LMFDB - Embedded newform 378.2.bf.a.101.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(5,378)]

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([5, 15]))

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

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

chi := DirichletCharacter("378.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.bf (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			101.22
Character	$\chi$	$=$	378.101
Dual form			378.2.bf.a.131.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.642788 - 0.766044i) q^{2} +(1.49557 + 0.873659i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(2.37114 - 1.98962i) q^{5} +(1.63059 - 0.584093i) q^{6} +(0.451749 + 2.60690i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(1.47344 + 2.61323i) q^{9} +O(q^{10})$	\(q+(0.642788 - 0.766044i) q^{2} +(1.49557 + 0.873659i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(2.37114 - 1.98962i) q^{5} +(1.63059 - 0.584093i) q^{6} +(0.451749 + 2.60690i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(1.47344 + 2.61323i) q^{9} -3.09530i q^{10} +(-2.81892 + 3.35945i) q^{11} +(0.600684 - 1.62455i) q^{12} +(1.81629 - 4.99023i) q^{13} +(2.28738 + 1.32962i) q^{14} +(5.28444 - 0.904044i) q^{15} +(-0.939693 + 0.342020i) q^{16} -7.67316 q^{17} +(2.94896 + 0.551033i) q^{18} +0.862980i q^{19} +(-2.37114 - 1.98962i) q^{20} +(-1.60192 + 4.29347i) q^{21} +(0.761526 + 4.31883i) q^{22} +(0.773805 - 2.12601i) q^{23} +(-0.858369 - 1.50439i) q^{24} +(0.795461 - 4.51129i) q^{25} +(-2.65524 - 4.59902i) q^{26} +(-0.0794470 + 5.19555i) q^{27} +(2.48885 - 0.897569i) q^{28} +(-3.14624 - 8.64421i) q^{29} +(2.70424 - 4.62923i) q^{30} +(1.66487 - 0.293562i) q^{31} +(-0.342020 + 0.939693i) q^{32} +(-7.15089 + 2.56151i) q^{33} +(-4.93221 + 5.87798i) q^{34} +(6.25790 + 5.28251i) q^{35} +(2.31767 - 1.90484i) q^{36} +(-2.35278 + 4.07514i) q^{37} +(0.661081 + 0.554713i) q^{38} +(7.07615 - 5.87639i) q^{39} +(-3.04828 + 0.537493i) q^{40} +(9.88578 + 3.59813i) q^{41} +(2.25929 + 3.98693i) q^{42} +(-0.314429 + 1.78322i) q^{43} +(3.79791 + 2.19273i) q^{44} +(8.69306 + 3.26474i) q^{45} +(-1.13123 - 1.95934i) q^{46} +(0.462883 - 2.62514i) q^{47} +(-1.70418 - 0.309457i) q^{48} +(-6.59185 + 2.35533i) q^{49} +(-2.94453 - 3.50916i) q^{50} +(-11.4757 - 6.70373i) q^{51} +(-5.22981 - 0.922157i) q^{52} +(-2.90888 - 1.67944i) q^{53} +(3.92895 + 3.40049i) q^{54} +13.5743i q^{55} +(0.912224 - 2.48352i) q^{56} +(-0.753951 + 1.29064i) q^{57} +(-8.64421 - 3.14624i) q^{58} +(-9.29301 - 3.38238i) q^{59} +(-1.80794 - 5.04718i) q^{60} +(5.22585 + 0.921459i) q^{61} +(0.845277 - 1.46406i) q^{62} +(-6.14681 + 5.02163i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-5.62197 - 15.4462i) q^{65} +(-2.63427 + 7.12441i) q^{66} +(-3.96204 + 3.32455i) q^{67} +(1.33243 + 7.55659i) q^{68} +(3.01469 - 2.50355i) q^{69} +(8.06913 - 1.39830i) q^{70} +(3.61889 - 2.08937i) q^{71} +(0.0305798 - 2.99984i) q^{72} +(-1.25873 + 0.726726i) q^{73} +(1.60940 + 4.42179i) q^{74} +(5.13099 - 6.05197i) q^{75} +(0.849870 - 0.149855i) q^{76} +(-10.0312 - 5.83100i) q^{77} +(0.0468797 - 9.19792i) q^{78} +(-1.35158 - 1.13411i) q^{79} +(-1.54765 + 2.68061i) q^{80} +(-4.65795 + 7.70087i) q^{81} +(9.11078 - 5.26011i) q^{82} +(-12.6880 + 4.61804i) q^{83} +(4.50641 + 0.832032i) q^{84} +(-18.1941 + 15.2667i) q^{85} +(1.16391 + 1.38710i) q^{86} +(2.84669 - 15.6767i) q^{87} +(4.12098 - 1.49991i) q^{88} +5.72472 q^{89} +(8.08873 - 4.56074i) q^{90} +(13.8295 + 2.48057i) q^{91} +(-2.22808 - 0.392871i) q^{92} +(2.74640 + 1.01549i) q^{93} +(-1.71344 - 2.04200i) q^{94} +(1.71700 + 2.04624i) q^{95} +(-1.33249 + 1.10656i) q^{96} +(16.1691 + 2.85104i) q^{97} +(-2.43287 + 6.56362i) q^{98} +(-12.9325 - 2.41653i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 18 q^{6} - 12 q^{9}+O(q^{10}) $ 144 * q + 18 * q^6 - 12 * q^9	$ 144 q + 18 q^{6} - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 6 q^{21} - 6 q^{23} - 6 q^{29} - 18 q^{30} - 54 q^{35} + 6 q^{36} - 6 q^{39} + 24 q^{42} - 54 q^{47} + 18 q^{49} + 12 q^{50} + 18 q^{51} + 90 q^{53} - 54 q^{54} - 12 q^{56} - 6 q^{57} - 90 q^{59} - 36 q^{60} - 24 q^{63} + 72 q^{64} - 84 q^{65} - 36 q^{69} - 18 q^{70} - 72 q^{71} + 12 q^{72} + 18 q^{74} - 90 q^{75} - 78 q^{77} - 60 q^{78} + 36 q^{79} - 6 q^{84} - 72 q^{85} + 24 q^{86} + 90 q^{87} - 18 q^{91} - 42 q^{92} - 12 q^{93} + 78 q^{95} - 36 q^{98} - 108 q^{99}+O(q^{100}) $ 144 * q + 18 * q^6 - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 6 * q^21 - 6 * q^23 - 6 * q^29 - 18 * q^30 - 54 * q^35 + 6 * q^36 - 6 * q^39 + 24 * q^42 - 54 * q^47 + 18 * q^49 + 12 * q^50 + 18 * q^51 + 90 * q^53 - 54 * q^54 - 12 * q^56 - 6 * q^57 - 90 * q^59 - 36 * q^60 - 24 * q^63 + 72 * q^64 - 84 * q^65 - 36 * q^69 - 18 * q^70 - 72 * q^71 + 12 * q^72 + 18 * q^74 - 90 * q^75 - 78 * q^77 - 60 * q^78 + 36 * q^79 - 6 * q^84 - 72 * q^85 + 24 * q^86 + 90 * q^87 - 18 * q^91 - 42 * q^92 - 12 * q^93 + 78 * q^95 - 36 * q^98 - 108 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.642788	−	0.766044i	0.454519	−	0.541675i
$2$	0.642788	−	0.766044i	0.454519	−	0.541675i
$3$	1.49557	+	0.873659i	0.863466	+	0.504407i
$3$	1.49557	+	0.873659i	0.863466	+	0.504407i
$4$	−0.173648	−	0.984808i	−0.0868241	−	0.492404i
$5$	2.37114	−	1.98962i	1.06040	−	0.889785i	0.0662557	−	0.997803i	$-0.478895\pi$
$5$	2.37114	−	1.98962i	1.06040	−	0.889785i	0.994149	+	0.108017i	$0.0344502\pi$
$6$	1.63059	−	0.584093i	0.665687	−	0.238455i
$7$	0.451749	+	2.60690i	0.170745	+	0.985315i
$7$	0.451749	+	2.60690i	0.170745	+	0.985315i
$8$	−0.866025	−	0.500000i	−0.306186	−	0.176777i
$9$	1.47344	+	2.61323i	0.491146	+	0.871077i
$10$		−	3.09530i		−	0.978820i
$11$	−2.81892	+	3.35945i	−0.849935	+	1.01291i	0.149772	+	0.988720i	$0.452146\pi$
$11$	−2.81892	+	3.35945i	−0.849935	+	1.01291i	−0.999707	+	0.0241925i	$0.992299\pi$
$12$	0.600684	−	1.62455i	0.173403	−	0.468969i
$13$	1.81629	−	4.99023i	0.503749	−	1.38404i	−0.383838	−	0.923400i	$-0.625398\pi$
$13$	1.81629	−	4.99023i	0.503749	−	1.38404i	0.887587	−	0.460639i	$-0.152380\pi$
$14$	2.28738	+	1.32962i	0.611328	+	0.355357i
$15$	5.28444	−	0.904044i	1.36444	−	0.233423i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−7.67316			−1.86102			−0.930508	−	0.366272i	$-0.880634\pi$
$17$	−7.67316			−1.86102			−0.930508	+	0.366272i	$0.880634\pi$
$18$	2.94896	+	0.551033i	0.695076	+	0.129880i
$19$			0.862980i			0.197981i	0.995088	+	0.0989906i	$0.0315614\pi$
$19$			0.862980i			0.197981i	−0.995088	+	0.0989906i	$0.968439\pi$
$20$	−2.37114	−	1.98962i	−0.530202	−	0.444893i
$21$	−1.60192	+	4.29347i	−0.349568	+	0.936911i
$22$	0.761526	+	4.31883i	0.162358	+	0.920777i
$23$	0.773805	−	2.12601i	0.161350	−	0.443304i	−0.832502	−	0.554021i	$-0.813093\pi$
$23$	0.773805	−	2.12601i	0.161350	−	0.443304i	0.993852	+	0.110717i	$0.0353148\pi$
$24$	−0.858369	−	1.50439i	−0.175214	−	0.307083i
$25$	0.795461	−	4.51129i	0.159092	−	0.902257i
$26$	−2.65524	−	4.59902i	−0.520736	−	0.901942i
$27$	−0.0794470	+	5.19555i	−0.0152896	+	0.999883i
$28$	2.48885	−	0.897569i	0.470348	−	0.169625i
$29$	−3.14624	−	8.64421i	−0.584241	−	1.60519i	−0.780858	−	0.624709i	$-0.785218\pi$
$29$	−3.14624	−	8.64421i	−0.584241	−	1.60519i	0.196616	−	0.980481i	$-0.437005\pi$
$30$	2.70424	−	4.62923i	0.493724	−	0.845177i
$31$	1.66487	−	0.293562i	0.299020	−	0.0527252i	−0.0221255	−	0.999755i	$-0.507043\pi$
$31$	1.66487	−	0.293562i	0.299020	−	0.0527252i	0.321145	+	0.947030i	$0.395932\pi$
$32$	−0.342020	+	0.939693i	−0.0604612	+	0.166116i
$33$	−7.15089	+	2.56151i	−1.24481	+	0.445902i
$34$	−4.93221	+	5.87798i	−0.845868	+	1.00807i
$35$	6.25790	+	5.28251i	1.05778	+	0.892907i
$36$	2.31767	−	1.90484i	0.386278	−	0.317473i
$37$	−2.35278	+	4.07514i	−0.386795	+	0.669949i	−0.992016	−	0.126108i	$-0.959751\pi$
$37$	−2.35278	+	4.07514i	−0.386795	+	0.669949i	0.605221	+	0.796057i	$0.293085\pi$
$38$	0.661081	+	0.554713i	0.107242	+	0.0899863i
