - 18 * q^91 + 12 * q^92 + 24 * q^93 - 120 * q^95 + 36 * q^98 + 144 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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