$39$	7.07615	−	5.87639i	1.13309	−	0.940976i
$40$	−3.04828	+	0.537493i	−0.481975	+	0.0849851i
$41$	9.88578	+	3.59813i	1.54390	+	0.561933i	0.966976	−	0.254866i	$-0.0820312\pi$
$41$	9.88578	+	3.59813i	1.54390	+	0.561933i	0.576923	+	0.816799i	$0.304253\pi$
$42$	2.25929	+	3.98693i	0.348616	+	0.615197i
$43$	−0.314429	+	1.78322i	−0.0479500	+	0.271938i	−0.999351	−	0.0360162i	$-0.988533\pi$
$43$	−0.314429	+	1.78322i	−0.0479500	+	0.271938i	0.951401	+	0.307954i	$0.0996443\pi$
$44$	3.79791	+	2.19273i	0.572557	+	0.330566i
$45$	8.69306	+	3.26474i	1.29589	+	0.486679i
$46$	−1.13123	−	1.95934i	−0.166790	−	0.288889i
$47$	0.462883	−	2.62514i	0.0675184	−	0.382916i	−0.932258	−	0.361793i	$-0.882165\pi$
$47$	0.462883	−	2.62514i	0.0675184	−	0.382916i	0.999777	−	0.0211229i	$-0.00672414\pi$
$48$	−1.70418	−	0.309457i	−0.245977	−	0.0446663i
$49$	−6.59185	+	2.35533i	−0.941692	+	0.336475i
$50$	−2.94453	−	3.50916i	−0.416420	−	0.496270i
$51$	−11.4757	−	6.70373i	−1.60692	−	0.938710i
$52$	−5.22981	−	0.922157i	−0.725244	−	0.127880i
$53$	−2.90888	−	1.67944i	−0.399565	−	0.230689i	0.286731	−	0.958011i	$-0.407431\pi$
$53$	−2.90888	−	1.67944i	−0.399565	−	0.230689i	−0.686296	+	0.727322i	$0.740765\pi$
$54$	3.92895	+	3.40049i	0.534662	+	0.462748i
$55$			13.5743i			1.83036i
$56$	0.912224	−	2.48352i	0.121901	−	0.331874i
$57$	−0.753951	+	1.29064i	−0.0998632	+	0.170950i
$58$	−8.64421	−	3.14624i	−1.13504	−	0.413121i
$59$	−9.29301	−	3.38238i	−1.20985	−	0.440348i	−0.343196	−	0.939264i	$-0.611509\pi$
$59$	−9.29301	−	3.38238i	−1.20985	−	0.440348i	−0.866650	+	0.498916i	$0.833732\pi$
$60$	−1.80794	−	5.04718i	−0.233404	−	0.651588i
$61$	5.22585	+	0.921459i	0.669102	+	0.117981i	0.497872	−	0.867250i	$-0.334115\pi$
$61$	5.22585	+	0.921459i	0.669102	+	0.117981i	0.171230	+	0.985231i	$0.445226\pi$
$62$	0.845277	−	1.46406i	0.107350	−	0.185936i
$63$	−6.14681	+	5.02163i	−0.774425	+	0.632666i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$	−5.62197	−	15.4462i	−0.697320	−	1.91587i
$66$	−2.63427	+	7.12441i	−0.324256	+	0.876954i
$67$	−3.96204	+	3.32455i	−0.484041	+	0.406158i	−0.851885	−	0.523729i	$-0.824540\pi$
$67$	−3.96204	+	3.32455i	−0.484041	+	0.406158i	0.367844	+	0.929887i	$0.380096\pi$
$68$	1.33243	+	7.55659i	0.161581	+	0.916371i
$69$	3.01469	−	2.50355i	0.362926	−	0.301392i
$70$	8.06913	−	1.39830i	0.964446	−	0.167129i
$71$	3.61889	−	2.08937i	0.429484	−	0.247962i	−0.269643	−	0.962960i	$-0.586906\pi$
$71$	3.61889	−	2.08937i	0.429484	−	0.247962i	0.699127	+	0.714998i	$0.253572\pi$
$72$	0.0305798	−	2.99984i	0.00360387	−	0.353535i
$73$	−1.25873	+	0.726726i	−0.147323	+	0.0850569i	−0.571849	−	0.820359i	$-0.693774\pi$
$73$	−1.25873	+	0.726726i	−0.147323	+	0.0850569i	0.424527	+	0.905415i	$0.360441\pi$
$74$	1.60940	+	4.42179i	0.187089	+	0.514022i
$75$	5.13099	−	6.05197i	0.592476	−	0.698821i
$76$	0.849870	−	0.149855i	0.0974867	−	0.0171895i
$77$	−10.0312	−	5.83100i	−1.14316	−	0.664504i
$78$	0.0468797	−	9.19792i	0.00530808	−	1.04146i
$79$	−1.35158	−	1.13411i	−0.152065	−	0.127597i	0.563581	−	0.826061i	$-0.309423\pi$
$79$	−1.35158	−	1.13411i	−0.152065	−	0.127597i	−0.715646	+	0.698463i	$0.753868\pi$
$80$	−1.54765	+	2.68061i	−0.173033	+	0.299701i
$81$	−4.65795	+	7.70087i	−0.517550	+	0.855653i
$82$	9.11078	−	5.26011i	1.00612	−	0.580882i
$83$	−12.6880	+	4.61804i	−1.39269	+	0.506896i	−0.925999	−	0.377526i	$-0.876775\pi$
$83$	−12.6880	+	4.61804i	−1.39269	+	0.506896i	−0.466687	+	0.884422i	$0.654553\pi$
$84$	4.50641	+	0.832032i	0.491690	+	0.0907821i
$85$	−18.1941	+	15.2667i	−1.97343	+	1.65590i
$86$	1.16391	+	1.38710i	0.125508	+	0.149574i
$87$	2.84669	−	15.6767i	0.305197	−	1.68072i
$88$	4.12098	−	1.49991i	0.439298	−	0.159891i
$89$	5.72472			0.606819			0.303410	−	0.952860i	$-0.401875\pi$
$89$	5.72472			0.606819			0.303410	+	0.952860i	$0.401875\pi$
$90$	8.08873	−	4.56074i	0.852627	−	0.480744i
$91$	13.8295	+	2.48057i	1.44973	+	0.260034i
$92$	−2.22808	−	0.392871i	−0.232294	−	0.0409597i
$93$	2.74640	+	1.01549i	0.284788	+	0.105301i
$94$	−1.71344	−	2.04200i	−0.176728	−	0.210616i
$95$	1.71700	+	2.04624i	0.176161	+	0.209940i
$96$	−1.33249	+	1.10656i	−0.135996	+	0.112938i
$97$	16.1691	+	2.85104i	1.64172	+	0.289480i	0.916798	−	0.399350i	$-0.130764\pi$
$97$	16.1691	+	2.85104i	1.64172	+	0.289480i	0.724923	+	0.688830i	$0.241875\pi$
$98$	−2.43287	+	6.56362i	−0.245757	+	0.663026i
$99$	−12.9325	−	2.41653i	−1.29977	−	0.242870i
$100$	−4.58088			−0.458088
$101$	−11.4636	+	4.17241i	−1.14067	+	0.415170i	−0.842155	−	0.539235i	$-0.818713\pi$
$101$	−11.4636	+	4.17241i	−1.14067	+	0.415170i	−0.298515	+	0.954405i	$0.596491\pi$
$102$	−12.5118	+	4.48184i	−1.23885	+	0.443769i
$103$	5.96689	+	7.11106i	0.587935	+	0.700674i	0.975208	−	0.221292i	$-0.0710273\pi$
$103$	5.96689	+	7.11106i	0.587935	+	0.700674i	−0.387273	+	0.921965i	$0.626583\pi$
$104$	−4.06807	+	3.41352i	−0.398907	+	0.334723i
$105$	4.74399	+	13.3676i	0.462966	+	1.30455i
$106$	−3.15632	+	1.14881i	−0.306569	+	0.111582i
$107$	3.33250	−	1.92402i	0.322165	−	0.186002i	−0.330192	−	0.943914i	$-0.607114\pi$
$107$	3.33250	−	1.92402i	0.322165	−	0.186002i	0.652357	+	0.757912i	$0.273780\pi$
$108$	5.13041	−	0.823957i	0.493674	−	0.0792853i
$109$	−4.32985	+	7.49952i	−0.414724	+	0.718324i	−0.995399	−	0.0958118i	$-0.969455\pi$
$109$	−4.32985	+	7.49952i	−0.414724	+	0.718324i	0.580675	+	0.814135i	$0.302789\pi$
$110$	10.3985	+	8.72539i	0.991459	+	0.831933i
$111$	−7.07903	+	4.03911i	−0.671912	+	0.383376i
$112$	−1.31612	−	2.29518i	−0.124361	−	0.216874i
$113$	9.38005	−	1.65396i	0.882401	−	0.155591i	0.285954	−	0.958243i	$-0.407690\pi$
$113$	9.38005	−	1.65396i	0.882401	−	0.155591i	0.596447	+	0.802652i	$0.296579\pi$
$114$	0.504061	+	1.40717i	0.0472096	+	0.131794i
$115$	−2.39516	−	6.58065i	−0.223350	−	0.613648i
$116$	−7.96655	+	4.59949i	−0.739675	+	0.427052i
$117$	15.7168	−	2.60640i	1.45302	−	0.240962i
$118$	−8.56448	+	4.94471i	−0.788424	+	0.455197i
$119$	−3.46634	−	20.0032i	−0.317759	−	1.83369i
$120$	−5.02848	−	1.85930i	−0.459036	−	0.169730i
$121$	−1.42951	−	8.10714i	−0.129955	−	0.737012i
$122$	4.06499	−	3.41093i	0.368027	−	0.308811i
$123$	11.6413	+	14.0180i	1.04966	+	1.26396i
$124$	−0.578204	−	1.58860i	−0.0519242	−	0.142661i
$125$	0.648651	+	1.12350i	0.0580171	+	0.100489i
$126$	−0.104298	+	7.93657i	−0.00929158	+	0.707046i
$127$	5.45056	−	9.44065i	0.483659	−	0.837723i	−0.516165	−	0.856489i	$-0.672641\pi$
$127$	5.45056	−	9.44065i	0.483659	−	0.837723i	0.999824	+	0.0187669i	$0.00597403\pi$
$128$	0.984808	+	0.173648i	0.0870455	+	0.0153485i
$129$	−2.02817	+	2.39221i	−0.178571	+	0.210623i
$130$	−15.4462	−	5.62197i	−1.35473	−	0.493080i
$131$	8.01794	+	2.91829i	0.700531	+	0.254972i	0.667638	−	0.744486i	$-0.267306\pi$
$131$	8.01794	+	2.91829i	0.700531	+	0.254972i	0.0328934	+	0.999459i	$0.489528\pi$
$132$	3.76434	+	6.59745i	0.327644	+	0.574234i
$133$	−2.24970	+	0.389850i	−0.195074	+	0.0338043i
$134$			5.17208i			0.446800i
$135$	10.1488	+	12.4774i	0.873468	+	1.07389i
$136$	6.64515	+	3.83658i	0.569817	+	0.328984i
$137$	5.95924	+	1.05077i	0.509132	+	0.0897737i	0.422312	−	0.906450i	$-0.361219\pi$
$137$	5.95924	+	1.05077i	0.509132	+	0.0897737i	0.0868195	+	0.996224i	$0.472330\pi$
$138$	0.0199724	−	3.91864i	0.00170016	−	0.333576i
$139$	1.38815	+	1.65433i	0.117741	+	0.140318i	0.821695	−	0.569927i	$-0.193028\pi$
$139$	1.38815	+	1.65433i	0.117741	+	0.140318i	−0.703954	+	0.710245i	$0.748584\pi$
$140$	4.11558	−	7.08012i	0.347830	−	0.598380i
$141$	2.98575	−	3.52167i	0.251445	−	0.296578i
$142$	0.725630	−	4.11525i	0.0608935	−	0.345344i
$143$	11.6444	+	20.1688i	0.973758	+	1.68660i
$144$	−2.27836	−	1.95169i	−0.189863	−	0.162641i
$145$	−24.6589	−	14.2368i	−2.04781	−	1.18230i
$146$	−0.252389	+	1.43137i	−0.0208879	+	0.118461i
$147$	−11.9163	−	2.23648i	−0.982840	−	0.184462i
$148$	4.42179	+	1.60940i	0.363469	+	0.132292i
$149$	−7.16375	+	1.26316i	−0.586877	+	0.103482i	−0.459199	−	0.888333i	$-0.651864\pi$
$149$	−7.16375	+	1.26316i	−0.586877	+	0.103482i	−0.127678	+	0.991816i	$0.540752\pi$
$150$	−1.33794	−	7.82070i	−0.109242	−	0.638557i
$151$	4.49880	+	3.77495i	0.366108	+	0.307201i	0.807219	−	0.590251i	$-0.200971\pi$
$151$	4.49880	+	3.77495i	0.366108	+	0.307201i	−0.441112	+	0.897452i	$0.645416\pi$
$152$	0.431490	−	0.747363i	0.0349985	−	0.0606191i
$153$	−11.3059	−	20.0518i	−0.914031	−	1.62109i
$154$	−10.9147	+	3.93625i	−0.879534	+	0.317192i
$155$	3.36356	−	4.00854i	0.270168	−	0.321973i
$156$	−7.01588	−	5.94822i	−0.561720	−	0.476239i
$157$	4.40468	−	12.1018i	0.351532	−	0.965825i	−0.630347	−	0.776314i	$-0.717087\pi$
$157$	4.40468	−	12.1018i	0.351532	−	0.965825i	0.981879	−	0.189511i	$-0.0606904\pi$
$158$	−1.73756	+	0.306378i	−0.138233	+	0.0243741i
$159$	−2.88316	−	5.05308i	−0.228649	−	0.400736i
$160$	1.05865	+	2.90863i	0.0836940	+	0.229947i
$161$	5.89187	+	1.05681i	0.464344	+	0.0832882i
$162$	2.90514	+	8.51823i	0.228249	+	0.669255i
$163$	−0.478456	−	0.828709i	−0.0374755	−	0.0649095i	0.846679	−	0.532104i	$-0.178598\pi$
$163$	−0.478456	−	0.828709i	−0.0374755	−	0.0649095i	−0.884155	+	0.467194i	$0.845265\pi$
$164$	1.82682	−	10.3604i	0.142651	−	0.809011i
$165$	−11.8593	+	20.3013i	−0.923246	+	1.58045i
$166$	−4.61804	+	12.6880i	−0.358430	+	0.984778i
$167$	−0.528130	−	2.99517i	−0.0408679	−	0.231774i	0.957532	−	0.288328i	$-0.0930995\pi$
$167$	−0.528130	−	2.99517i	−0.0408679	−	0.231774i	−0.998399	+	0.0565549i	$0.981988\pi$
$168$	3.53404	−	2.91729i	0.272657	−	0.225074i
$169$	−11.6449	−	9.77120i	−0.895759	−	0.751631i
$170$			23.7507i			1.82160i
$171$	−2.25517	+	1.27155i	−0.172457	+	0.0972378i
$172$	1.81072			0.138066
$173$	2.70544	−	0.984698i	0.205690	−	0.0748652i	−0.237120	−	0.971480i	$-0.576204\pi$
$173$	2.70544	−	0.984698i	0.205690	−	0.0748652i	0.442811	+	0.896615i	$0.353981\pi$
$174$	−10.1793	−	12.2575i	−0.771687	−	0.929239i
$175$	12.1198	+	0.0357196i	0.916172	+	0.00270015i
$176$	1.49991	−	4.12098i	0.113060	−	0.310630i
$177$	−10.9433	−	13.1775i	−0.822546	−	0.990481i
$178$	3.67978	−	4.38539i	0.275811	−	0.328699i
$179$		−	23.9492i		−	1.79005i	−0.446018	−	0.895024i	$-0.647158\pi$
$179$		−	23.9492i		−	1.79005i	0.446018	−	0.895024i	$-0.352842\pi$
$180$	1.70561	−	9.12791i	0.127129	−	0.680355i
$181$	11.4199	+	6.59328i	0.848834	+	0.490074i	0.860257	−	0.509860i	$-0.170303\pi$
$181$	11.4199	+	6.59328i	0.848834	+	0.490074i	−0.0114234	+	0.999935i	$0.503636\pi$
$182$	10.7897	−	8.99955i	0.799784	−	0.667091i
$183$	7.01057	+	5.94372i	0.518236	+	0.439372i
$184$	−1.73314	+	1.45428i	−0.127769	+	0.107211i
$185$	2.52921	+	14.3439i	0.185951	+	1.05458i
$186$	2.54326	−	1.45112i	0.186481	−	0.106401i
$187$	21.6300	−	25.7776i	1.58174	−	1.88505i
$188$	−2.66564			−0.194411
$189$	−13.5802	+	2.13997i	−0.987811	+	0.155660i
$190$	2.67118			0.193788
$191$	12.3944	−	14.7710i	0.896825	−	1.06879i	−0.100444	−	0.994943i	$-0.532026\pi$
$191$	12.3944	−	14.7710i	0.896825	−	1.06879i	0.997269	−	0.0738521i	$-0.0235293\pi$
$192$	−0.00882775	+	1.73203i	−0.000637088	+	0.124998i
$193$	−3.25628	−	18.4673i	−0.234392	−	1.32930i	−0.843890	−	0.536516i	$-0.819740\pi$
$193$	−3.25628	−	18.4673i	−0.234392	−	1.32930i	0.609498	−	0.792787i	$-0.291371\pi$
$194$	12.5773	−	10.5536i	0.902998	−	0.757706i
$195$	5.08672	−	28.0126i	0.364268	−	2.00602i
$196$	3.46421	+	6.08270i	0.247443	+	0.434479i
$197$	−10.3579	−	5.98011i	−0.737966	−	0.426065i	0.0833631	−	0.996519i	$-0.473434\pi$
$197$	−10.3579	−	5.98011i	−0.737966	−	0.426065i	−0.821329	+	0.570454i	$0.806767\pi$
$198$	−10.1640	+	8.35357i	−0.722327	+	0.593663i
$199$			24.7806i			1.75665i	0.478064	+	0.878325i	$0.341339\pi$
$199$			24.7806i			1.75665i	−0.478064	+	0.878325i	$0.658661\pi$
$200$	−2.94453	+	3.50916i	−0.208210	+	0.248135i
$201$	−8.83002	+	1.51061i	−0.622822	+	0.106550i
$202$	−4.17241	+	11.4636i	−0.293569	+	0.806575i
$203$	21.1133	−	12.1069i	1.48186	−	0.849740i
$204$	−4.60915	+	12.4655i	−0.322705	+	0.872758i
$205$	30.5994	−	11.1373i	2.13716	−	0.777862i
$206$	9.28283			0.646765
$207$	6.69592	−	1.11042i	0.465398	−	0.0771794i
$208$			5.31049i			0.368216i
$209$	−2.89914	−	2.43267i	−0.200538	−	0.168271i
$210$	13.2896	+	4.95843i	0.917067	+	0.342164i
$211$	−1.19972	−	6.80394i	−0.0825920	−	0.468402i	−0.997850	−	0.0655348i	$-0.979125\pi$
$211$	−1.19972	−	6.80394i	−0.0825920	−	0.468402i	0.915258	−	0.402867i	$-0.131986\pi$
$212$	−1.14881	+	3.15632i	−0.0789003	+	0.216777i
$213$	7.23769	+	0.0368889i	0.495919	+	0.00252758i
$214$	0.668204	−	3.78957i	0.0456775	−	0.259050i
$215$	2.80237	+	4.85384i	0.191120	+	0.331029i
$216$	2.66658	−	4.45975i	0.181437	−	0.303448i
$217$	1.51739	+	4.20753i	0.103007	+	0.285626i
$218$	2.96179	+	8.13745i	0.200598	+	0.551138i
$219$	−2.51742	−	0.0128307i	−0.170112	−	0.000867020i
$220$	13.3681	−	2.35715i	0.901275	−	0.158919i
$221$	−13.9367	+	38.2908i	−0.937485	+	2.57572i
$222$	−1.45617	+	8.01914i	−0.0977318	+	0.538210i
$223$	−0.554883	+	0.661284i	−0.0371577	+	0.0442829i	−0.784303	−	0.620378i	$-0.786979\pi$
$223$	−0.554883	+	0.661284i	−0.0371577	+	0.0442829i	0.747146	+	0.664660i	$0.231424\pi$
$224$	−2.60419	−	0.467107i	−0.174000	−	0.0312099i
$225$	12.9611	−	4.56838i	0.864073	−	0.304559i
$226$	4.76237	−	8.24868i	0.316788	−	0.548694i
$227$	19.2798	+	16.1777i	1.27965	+	1.07375i	0.993293	+	0.115626i	$0.0368874\pi$
$227$	19.2798	+	16.1777i	1.27965	+	1.07375i	0.286353	+	0.958124i	$0.407557\pi$
$228$	1.40196	+	0.518378i	0.0928470	+	0.0343304i
$229$	17.5043	−	3.08647i	1.15671	−	0.203960i	0.437809	−	0.899068i	$-0.355755\pi$
$229$	17.5043	−	3.08647i	1.15671	−	0.203960i	0.718905	+	0.695108i	$0.244643\pi$
$230$	−6.58065	−	2.39516i	−0.433915	−	0.157932i
$231$	−9.90801	−	17.4845i	−0.651899	−	1.15040i
$232$	−1.59739	+	9.05922i	−0.104874	+	0.594767i
$233$	−13.5165	−	7.80375i	−0.885495	−	0.511241i	−0.0130289	−	0.999915i	$-0.504147\pi$
$233$	−13.5165	−	7.80375i	−0.885495	−	0.511241i	−0.872466	+	0.488674i	$0.837481\pi$
$234$	8.10596	−	13.7151i	0.529903	−	0.896587i
$235$	−4.12547	−	7.14552i	−0.269116	−	0.466123i
$236$	−1.71728	+	9.73917i	−0.111785	+	0.633966i
$237$	−1.03055	−	2.87696i	−0.0669415	−	0.186878i
$238$	−17.5514	−	10.2024i	−1.13769	−	0.661324i
$239$	−1.75056	−	2.08623i	−0.113234	−	0.134947i	0.706450	−	0.707763i	$-0.250295\pi$
$239$	−1.75056	−	2.08623i	−0.113234	−	0.134947i	−0.819684	+	0.572816i	$0.805851\pi$
$240$	−4.65655	+	2.65691i	−0.300579	+	0.171503i
$241$	−2.45018	−	0.432034i	−0.157830	−	0.0278297i	0.0941747	−	0.995556i	$-0.469979\pi$
$241$	−2.45018	−	0.432034i	−0.157830	−	0.0278297i	−0.252005	+	0.967726i	$0.581090\pi$
$242$	−7.12930	−	4.11610i	−0.458288	−	0.264593i
$243$	−13.6942	+	7.44771i	−0.878485	+	0.477771i
$244$		−	5.30647i		−	0.339712i
$245$	−10.9440	+	18.7001i	−0.699184	+	1.19470i
$246$	18.2213	+	0.0928699i	1.16175	+	0.00592117i
$247$	4.30647	+	1.56743i	0.274014	+	0.0997329i
$248$	−1.58860	−	0.578204i	−0.100876	−	0.0367160i
$249$	−23.0103	−	4.17837i	−1.45822	−	0.264794i
$250$	1.27759	+	0.225274i	0.0808021	+	0.0142476i
$251$	−1.23242	+	2.13461i	−0.0777894	+	0.134735i	−0.902296	−	0.431117i	$-0.858119\pi$
$251$	−1.23242	+	2.13461i	−0.0777894	+	0.134735i	0.824507	+	0.565852i	$0.191453\pi$
$252$	6.01272	+	5.18142i	0.378766	+	0.326399i
$253$	4.96095	+	8.59261i	0.311892	+	0.540213i
$254$	−3.72841	−	10.2437i	−0.233941	−	0.642748i
$255$	−40.5484	+	6.93688i	−2.53924	+	0.434404i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	1.78168	+	10.1044i	0.111138	+	0.630295i	0.988590	+	0.150630i	$0.0481304\pi$
$257$	1.78168	+	10.1044i	0.111138	+	0.630295i	−0.877452	+	0.479664i	$0.840759\pi$
$258$	0.528858	+	3.09136i	0.0329253	+	0.192459i
$259$	−11.6863	−	4.29253i	−0.726154	−	0.266725i
$260$	−14.2353	+	8.21878i	−0.882838	+	0.509707i
$261$	17.9535	−	20.9586i	1.11130	−	1.29730i
$262$	7.38938	−	4.26626i	0.456517	−	0.263570i
$263$	−3.71126	−	10.1966i	−0.228846	−	0.628750i	0.771122	−	0.636687i	$-0.219696\pi$
$263$	−3.71126	−	10.1966i	−0.228846	−	0.628750i	−0.999968	+	0.00793724i	$0.997473\pi$
$264$	7.47361	+	1.35711i	0.459969	+	0.0835244i
$265$	−10.2388	+	1.80538i	−0.628964	+	0.110903i
$266$	−1.14744	+	1.97396i	−0.0703539	+	0.121031i
$267$	8.56171	+	5.00146i	0.523968	+	0.306084i
$268$	3.96204	+	3.32455i	0.242020	+	0.203079i
$269$	−3.06949	+	5.31652i	−0.187150	+	0.324154i	−0.944299	−	0.329089i	$-0.893258\pi$
$269$	−3.06949	+	5.31652i	−0.187150	+	0.324154i	0.757149	+	0.653243i	$0.226592\pi$
$270$	16.0818	+	0.245912i	0.978705	+	0.0149657i
$271$	−5.55275	+	3.20588i	−0.337306	+	0.194743i	−0.659080	−	0.752073i	$-0.729054\pi$
$271$	−5.55275	+	3.20588i	−0.337306	+	0.194743i	0.321774	+	0.946816i	$0.395721\pi$
$272$	7.21042	−	2.62438i	0.437196	−	0.159126i
$273$	18.5158	+	15.7921i	1.12063	+	0.955784i
$274$	4.63546	−	3.88961i	0.280038	−	0.234980i
$275$	12.9131	+	15.3892i	0.778690	+	0.928007i
$276$	−2.98901	−	2.53415i	−0.179917	−	0.152538i
$277$	−4.41032	+	1.60522i	−0.264990	+	0.0964486i	−0.471098	−	0.882081i	$-0.656142\pi$
$277$	−4.41032	+	1.60522i	−0.264990	+	0.0964486i	0.206108	+	0.978529i	$0.433920\pi$
$278$	2.15957			0.129523
$279$	3.22023	+	3.91815i	0.192790	+	0.234573i
$280$	−2.77825	−	7.70373i	−0.166032	−	0.460386i
$281$	−2.72752	−	0.480935i	−0.162710	−	0.0286902i	0.0916995	−	0.995787i	$-0.470770\pi$
$281$	−2.72752	−	0.480935i	−0.162710	−	0.0286902i	−0.254410	+	0.967097i	$0.581881\pi$
$282$	−0.778552	−	4.55090i	−0.0463621	−	0.271002i
$283$	−7.36546	−	8.77782i	−0.437831	−	0.521787i	0.501333	−	0.865254i	$-0.332843\pi$
$283$	−7.36546	−	8.77782i	−0.437831	−	0.521787i	−0.939165	+	0.343467i	$0.888399\pi$
$284$	−2.68604	−	3.20110i	−0.159387	−	0.189950i
$285$	0.780172	+	4.56037i	0.0462134	+	0.270133i
$286$	22.9351	+	4.04407i	1.35618	+	0.239131i
$287$	−4.91407	+	27.3967i	−0.290068	+	1.61717i
$288$	−2.95958	+	0.490802i	−0.174395	+	0.0289208i
$289$	41.8774			2.46338
$290$	−26.7564	+	9.73854i	−1.57119	+	0.571867i
$291$	21.6911	+	18.3902i	1.27155	+	1.07805i
$292$	0.934261	+	1.11341i	0.0546735	+	0.0651574i
$293$	6.32685	−	5.30886i	0.369619	−	0.310147i	−0.438992	−	0.898491i	$-0.644664\pi$
$293$	6.32685	−	5.30886i	0.369619	−	0.310147i	0.808611	+	0.588344i	$0.200220\pi$
$294$	−9.37289	+	7.69083i	−0.546638	+	0.448539i
$295$	−28.7646	+	10.4695i	−1.67474	+	0.609556i
$296$	4.07514	−	2.35278i	0.236863	−	0.136753i
$297$	−17.2302	−	14.9127i	−0.999799	−	0.865323i
$298$	−3.63713	+	6.29969i	−0.210693	+	0.364931i
$299$	−9.20383	−	7.72293i	−0.532271	−	0.446628i
$300$	−6.85101	−	4.00213i	−0.395543	−	0.231063i
$301$	−4.79071	−	0.0141192i	−0.276132	−	0.000813817i
$302$	5.78355	−	1.01980i	0.332806	−	0.0586827i
$303$	−20.7898	−	3.77516i	−1.19434	−	0.216877i
$304$	−0.295157	−	0.810936i	−0.0169284	−	0.0465104i
$305$	14.2246	−	8.21256i	0.814496	−	0.470250i
$306$	−22.6279	−	4.22816i	−1.29355	−	0.241708i
$307$	3.49655	−	2.01873i	0.199558	−	0.115215i	−0.396891	−	0.917866i	$-0.629911\pi$
$307$	3.49655	−	2.01873i	0.199558	−	0.115215i	0.596449	+	0.802651i	$0.296578\pi$
$308$	−4.00051	+	10.8913i	−0.227950	+	0.620592i
$309$	2.71124	+	15.8481i	0.154237	+	0.901566i
$310$	−0.908661	−	5.15327i	−0.0516085	−	0.292686i
$311$	18.3514	−	15.3986i	1.04061	−	0.873177i	0.0485366	−	0.998821i	$-0.484544\pi$
$311$	18.3514	−	15.3986i	1.04061	−	0.873177i	0.992075	+	0.125644i	$0.0400998\pi$
$312$	−9.06632	+	1.55103i	−0.513279	+	0.0878100i
$313$	−9.19190	−	25.2545i	−0.519557	−	1.42747i	−0.871010	−	0.491266i	$-0.836534\pi$
$313$	−9.19190	−	25.2545i	−0.519557	−	1.42747i	0.351453	−	0.936206i	$-0.385688\pi$
$314$	−6.43921	−	11.1530i	−0.363386	−	0.629402i
$315$	−4.58378	+	24.1368i	−0.258267	+	1.35995i
$316$	−0.882181	+	1.52798i	−0.0496265	+	0.0859557i
$317$	−17.6661	−	3.11502i	−0.992229	−	0.174957i	−0.346111	−	0.938194i	$-0.612498\pi$
$317$	−17.6661	−	3.11502i	−0.992229	−	0.174957i	−0.646119	+	0.763237i	$0.723609\pi$
$318$	−5.72415	−	1.03943i	−0.320994	−	0.0582883i
$319$	37.9088	+	13.7977i	2.12248	+	0.772521i
$320$	2.90863	+	1.05865i	0.162597	+	0.0591806i
$321$	6.66490	+	0.0339695i	0.371999	+	0.00189599i
$322$	4.59678	−	3.83413i	0.256169	−	0.213668i
$323$		−	6.62179i		−	0.368446i
$324$	8.39273	+	3.24995i	0.466263	+	0.180553i
$325$	−21.0675	−	12.1634i	−1.16862	−	0.674702i
$326$	−0.942374	−	0.166166i	−0.0521933	−	0.00920308i
$327$	−13.0276	+	7.43322i	−0.720428	+	0.411058i
$328$	−6.76227	−	8.05896i	−0.373384	−	0.444982i
$329$	7.05258	+	0.0207854i	0.388821	+	0.00114594i
$330$	7.92865	+	22.1342i	0.436458	+	1.21845i
$331$	−4.69437	+	26.6231i	−0.258026	+	1.46334i	0.530159	+	0.847898i	$0.322132\pi$
$331$	−4.69437	+	26.6231i	−0.258026	+	1.46334i	−0.788185	+	0.615439i	$0.788979\pi$
$332$	6.75113	+	11.6933i	0.370516	+	0.641753i
$333$	−14.1160	−	0.143895i	−0.773550	−	0.00788542i
$334$	−2.63391	−	1.52069i	−0.144121	−	0.0832085i
$335$	−2.77996	+	15.7659i	−0.151885	+	0.861384i
$336$	0.0368615	−	4.58243i	0.00201096	−	0.249992i
$337$	−15.6259	−	5.68738i	−0.851200	−	0.309811i	−0.120670	−	0.992693i	$-0.538504\pi$
$337$	−15.6259	−	5.68738i	−0.851200	−	0.309811i	−0.730529	+	0.682881i	$0.760727\pi$
$338$	−14.9703	+	2.63968i	−0.814279	+	0.143579i
$339$	15.4735	+	5.72136i	0.840404	+	0.310742i
$340$	18.1941	+	15.2667i	0.986715	+	0.827952i
$341$	−3.70692	+	6.42058i	−0.200741	+	0.347694i
$342$	−0.475530	+	2.54489i	−0.0257137	+	0.137612i
$343$	−9.11796	−	16.1203i	−0.492324	−	0.870412i
$344$	1.16391	−	1.38710i	0.0627539	−	0.0747872i
$345$	2.16712	−	11.9343i	0.116674	−	0.642524i
$346$	0.984698	−	2.70544i	0.0529377	−	0.145445i
$347$	14.8792	−	2.62360i	0.798757	−	0.140842i	0.240651	−	0.970612i	$-0.422639\pi$
$347$	14.8792	−	2.62360i	0.798757	−	0.140842i	0.558106	+	0.829769i	$0.311528\pi$
$348$	−15.9329	−	0.0812063i	−0.854092	−	0.00435311i
$349$	−8.29251	−	22.7835i	−0.443888	−	1.21957i	−0.936915	−	0.349558i	$-0.886332\pi$
$349$	−8.29251	−	22.7835i	−0.443888	−	1.21957i	0.493026	−	0.870014i	$-0.335891\pi$
$350$	7.81783	−	9.26136i	0.417881	−	0.495040i
$351$	25.7826	+	9.83310i	1.37618	+	0.524852i
$352$	−2.19273	−	3.79791i	−0.116873	−	0.202430i
$353$	−4.87031	+	27.6209i	−0.259220	+	1.47011i	0.525782	+	0.850619i	$0.323773\pi$
$353$	−4.87031	+	27.6209i	−0.259220	+	1.47011i	−0.785003	+	0.619493i	$0.787338\pi$
$354$	−17.1287	−	0.0873013i	−0.910382	−	0.00464001i
$355$	4.42384	−	12.1544i	0.234793	−	0.645089i
$356$	−0.994088	−	5.63775i	−0.0526865	−	0.298800i
$357$	12.2918	−	32.9445i	0.650551	−	1.74361i
$358$	−18.3462	−	15.3943i	−0.969625	−	0.813612i
$359$			19.6696i			1.03812i	0.854738	+	0.519060i	$0.173718\pi$
$359$			19.6696i			1.03812i	−0.854738	+	0.519060i	$0.826282\pi$
$360$	−5.89604	−	7.17388i	−0.310749	−	0.378097i
$361$	18.2553			0.960803
$362$	12.3913	−	4.51007i	0.651273	−	0.237044i
$363$	4.94495	−	13.3737i	0.259543	−	0.701935i
$364$	0.0414088	−	14.0502i	0.00217041	−	0.736429i
$365$	−1.53870	+	4.22756i	−0.0805395	+	0.221280i
$366$	9.05946	−	1.54986i	0.473545	−	0.0810125i
$367$	−2.33471	+	2.78240i	−0.121871	+	0.145240i	−0.823530	−	0.567273i	$-0.807998\pi$
$367$	−2.33471	+	2.78240i	−0.121871	+	0.145240i	0.701659	+	0.712513i	$0.252443\pi$
$368$			2.26246i			0.117939i
$369$	5.16335	+	31.1354i	0.268793	+	1.62085i
$370$	12.6138	+	7.28257i	0.655759	+	0.378603i
$371$	3.06405	−	8.34183i	0.159078	−	0.433086i
$372$	0.523154	−	2.88101i	0.0271243	−	0.149374i
$373$	−7.21812	+	6.05672i	−0.373740	+	0.313605i	−0.810239	−	0.586100i	$-0.800663\pi$
$373$	−7.21812	+	6.05672i	−0.373740	+	0.313605i	0.436499	+	0.899705i	$0.356218\pi$
$374$	−5.84331	−	33.1391i	−0.302151	−	1.71358i
$375$	−0.0114523	+	2.24696i	−0.000591392	+	0.116033i
$376$	−1.71344	+	2.04200i	−0.0883638	+	0.105308i
$377$	−48.8511			−2.51596
$378$	−7.08984	+	11.7785i	−0.364662	+	0.605823i
$379$	13.1571			0.675834			0.337917	−	0.941176i	$-0.390278\pi$
$379$	13.1571			0.675834			0.337917	+	0.941176i	$0.390278\pi$
$380$	1.71700	−	2.04624i	0.0880804	−	0.104970i
$381$	16.3996	−	9.35719i	0.840177	−	0.479383i
$382$	−3.34832	−	18.9893i	−0.171315	−	0.971576i
$383$	−11.1332	+	9.34184i	−0.568878	+	0.477346i	−0.881274	−	0.472607i	$-0.843313\pi$
$383$	−11.1332	+	9.34184i	−0.568878	+	0.477346i	0.312395	+	0.949952i	$0.398869\pi$
$384$	1.32114	+	1.12009i	0.0674190	+	0.0571593i
$385$	−35.3868	+	6.13217i	−1.80348	+	0.312524i
$386$	−16.2398	−	9.37608i	−0.826586	−	0.477230i
$387$	−5.12325	+	1.80578i	−0.260429	+	0.0917932i
$388$		−	16.4185i		−	0.833524i
$389$	−7.37134	+	8.78482i	−0.373742	+	0.445408i	−0.919829	−	0.392321i	$-0.871672\pi$
$389$	−7.37134	+	8.78482i	−0.373742	+	0.445408i	0.546087	+	0.837729i	$0.316117\pi$
$390$	−18.1892	−	21.9028i	−0.921046	−	1.10909i
$391$	−5.93753	+	16.3132i	−0.300274	+	0.824996i
$392$	6.88637	+	1.25615i	0.347814	+	0.0634451i
$393$	9.44178	+	11.3695i	0.476275	+	0.573513i
$394$	−11.2389	+	4.09063i	−0.566209	+	0.206083i
$395$	−5.46123			−0.274784
$396$	−0.134106	+	13.1557i	−0.00673910	+	0.661098i
$397$		−	3.95232i		−	0.198361i	−0.995069	−	0.0991807i	$-0.968378\pi$
$397$		−	3.95232i		−	0.198361i	0.995069	−	0.0991807i	$-0.0316222\pi$
$398$	18.9830	+	15.9287i	0.951534	+	0.798432i
$399$	−3.70518	−	1.38243i	−0.185491	−	0.0692079i
$400$	0.795461	+	4.51129i	0.0397731	+	0.225564i
$401$	−3.37460	+	9.27165i	−0.168520	+	0.463004i	−0.994990	−	0.0999765i	$-0.968123\pi$
$401$	−3.37460	+	9.27165i	−0.168520	+	0.463004i	0.826470	+	0.562981i	$0.190345\pi$
$402$	−4.51863	+	7.73519i	−0.225369	+	0.385796i
$403$	1.55896	−	8.84128i	0.0776571	−	0.440415i
$404$	6.09965	+	10.5649i	0.303469	+	0.525624i
$405$	4.27717	+	27.5274i	0.212534	+	1.36785i
$406$	4.29691	−	23.9559i	0.213252	−	1.18891i
$407$	−7.05794	−	19.3915i	−0.349849	−	0.961203i
$408$	6.58641	+	11.5435i	0.326076	+	0.571487i
$409$	18.0707	−	3.18635i	0.893537	−	0.157555i	0.292018	−	0.956413i	$-0.405673\pi$
$409$	18.0707	−	3.18635i	0.893537	−	0.157555i	0.601519	+	0.798858i	$0.294562\pi$
$410$	11.1373	−	30.5994i	0.550031	−	1.51120i
$411$	7.99441	+	6.77784i	0.394335	+	0.334326i
$412$	5.96689	−	7.11106i	0.293967	−	0.350337i
$413$	4.61941	−	25.7539i	0.227306	−	1.26727i
$414$	3.45342	−	5.84313i	0.169726	−	0.287174i
$415$	−20.8968	+	36.1943i	−1.02578	+	1.77671i
$416$	4.06807	+	3.41352i	0.199454	+	0.167361i
$417$	0.630747	+	3.68693i	0.0308878	+	0.180550i
$418$	−3.72706	+	0.657182i	−0.182297	+	0.0321438i
$419$	−31.0549	−	11.3030i	−1.51713	−	0.552190i	−0.556700	−	0.830714i	$-0.687933\pi$
$419$	−31.0549	−	11.3030i	−1.51713	−	0.552190i	−0.960429	+	0.278524i	$0.910155\pi$
$420$	12.3407	−	6.99318i	0.602166	−	0.341232i
$421$	2.75256	−	15.6106i	0.134152	−	0.760812i	−0.841295	−	0.540576i	$-0.818206\pi$
$421$	2.75256	−	15.6106i	0.134152	−	0.760812i	0.975447	−	0.220236i	$-0.0706827\pi$
$422$	−5.98328	−	3.45445i	−0.291262	−	0.168160i
$423$	7.54212	−	2.65836i	0.366711	−	0.129254i
$424$	1.67944	+	2.90888i	0.0815609	+	0.141268i
$425$	−6.10371	+	34.6158i	−0.296073	+	1.67911i
$426$	4.68056	−	5.52068i	0.226774	−	0.267478i
$427$	−0.0413774	+	14.0395i	−0.00200239	+	0.679421i
$428$	−2.47347	−	2.94777i	−0.119560	−	0.142486i
$429$	−0.205589	+	40.3370i	−0.00992591	+	1.94749i
$430$	5.51959	+	0.973252i	0.266178	+	0.0469344i
$431$	7.55638	+	4.36268i	0.363978	+	0.210143i	0.670824	−	0.741616i	$-0.265940\pi$
$431$	7.55638	+	4.36268i	0.363978	+	0.210143i	−0.306846	+	0.951759i	$0.599274\pi$
$432$	−1.70233	−	4.90939i	−0.0819032	−	0.236203i
$433$			18.5686i			0.892348i	0.894946	+	0.446174i	$0.147214\pi$
$433$			18.5686i			0.892348i	−0.894946	+	0.446174i	$0.852786\pi$
$434$	4.19852	+	1.54216i	0.201535	+	0.0740262i
$435$	−24.4409	−	42.8355i	−1.17185	−	2.05381i
$436$	8.13745	+	2.96179i	0.389713	+	0.141844i
$437$	1.83471	+	0.667779i	0.0877659	+	0.0319442i
$438$	−1.62800	+	1.92021i	−0.0777887	+	0.0917512i
$439$	−29.1741	−	5.14418i	−1.39240	−	0.245518i	−0.573385	−	0.819286i	$-0.694370\pi$
$439$	−29.1741	−	5.14418i	−1.39240	−	0.245518i	−0.819018	+	0.573768i	$0.805481\pi$
$440$	6.78715	−	11.7557i	0.323564	−	0.560430i
$441$	−15.8677	−	13.7556i	−0.755605	−	0.655028i
$442$	20.3741	+	35.2890i	0.969098	+	1.67853i
$443$	1.81365	+	4.98297i	0.0861693	+	0.236748i	0.975292	−	0.220921i	$-0.0709064\pi$
$443$	1.81365	+	4.98297i	0.0861693	+	0.236748i	−0.889122	+	0.457670i	$0.848684\pi$
$444$	5.20701	+	6.27010i	0.247114	+	0.297566i
$445$	13.5741	−	11.3900i	0.643474	−	0.539939i
$446$	0.149901	+	0.850131i	0.00709802	+	0.0402549i
$447$	−11.8174	−	4.36953i	−0.558945	−	0.206672i
$448$	−2.03177	+	1.69468i	−0.0959919	+	0.0800659i
$449$	11.4827	−	6.62952i	0.541900	−	0.312866i	−0.203949	−	0.978982i	$-0.565378\pi$
$449$	11.4827	−	6.62952i	0.541900	−	0.312866i	0.745849	+	0.666115i	$0.232044\pi$
$450$	4.83165	−	12.8653i	0.227766	−	0.606475i
$451$	−39.9549	+	23.0680i	−1.88140	+	1.08623i
$452$	−3.25766	−	8.95034i	−0.153227	−	0.420988i
$453$	3.43025	+	9.57610i	0.161167	+	0.449925i
$454$	24.7856	−	4.37038i	1.16325	−	0.205112i
$455$	37.7271	−	21.6337i	1.76867	−	1.01421i
$456$	1.29826	−	0.740756i	0.0607967	−	0.0346891i
$457$	−29.8354	−	25.0349i	−1.39564	−	1.17108i	−0.962995	−	0.269519i	$-0.913135\pi$
$457$	−29.8354	−	25.0349i	−1.39564	−	1.17108i	−0.432647	−	0.901564i	$-0.642420\pi$
$458$	8.88715	−	15.3930i	0.415269	−	0.719267i
$459$	0.609610	−	39.8663i	0.0284542	−	1.86080i
$460$	−6.06476	+	3.50149i	−0.282771	+	0.163258i
$461$	−1.97136	+	0.717518i	−0.0918155	+	0.0334181i	−0.387520	−	0.921861i	$-0.626668\pi$
$461$	−1.97136	+	0.717518i	−0.0918155	+	0.0334181i	0.295704	+	0.955280i	$0.404446\pi$
$462$	−19.7626	−	3.64884i	−0.919442	−	0.169759i
$463$	−8.64421	+	7.25335i	−0.401730	+	0.337092i	−0.821162	−	0.570695i	$-0.806674\pi$
$463$	−8.64421	+	7.25335i	−0.401730	+	0.337092i	0.419432	+	0.907787i	$0.362229\pi$
$464$	5.91299	+	7.04683i	0.274504	+	0.327141i
$465$	8.53252	−	3.05643i	0.395686	−	0.141738i
$466$	−14.6663	+	5.33808i	−0.679401	+	0.247282i
$467$	−18.0315			−0.834397			−0.417199	−	0.908815i	$-0.636988\pi$
$467$	−18.0315			−0.834397			−0.417199	+	0.908815i	$0.636988\pi$
$468$	−5.29600	−	15.0254i	−0.244808	−	0.694551i
$469$	−10.4566	−	8.82678i	−0.482841	−	0.407583i
$470$	−8.12559	−	1.43276i	−0.374806	−	0.0660883i
$471$	17.1603	−	14.2508i	0.790705	−	0.656642i
$472$	6.35679	+	7.57573i	0.292595	+	0.348701i
$473$	−5.10428	−	6.08304i	−0.234695	−	0.279699i
$474$	−2.86630	−	1.05982i	−0.131654	−	0.0486793i
$475$	3.89315	+	0.686467i	0.178630	+	0.0314973i
$476$	−19.0973	+	6.88719i	−0.875325	+	0.315674i
$477$	0.102714	−	10.0761i	0.00470295	−	0.461354i
$478$	−2.72338			−0.124565
$479$	12.7738	−	4.64930i	0.583652	−	0.212432i	−0.0332832	−	0.999446i	$-0.510596\pi$
$479$	12.7738	−	4.64930i	0.583652	−	0.212432i	0.616935	+	0.787014i	$0.288374\pi$
$480$	−0.957863	+	5.27495i	−0.0437203	+	0.240768i
$481$	16.0625	+	19.1426i	0.732388	+	0.872826i
$482$	−1.90590	+	1.59924i	−0.0868116	+	0.0728436i
$483$	7.88839	+	6.72801i	0.358934	+	0.306135i
$484$	−7.73574	+	2.81558i	−0.351625	+	0.127981i
$485$	44.0116	−	25.4101i	1.99846	−	1.15381i
$486$	−3.09720	+	15.2777i	−0.140492	+	0.693009i
$487$	−1.66800	+	2.88906i	−0.0755843	+	0.130916i	−0.901340	−	0.433112i	$-0.857416\pi$
$487$	−1.66800	+	2.88906i	−0.0755843	+	0.130916i	0.825756	+	0.564028i	$0.190749\pi$
$488$	−4.06499	−	3.41093i	−0.184013	−	0.154406i
$489$	0.00844738	−	1.65740i	0.000382004	−	0.0749501i
$490$	7.29044	+	20.4037i	0.329349	+	0.921747i
$491$	−39.9658	+	7.04705i	−1.80363	+	0.318029i	−0.971587	−	0.236681i	$-0.923940\pi$
$491$	−39.9658	+	7.04705i	−1.80363	+	0.318029i	−0.832044	+	0.554710i	$0.812829\pi$
$492$	11.7836	−	13.8987i	0.531245	−	0.626600i
$493$	24.1416	+	66.3284i	1.08728	+	2.98728i
$494$	3.96886	−	2.29142i	0.178568	−	0.103096i
$495$	−35.4728	+	20.0009i	−1.59438	+	0.898973i
$496$	−1.46406	+	0.845277i	−0.0657384	+	0.0379541i
$497$	7.08161	+	8.49022i	0.317653	+	0.380838i
$498$	−17.9916	+	14.9411i	−0.806221	+	0.669527i
$499$	2.95055	+	16.7334i	0.132085	+	0.749090i	0.976845	+	0.213946i	$0.0686317\pi$
$499$	2.95055	+	16.7334i	0.132085	+	0.749090i	−0.844761	+	0.535144i	$0.820257\pi$
$500$	0.993791	−	0.833890i	0.0444437	−	0.0372927i
$501$	1.82691	−	4.94089i	0.0816202	−	0.220743i
$502$	0.843022	+	2.31618i	0.0376259	+	0.103376i
$503$	16.5235	+	28.6196i	0.736747	+	1.27608i	0.953953	+	0.299958i	$0.0969725\pi$
$503$	16.5235	+	28.6196i	0.736747	+	1.27608i	−0.217205	+	0.976126i	$0.569694\pi$
$504$	7.83411	−	1.27546i	0.348959	−	0.0568134i
$505$	−18.8802	+	32.7015i	−0.840160	+	1.45520i
$506$	9.77116	+	1.72292i	0.434381	+	0.0765931i
$507$	−8.87897	−	24.7871i	−0.394329	−	1.10083i
$508$	−10.2437	−	3.72841i	−0.454491	−	0.165421i
$509$	10.3038	+	3.75026i	0.456706	+	0.166228i	0.560121	−	0.828411i	$-0.310755\pi$
$509$	10.3038	+	3.75026i	0.456706	+	0.166228i	−0.103415	+	0.994638i	$0.532977\pi$
$510$	−20.7501	+	35.5208i	−0.918828	+	1.57289i
$511$	−2.46313	−	2.95308i	−0.108962	−	0.130636i
$512$		−	1.00000i		−	0.0441942i
$513$	−4.48365	−	0.0685612i	−0.197958	−	0.00302705i
$514$	8.88565	+	5.13013i	0.391929	+	0.226280i
$515$	28.2966	+	4.98946i	1.24690	+	0.219862i
$516$	2.70806	+	1.58196i	0.119216	+	0.0696417i
$517$	7.51420	+	8.95508i	0.330474	+	0.393844i
$518$	−10.8001	+	6.19308i	−0.474529	+	0.272108i
$519$	4.90645	+	0.890947i	0.215369	+	0.0391082i
$520$	−2.85435	+	16.1878i	−0.125172	+	0.709883i
$521$	3.87870	+	6.71810i	0.169929	+	0.294325i	0.938395	−	0.345566i	$-0.112313\pi$
$521$	3.87870	+	6.71810i	0.169929	+	0.294325i	−0.768466	+	0.639891i	$0.778980\pi$
$522$	−4.51488	−	27.2251i	−0.197611	−	1.19161i
$523$	−0.516592	−	0.298254i	−0.0225890	−	0.0130418i	0.488663	−	0.872473i	$-0.337485\pi$
$523$	−0.516592	−	0.298254i	−0.0225890	−	0.0130418i	−0.511252	+	0.859431i	$0.670818\pi$
$524$	1.48166	−	8.40289i	0.0647264	−	0.367082i
$525$	18.0948	+	10.6420i	0.789721	+	0.464455i
$526$	−10.1966	−	3.71126i	−0.444593	−	0.161819i
$527$	−12.7748	+	2.25255i	−0.556480	+	0.0981225i
$528$	5.84355	−	4.85278i	0.254308	−	0.211190i
$529$	13.6979	+	11.4939i	0.595559	+	0.499734i
$530$	−5.19837	+	9.00385i	−0.225803	+	0.391102i
$531$	−4.85374	−	29.2685i	−0.210635	−	1.27014i
$532$	0.774584	+	2.14783i	0.0335825	+	0.0931201i
$533$	35.9110	−	42.7970i	1.55548	−	1.85374i
$534$	9.33470	−	3.34377i	0.403952	−	0.144699i
$535$	4.07374	−	11.1925i	0.176123	−	0.483894i
$536$	5.09350	−	0.898122i	0.220006	−	0.0387930i
$537$	20.9235	−	35.8176i	0.902914	−	1.54565i
$538$	2.09966	+	5.76876i	0.0905226	+	0.248709i
$539$	10.6692	−	28.7845i	0.459557	−	1.23983i
$540$	10.5255	−	12.1613i	0.452947	−	0.523338i
$541$	6.42565	+	11.1295i	0.276260	+	0.478497i	0.970452	−	0.241293i	$-0.0775716\pi$
$541$	6.42565	+	11.1295i	0.276260	+	0.478497i	−0.694192	+	0.719790i	$0.744238\pi$
$542$	−1.11339	+	6.31435i	−0.0478242	+	0.271225i
$543$	11.3189	+	19.8378i	0.485742	+	0.851321i
$544$	2.62438	−	7.21042i	0.112519	−	0.309144i
$545$	4.65453	+	26.3971i	0.199378	+	1.13073i
$546$	23.9992	−	4.03294i	1.02707	−	0.172594i
$547$	12.6086	+	10.5799i	0.539104	+	0.452362i	0.871231	−	0.490873i	$-0.163322\pi$
$547$	12.6086	+	10.5799i	0.539104	+	0.452362i	−0.332127	+	0.943235i	$0.607766\pi$
$548$		−	6.05117i		−	0.258493i
$549$	5.29199	+	15.0141i	0.225857	+	0.640785i
$550$	20.0892			0.856608
$551$	7.45978	−	2.71514i	0.317797	−	0.115669i
$552$	−3.86257	+	0.660795i	−0.164402	+	0.0281253i
$553$	2.34594	−	4.03576i	0.0997593	−	0.171618i
$554$	−1.60522	+	4.41032i	−0.0681994	+	0.187376i
$555$	−8.74905	+	23.6619i	−0.371376	+	1.00439i
$556$	1.38815	−	1.65433i	0.0588706	−	0.0701592i
$557$		−	25.2883i		−	1.07150i	−0.844377	−	0.535749i	$-0.820029\pi$
$557$		−	25.2883i		−	1.07150i	0.844377	−	0.535749i	$-0.179971\pi$
$558$	5.07140	+	0.0516969i	0.214689	+	0.00218850i
$559$	8.32755	+	4.80792i	0.352218	+	0.203353i
$560$	−7.68722	−	2.82361i	−0.324844	−	0.119319i
$561$	54.8700	−	19.6549i	2.31661	−	0.829831i
$562$	−2.12163	+	1.78026i	−0.0894957	+	0.0750958i
$563$	−0.517886	−	2.93708i	−0.0218263	−	0.123783i	0.971948	−	0.235196i	$-0.0755733\pi$
$563$	−0.517886	−	2.93708i	−0.0218263	−	0.123783i	−0.993774	+	0.111413i	$0.964462\pi$
$564$	−3.98664	−	2.32886i	−0.167868	−	0.0980626i
$565$	18.9506	−	22.5845i	0.797259	−	0.950137i
$566$	−11.4586			−0.481642
$567$	−22.1796	−	8.66396i	−0.931457	−	0.363852i
$568$	−4.17874			−0.175336
$569$	−7.01355	+	8.35843i	−0.294023	+	0.350403i	−0.892752	−	0.450549i	$-0.851228\pi$
$569$	−7.01355	+	8.35843i	−0.294023	+	0.350403i	0.598729	+	0.800952i	$0.295673\pi$
$570$	3.99493	+	2.33370i	0.167329	+	0.0977481i
$571$	−4.44977	−	25.2359i	−0.186217	−	1.05609i	−0.924382	−	0.381468i	$-0.875419\pi$
$571$	−4.44977	−	25.2359i	−0.186217	−	1.05609i	0.738165	−	0.674620i	$-0.235693\pi$
$572$	17.8403	−	14.9698i	0.745942	−	0.625919i
$573$	31.4415	−	11.2626i	1.31349	−	0.470502i
$574$	17.8284	+	21.3746i	0.744142	+	0.892160i
$575$	−8.97552	−	5.18202i	−0.374305	−	0.216105i
$576$	−1.52640	+	2.58265i	−0.0636002	+	0.107610i
$577$		−	46.6286i		−	1.94117i	−0.240752	−	0.970587i	$-0.577394\pi$
$577$		−	46.6286i		−	1.94117i	0.240752	−	0.970587i	$-0.422606\pi$
$578$	26.9183	−	32.0800i	1.11965	−	1.33435i
$579$	11.2641	−	30.4639i	0.468121	−	1.26604i
$580$	−9.73854	+	26.7564i	−0.404371	+	1.11100i
$581$	−17.7706	−	30.9901i	−0.737247	−	1.28568i
$582$	28.0305	−	4.79535i	1.16190	−	0.198774i
$583$	13.8419	−	5.03803i	0.573272	−	0.208654i
$584$	1.45345			0.0601443
$585$	32.0810	−	37.4506i	1.32639	−	1.54839i
$586$		−	8.25912i		−	0.341181i
$587$	−0.140699	−	0.118060i	−0.00580726	−	0.00487287i	0.639879	−	0.768475i	$-0.278984\pi$
$587$	−0.140699	−	0.118060i	−0.00580726	−	0.00487287i	−0.645687	+	0.763603i	$0.723429\pi$
$588$	−0.133258	+	12.1236i	−0.00549545	+	0.499970i
$589$	0.253338	+	1.43675i	0.0104386	+	0.0592003i
$590$	−10.4695	+	28.7646i	−0.431021	+	1.18422i
$591$	−10.2663	−	17.9929i	−0.422298	−	0.740128i
$592$	0.817113	−	4.63408i	0.0335831	−	0.190459i
$593$	10.8668	+	18.8219i	0.446248	+	0.772924i	0.998138	−	0.0609927i	$-0.0194266\pi$
$593$	10.8668	+	18.8219i	0.446248	+	0.772924i	−0.551890	+	0.833917i	$0.686093\pi$
$594$	−22.4992	+	3.61342i	−0.923152	+	0.148261i
$595$	−48.0179	−	40.5335i	−1.96854	−	1.66171i
$596$	2.48794	+	6.83557i	0.101910	+	0.279996i
$597$	−21.6498	+	37.0610i	−0.886067	+	1.51681i
$598$	−11.8322	+	2.08634i	−0.483855	+	0.0853167i
$599$	−3.64720	+	10.0206i	−0.149021	+	0.409431i	−0.991633	−	0.129090i	$-0.958794\pi$
$599$	−3.64720	+	10.0206i	−0.149021	+	0.409431i	0.842612	+	0.538521i	$0.181017\pi$
$600$	−7.46955	+	2.67566i	−0.304943	+	0.109233i
$601$	−8.15978	+	9.72445i	−0.332844	+	0.396668i	−0.906346	−	0.422536i	$-0.861140\pi$
$601$	−8.15978	+	9.72445i	−0.332844	+	0.396668i	0.573502	+	0.819204i	$0.305585\pi$
$602$	−3.09022	+	3.66082i	−0.125948	+	0.149204i
$603$	−14.5256	−	5.45521i	−0.591530	−	0.222153i
$604$	2.93639	−	5.08597i	0.119480	−	0.206945i
$605$	−19.5197	−	16.3790i	−0.793588	−	0.665899i
$606$	−16.2554	+	13.4993i	−0.660330	+	0.548372i
$607$	−39.9909	+	7.05147i	−1.62318	+	0.286210i	−0.909949	−	0.414720i	$-0.863880\pi$
$607$	−39.9909	+	7.05147i	−1.62318	+	0.286210i	−0.713230	+	0.700930i	$0.752768\pi$
$608$	−0.810936	−	0.295157i	−0.0328878	−	0.0119702i
$609$	42.1536	+	0.339088i	1.70815	+	0.0137405i
$610$	2.85219	−	16.1756i	0.115482	−	0.654930i
$611$	−12.2593	−	7.07791i	−0.495958	−	0.286342i
$612$	−17.7839	+	14.6161i	−0.718870	+	0.590822i
$613$	−16.1606	−	27.9909i	−0.652720	−	1.13054i	−0.982460	−	0.186472i	$-0.940295\pi$
$613$	−16.1606	−	27.9909i	−0.652720	−	1.13054i	0.329741	−	0.944072i	$-0.393039\pi$
$614$	0.701098	−	3.97612i	0.0282940	−	0.160463i
$615$	55.4937	+	10.0769i	2.23772	+	0.406341i
$616$	5.77177	+	10.0654i	0.232551	+	0.405546i
$617$	17.5784	+	20.9491i	0.707680	+	0.843380i	0.993372	−	0.114942i	$-0.0366681\pi$
$617$	17.5784	+	20.9491i	0.707680	+	0.843380i	−0.285693	+	0.958321i	$0.592224\pi$
$618$	13.8831	+	8.11003i	0.558460	+	0.326233i
$619$	−32.7782	−	5.77969i	−1.31747	−	0.232305i	−0.529652	−	0.848215i	$-0.677678\pi$
$619$	−32.7782	−	5.77969i	−1.31747	−	0.232305i	−0.787817	+	0.615910i	$0.788789\pi$
$620$	−4.53171	−	2.61639i	−0.181998	−	0.105077i
$621$	10.9843	+	4.18925i	0.440785	+	0.168109i
$622$		−	23.9560i		−	0.960550i
$623$	2.58614	+	14.9238i	0.103611	+	0.597908i
$624$	−4.63956	+	7.94219i	−0.185731	+	0.317942i
$625$	25.2965	+	9.20716i	1.01186	+	0.368286i
$626$	−25.2545	−	9.19190i	−1.00937	−	0.367382i
$627$	−2.21054	−	6.17108i	−0.0882803	−	0.246449i
$628$	−12.6828	−	2.23631i	−0.506097	−	0.0892386i
$629$	18.0533	−	31.2692i	0.719832	−	1.24679i
$630$	15.5435	+	19.0262i	0.619266	+	0.758022i
$631$	−4.62072	−	8.00333i	−0.183948	−	0.318607i	0.759273	−	0.650772i	$-0.225554\pi$
$631$	−4.62072	−	8.00333i	−0.183948	−	0.318607i	−0.943222	+	0.332164i	$0.892221\pi$
$632$	0.603447	+	1.65796i	0.0240038	+	0.0659500i
$633$	4.15006	−	11.2239i	0.164950	−	0.446109i
$634$	−13.7418	+	11.5308i	−0.545757	+	0.457945i
$635$	−5.85928	−	33.2296i	−0.232519	−	1.31868i
$636$	−4.47566	+	3.71682i	−0.177471	+	0.147381i
$637$	−0.219114	+	37.1728i	−0.00868160	+	1.47284i
$638$	34.9369	−	20.1708i	1.38317	−	0.798571i
$639$	10.7922	+	6.37845i	0.426934	+	0.252327i
$640$	2.68061	−	1.54765i	0.105960	−	0.0611762i
$641$	11.0009	+	30.2248i	0.434511	+	1.19381i	0.943015	+	0.332749i	$0.107976\pi$
$641$	11.0009	+	30.2248i	0.434511	+	1.19381i	−0.508505	+	0.861059i	$0.669802\pi$
$642$	4.31014	−	5.08378i	0.170108	−	0.200641i
$643$	−4.85357	+	0.855815i	−0.191406	+	0.0337501i	−0.268529	−	0.963272i	$-0.586538\pi$
$643$	−4.85357	+	0.855815i	−0.191406	+	0.0337501i	0.0771232	+	0.997022i	$0.475427\pi$
$644$	0.0176416	−	5.98587i	0.000695176	−	0.235876i
$645$	−0.0494772	+	9.70756i	−0.00194816	+	0.382235i
$646$	−5.07258	−	4.25640i	−0.199578	−	0.167466i
$647$	12.3052	−	21.3132i	0.483768	−	0.837910i	−0.516059	−	0.856553i	$-0.672601\pi$
$647$	12.3052	−	21.3132i	0.483768	−	0.837910i	0.999826	+	0.0186432i	$0.00593467\pi$
$648$	7.88434	−	4.34018i	0.309726	−	0.170498i
$649$	37.5591	−	21.6848i	1.47432	−	0.851202i
$650$	−22.8596	+	8.32022i	−0.896628	+	0.326346i
$651$	−1.40659	+	7.61833i	−0.0551288	+	0.298586i
$652$	−0.733037	+	0.615091i	−0.0287079	+	0.0240888i
$653$	−15.1826	−	18.0939i	−0.594141	−	0.708070i	0.382255	−	0.924057i	$-0.375148\pi$
$653$	−15.1826	−	18.0939i	−0.594141	−	0.708070i	−0.976396	+	0.215987i	$0.930703\pi$
$654$	−2.67981	+	14.7577i	−0.104789	+	0.577072i
$655$	24.8179	−	9.03299i	0.969717	−	0.352948i
$656$	−10.5202			−0.410746
$657$	−3.75376	−	2.21856i	−0.146448	−	0.0865542i
$658$	4.54923	−	5.38923i	0.177348	−	0.210094i
$659$	−8.20553	−	1.44686i	−0.319642	−	0.0563615i	0.0115253	−	0.999934i	$-0.496331\pi$
$659$	−8.20553	−	1.44686i	−0.319642	−	0.0563615i	−0.331167	+	0.943572i	$0.607442\pi$
$660$	22.0522	+	8.15386i	0.858380	+	0.317389i
$661$	9.93870	+	11.8445i	0.386571	+	0.460697i	0.923877	−	0.382690i	$-0.125002\pi$
$661$	9.93870	+	11.8445i	0.386571	+	0.460697i	−0.537306	+	0.843387i	$0.680558\pi$
$662$	17.3770	+	20.7091i	0.675376	+	0.804881i
$663$	−54.2964	+	45.0905i	−2.10870	+	1.75117i
$664$	13.2971	+	2.34464i	0.516029	+	0.0909898i
$665$	−4.55870	+	5.40044i	−0.176779	+	0.209420i
$666$	−9.18380	+	10.7210i	−0.355865	+	0.415429i
$667$	−20.8123			−0.805854
$668$	−2.85796	+	1.04021i	−0.110578	+	0.0402471i
$669$	−1.40760	+	0.504216i	−0.0544211	+	0.0194941i
$670$	10.2905	+	12.2637i	0.397556	+	0.473788i
$671$	−17.8268	+	14.9585i	−0.688197	+	0.577466i
$672$	−3.48665	−	2.97377i	−0.134500	−	0.114715i
$673$	16.7858	−	6.10955i	0.647047	−	0.235506i	0.00241265	−	0.999997i	$-0.499232\pi$
$673$	16.7858	−	6.10955i	0.647047	−	0.235506i	0.644634	+	0.764491i	$0.277010\pi$
$674$	−14.4009	+	8.31439i	−0.554704	+	0.320258i
$675$	23.3754	+	4.49126i	0.899719	+	0.172869i
$676$	−7.60064	+	13.1647i	−0.292332	+	0.506335i
$677$	−17.1841	−	14.4192i	−0.660438	−	0.554173i	0.249780	−	0.968303i	$-0.419642\pi$
$677$	−17.1841	−	14.4192i	−0.660438	−	0.554173i	−0.910218	+	0.414129i	$0.864086\pi$
$678$	14.3290	−	8.17575i	0.550301	−	0.313988i
$679$	−0.128024	+	43.4391i	−0.00491311	+	1.66704i
$680$	23.3899	−	4.12427i	0.896962	−	0.158159i
$681$	14.7005	+	41.0388i	0.563323	+	1.57261i
$682$	2.53569	+	6.96674i	0.0970964	+	0.266770i
$683$	19.1890	−	11.0788i	0.734247	−	0.423918i	−0.0857266	−	0.996319i	$-0.527321\pi$
$683$	19.1890	−	11.0788i	0.734247	−	0.423918i	0.819974	+	0.572401i	$0.193988\pi$
$684$	1.64384	+	2.00010i	0.0628537	+	0.0764759i
$685$	16.2208	−	9.36509i	0.619765	−	0.357822i
$686$	−18.2097	−	3.37714i	−0.695251	−	0.128940i
$687$	28.8753	+	10.6767i	1.10166	+	0.407343i
$688$	−0.314429	−	1.78322i	−0.0119875	−	0.0679845i
$689$	−13.6642	+	11.4656i	−0.520563	+	0.436804i
$690$	−7.74924	−	9.33136i	−0.295009	−	0.355239i
$691$	10.4810	+	28.7963i	0.398715	+	1.09546i	0.962911	+	0.269820i	$0.0869642\pi$
$691$	10.4810	+	28.7963i	0.398715	+	1.09546i	−0.564196	+	0.825641i	$0.690814\pi$
$692$	−1.43953	−	2.49334i	−0.0547228	−	0.0947827i
$693$	0.457393	−	34.8055i	0.0173749	−	1.32215i
$694$	7.55437	−	13.0845i	0.286760	−	0.496683i
$695$	6.58298	+	1.16076i	0.249707	+	0.0440300i
$696$	−10.3037	+	12.1531i	−0.390560	+	0.460662i
$697$	−75.8552	−	27.6090i	−2.87322	−	1.04577i
$698$	−22.7835	−	8.29251i	−0.862368	−	0.313876i
$699$	−13.3970	−	23.4798i	−0.506721	−	0.888089i
$700$	−2.06941	−	11.9419i	−0.0782162	−	0.451361i
$701$			26.5390i			1.00236i	0.865342	+	0.501182i	$0.167101\pi$
$701$			26.5390i			1.00236i	−0.865342	+	0.501182i	$0.832899\pi$
$702$	24.1054	−	13.4301i	0.909798	−	0.506885i
$703$	−3.51677	−	2.03041i	−0.132637	−	0.0765782i
$704$	−4.31883	−	0.761526i	−0.162772	−	0.0287011i
$705$	0.0728373	−	14.2909i	0.00274321	−	0.538225i
$706$	18.0283	+	21.4852i	0.678502	+	0.808608i
$707$	−16.0557	−	27.9995i	−0.603837	−	1.05303i
$708$	−11.0770	+	13.0653i	−0.416300	+	0.491022i
$709$	0.740863	−	4.20164i	0.0278237	−	0.157796i	−0.967730	−	0.251988i	$-0.918916\pi$
$709$	0.740863	−	4.20164i	0.0278237	−	0.157796i	0.995554	+	0.0941920i	$0.0300267\pi$
$710$	−6.46722	−	11.2016i	−0.242711	−	0.420387i
$711$	0.972221	−	5.20303i	0.0364611	−	0.195129i
$712$	−4.95776	−	2.86236i	−0.185800	−	0.107272i
$713$	0.664170	−	3.76670i	0.0248734	−	0.141064i
$714$	−17.3359	−	30.5924i	−0.648780	−	1.14489i
$715$	67.7388	+	24.6549i	2.53329	+	0.922041i
$716$	−23.5854	+	4.15874i	−0.881427	+	0.155419i
$717$	−0.795418	−	4.64949i	−0.0297054	−	0.173638i
$718$	15.0678	+	12.6434i	0.562324	+	0.471846i
$719$	−19.8711	+	34.4178i	−0.741069	+	1.28357i	0.210941	+	0.977499i	$0.432347\pi$
$719$	−19.8711	+	34.4178i	−0.741069	+	1.28357i	−0.952009	+	0.306070i	$0.900986\pi$
$720$	−9.28542	−	0.0946537i	−0.346047	−	0.00352754i
$721$	−15.8423	+	18.7675i	−0.589997	+	0.698938i
$722$	11.7343	−	13.9843i	0.436704	−	0.520443i
$723$	−3.28696	−	2.78676i	−0.122243	−	0.103641i
$724$	4.51007	−	12.3913i	0.167615	−	0.460519i
$725$	−41.4992	+	7.31743i	−1.54124	+	0.271763i
$726$	−7.06627	−	12.3845i	−0.262254	−	0.459631i
$727$	−9.27181	−	25.4741i	−0.343872	−	0.944781i	−0.984260	−	0.176729i	$-0.943448\pi$
$727$	−9.27181	−	25.4741i	−0.343872	−	0.944781i	0.640387	−	0.768052i	$-0.278774\pi$
$728$	−10.7364	−	9.06300i	−0.397919	−	0.335897i
$729$	−26.9874	−	0.825541i	−0.999532	−	0.0305756i
$730$	2.24944	+	3.89614i	0.0832554	+	0.144203i
$731$	2.41267	−	13.6829i	0.0892356	−	0.506080i
$732$	4.63605	−	7.93618i	0.171353	−	0.293330i
$733$	3.28420	−	9.02328i	0.121305	−	0.333282i	−0.864146	−	0.503240i	$-0.832141\pi$
$733$	3.28420	−	9.02328i	0.121305	−	0.333282i	0.985451	+	0.169958i	$0.0543632\pi$
$734$	0.630718	+	3.57698i	0.0232802	+	0.132029i
$735$	−32.7049	+	18.4059i	−1.20634	+	0.678912i
$736$	1.73314	+	1.45428i	0.0638844	+	0.0536054i
$737$		−	22.6819i		−	0.835499i
$738$	27.1701	+	16.0581i	1.00014	+	0.591108i
$739$	−40.0907			−1.47476			−0.737380	−	0.675479i	$-0.763937\pi$
$739$	−40.0907			−1.47476			−0.737380	+	0.675479i	$0.763937\pi$
$740$	13.6868	−	4.98157i	0.503135	−	0.183126i
$741$	5.07121	+	6.10657i	0.186296	+	0.224331i
$742$	−4.42068	−	7.70923i	−0.162288	−	0.283015i
$743$	−4.79571	+	13.1761i	−0.175938	+	0.483385i	−0.996048	−	0.0888213i	$-0.971690\pi$
$743$	−4.79571	+	13.1761i	−0.175938	+	0.483385i	0.820110	+	0.572206i	$0.193912\pi$
$744$	−1.87071	−	2.25264i	−0.0685834	−	0.0825857i
$745$	−14.4730	+	17.2483i	−0.530250	+	0.631928i
$746$			9.42258i			0.344985i
$747$	−30.7630	−	26.3522i	−1.12556	−	0.964177i
$748$	−29.1420	−	16.8252i	−1.06554	−	0.615188i
$749$	6.52117	+	7.81831i	0.238278	+	0.285675i
$750$	1.71391	+	1.45309i	0.0625833	+	0.0530595i
$751$	17.1248	−	14.3694i	0.624894	−	0.524349i	−0.274443	−	0.961603i	$-0.588494\pi$
$751$	17.1248	−	14.3694i	0.624894	−	0.524349i	0.899338	+	0.437255i	$0.144049\pi$
$752$	0.462883	+	2.62514i	0.0168796	+	0.0957290i
$753$	−3.70808	+	2.11573i	−0.135130	+	0.0771016i
$754$	−31.4009	+	37.4221i	−1.14355	+	1.36283i
$755$	18.1780			0.661565
$756$	4.46563	+	13.0022i	0.162413	+	0.472887i
$757$	6.77594			0.246276			0.123138	−	0.992390i	$-0.460704\pi$
$757$	6.77594			0.246276			0.123138	+	0.992390i	$0.460704\pi$
$758$	8.45721	−	10.0789i	0.307180	−	0.366083i
$759$	−0.0875880	+	17.1850i	−0.00317924	+	0.623776i
$760$	−0.463846	−	2.63060i	−0.0168255	−	0.0954219i
$761$	−20.1630	+	16.9188i	−0.730908	+	0.613304i	−0.930379	−	0.366599i	$-0.880522\pi$
$761$	−20.1630	+	16.9188i	−0.730908	+	0.613304i	0.199471	+	0.979904i	$0.436078\pi$
$762$	3.37343	−	18.5775i	0.122207	−	0.672992i
$763$	−21.5065	−	7.89958i	−0.778587	−	0.285984i
$764$	−16.6989	−	9.64111i	−0.604145	−	0.348803i
$765$	−66.7033	−	25.0509i	−2.41166	−	0.905718i
$766$			14.5333i			0.525110i
$767$	−33.7577	+	40.2308i	−1.21892	+	1.45265i
$768$	1.70725	−	0.292070i	0.0616050	−	0.0105392i
$769$	11.5703	−	31.7892i	0.417237	−	1.14635i	−0.536025	−	0.844202i	$-0.680075\pi$
$769$	11.5703	−	31.7892i	0.417237	−	1.14635i	0.953262	−	0.302146i	$-0.0977032\pi$
$770$	−18.0487	+	31.0496i	−0.650430	+	1.11895i
$771$	−6.16318	+	16.6684i	−0.221961	+	0.600297i
$772$	−17.6213	+	6.41362i	−0.634203	+	0.230831i
$773$	23.8591			0.858151			0.429075	−	0.903269i	$-0.358839\pi$
$773$	23.8591			0.858151			0.429075	+	0.903269i	$0.358839\pi$
$774$	−1.90985	+	5.08537i	−0.0686481	+	0.182790i
$775$		−	7.74423i		−	0.278181i
$776$	−12.5773	−	10.5536i	−0.451499	−	0.378853i
$777$	−13.7275	−	16.6296i	−0.492471	−	0.596585i
$778$	1.99136	+	11.2935i	0.0713936	+	0.404893i
$779$	−3.10511	+	8.53123i	−0.111252	+	0.305663i
$780$	−28.4703	−	0.145107i	−1.01940	−	0.00519565i
$781$	−3.18222	+	18.0473i	−0.113869	+	0.645782i
$782$	8.68009	+	15.0344i	0.310400	+	0.537628i
$783$	45.1613	−	15.6597i	1.61393	−	0.559630i
$784$	5.38874	−	4.46783i	0.192455	−	0.159565i
$785$	−13.6338	−	37.4586i	−0.486611	−	1.33695i
$786$	14.7786	+	0.0753229i	0.527134	+	0.00268668i
$787$	48.3970	−	8.53369i	1.72517	−	0.304193i	0.778795	−	0.627278i	$-0.215831\pi$
$787$	48.3970	−	8.53369i	1.72517	−	0.304193i	0.946370	+	0.323085i	$0.104720\pi$
$788$	−4.09063	+	11.2389i	−0.145723	+	0.400370i
$789$	3.35792	−	18.4921i	0.119545	−	0.658336i
$790$	−3.51041	+	4.18354i	−0.124895	+	0.148844i
$791$	8.54912	+	23.7057i	0.303972	+	0.842876i
$792$	9.99163	+	8.55904i	0.355037	+	0.304132i
$793$	14.0900	−	24.4045i	0.500350	−	0.866631i
$794$	−3.02766	−	2.54050i	−0.107447	−	0.0901591i
$795$	−16.8901	−	6.24516i	−0.599030	−	0.221493i
$796$	24.4041	−	4.30311i	0.864981	−	0.152520i
$797$	−12.6284	−	4.59636i	−0.447321	−	0.162812i	0.108530	−	0.994093i	$-0.465385\pi$
$797$	−12.6284	−	4.59636i	−0.447321	−	0.162812i	−0.555852	+	0.831282i	$0.687608\pi$
$798$	−3.44064	+	1.94972i	−0.121797	+	0.0690195i
$799$	−3.55178	+	20.1431i	−0.125653	+	0.712612i
$800$	3.96716	+	2.29044i	0.140260	+	0.0809793i
$801$	8.43503	+	14.9600i	0.298037	+	0.528587i
$802$	4.93334	+	8.54480i	0.174202	+	0.301727i
$803$	1.10684	−	6.27721i	0.0390596	−	0.221518i
$804$	3.02098	+	8.43356i	0.106542	+	0.297429i
$805$	16.0731	−	9.21674i	0.566501	−	0.324847i
$806$	−5.77073	−	6.87729i	−0.203265	−	0.242242i
$807$	−9.23545	+	5.26951i	−0.325103	+	0.185496i
$808$	12.0140	+	2.11839i	0.422650	+	0.0745246i
$809$	36.0375	+	20.8063i	1.26701	+	0.731510i	0.974422	−	0.224728i	$-0.0721493\pi$
$809$	36.0375	+	20.8063i	1.26701	+	0.731510i	0.292591	+	0.956238i	$0.405483\pi$
$810$	23.8365	+	14.4178i	0.837530	+	0.506589i
$811$			2.25982i			0.0793531i	0.999213	+	0.0396765i	$0.0126327\pi$
$811$			2.25982i			0.0793531i	−0.999213	+	0.0396765i	$0.987367\pi$
$812$	−15.5893	−	18.6902i	−0.547077	−	0.655896i
$813$	−11.1054	−	0.0566014i	−0.389482	−	0.00198510i
$814$	−19.3915	−	7.05794i	−0.679673	−	0.247381i
$815$	−2.78330	−	1.01304i	−0.0974948	−	0.0354852i
$816$	13.0765	+	2.37452i	0.457768	+	0.0831247i
$817$	−1.53888	−	0.271346i	−0.0538386	−	0.00949320i
$818$	9.17472	−	15.8911i	0.320787	−	0.555619i
$819$	13.8947	+	39.7947i	0.485519	+	1.39054i
$820$	−16.2816	−	28.2006i	−0.568579	−	0.984808i
$821$	13.5258	+	37.1619i	0.472055	+	1.29696i	0.916098	+	0.400954i	$0.131321\pi$
$821$	13.5258	+	37.1619i	0.472055	+	1.29696i	−0.444044	+	0.896005i	$0.646456\pi$
$822$	10.3308	−	1.76736i	0.360329	−	0.0616439i
$823$	−39.7962	+	33.3930i	−1.38721	+	1.16401i	−0.420754	+	0.907175i	$0.638234\pi$
$823$	−39.7962	+	33.3930i	−1.38721	+	1.16401i	−0.966456	+	0.256832i	$0.917321\pi$
$824$	−1.61195	−	9.14180i	−0.0561548	−	0.318470i
$825$	5.86746	+	34.2973i	0.204279	+	1.19408i
$826$	−16.7593	−	20.0930i	−0.583132	−	0.699124i
$827$	12.4125	−	7.16639i	0.431627	−	0.249200i	−0.268413	−	0.963304i	$-0.586499\pi$
$827$	12.4125	−	7.16639i	0.431627	−	0.249200i	0.700039	+	0.714104i	$0.253166\pi$
$828$	−2.25628	−	6.40137i	−0.0784112	−	0.222463i
$829$	12.0173	−	6.93819i	0.417378	−	0.240973i	−0.276577	−	0.960992i	$-0.589200\pi$
$829$	12.0173	−	6.93819i	0.417378	−	0.240973i	0.693955	+	0.720019i	$0.255867\pi$
$830$	14.2942	+	39.2731i	0.496160	+	1.36319i
$831$	−7.99834	−	1.45239i	−0.277459	−	0.0503830i
$832$	5.22981	−	0.922157i	0.181311	−	0.0319700i
$833$	50.5803	−	18.0728i	1.75250	−	0.626186i
$834$	3.22979	+	1.88673i	0.111838	+	0.0653322i
$835$	−7.21153	−	6.05119i	−0.249565	−	0.209410i
$836$	−1.89228	+	3.27752i	−0.0654459	+	0.113356i
$837$	1.39294	+	8.67323i	0.0481472	+	0.299791i
$838$	−28.6203	+	16.5239i	−0.988672	+	0.570810i
$839$	40.1133	−	14.6000i	1.38487	−	0.504050i	0.461216	−	0.887288i	$-0.347413\pi$
$839$	40.1133	−	14.6000i	1.38487	−	0.504050i	0.923649	+	0.383238i	$0.125191\pi$
$840$	2.57539	−	13.9487i	0.0888593	−	0.481275i
$841$	−42.6083	+	35.7526i	−1.46925	+	1.23285i
$842$	−10.1891	−	12.1429i	−0.351138	−	0.418471i
$843$	−3.65901	−	3.10219i	−0.126023	−	0.106845i
$844$	−6.49224	+	2.36298i	−0.223472	+	0.0813372i
$845$	−47.0525			−1.61866
$846$	2.81156	−	7.48636i	0.0966634	−	0.257386i
$847$	20.4887	−	7.38897i	0.704000	−	0.253888i
$848$	3.30785	+	0.583264i	0.113592	+	0.0200294i
$849$	−3.34672	−	19.5627i	−0.114859	−	0.671391i
$850$	22.5939	+	26.9263i	0.774964	+	0.923566i
$851$	6.84320	+	8.15541i	0.234582	+	0.279564i
$852$	−1.22048	−	7.13414i	−0.0418131	−	0.244412i
$853$	−41.5364	−	7.32398i	−1.42218	−	0.250768i	−0.590954	−	0.806705i	$-0.701249\pi$
$853$	−41.5364	−	7.32398i	−1.42218	−	0.250768i	−0.831225	+	0.555937i	$0.812360\pi$
$854$	10.7283	+	9.05614i	0.367115	+	0.309895i
$855$	−2.81741	+	7.50194i	−0.0963534	+	0.256561i
$856$	−3.84803			−0.131523
$857$	−31.0775	+	11.3113i	−1.06159	+	0.386386i	−0.813024	−	0.582230i	$-0.802180\pi$
$857$	−31.0775	+	11.3113i	−1.06159	+	0.386386i	−0.248562	+	0.968616i	$0.579958\pi$
$858$	30.7678	+	26.0856i	1.05040	+	0.890549i
$859$	5.52947	+	6.58976i	0.188663	+	0.224840i	0.852082	−	0.523408i	$-0.175340\pi$
$859$	5.52947	+	6.58976i	0.188663	+	0.224840i	−0.663419	+	0.748248i	$0.730895\pi$
$860$	4.29348	−	3.60265i	0.146406	−	0.122849i
$861$	−31.2847	+	36.6803i	−1.06618	+	1.25006i
$862$	8.19915	−	2.98425i	0.279264	−	0.101644i
$863$	−40.4065	+	23.3287i	−1.37545	+	0.794118i	−0.991608	−	0.129279i	$-0.958734\pi$
$863$	−40.4065	+	23.3287i	−1.37545	+	0.794118i	−0.383845	+	0.923397i	$0.625400\pi$
$864$	−4.85504	−	1.85164i	−0.165172	−	0.0629940i
$865$	4.45578	−	7.71764i	0.151501	−	0.262408i
$866$	14.2243	+	11.9356i	0.483363	+	0.405589i
$867$	62.6305	+	36.5866i	2.12704	+	1.24255i
$868$	3.88012	−	2.22497i	0.131700	−	0.0755203i
$869$	7.61997	−	1.34361i	0.258490	−	0.0455788i
$870$	−48.5242	−	8.81136i	−1.64512	−	0.298733i
$871$	9.39402	+	25.8098i	0.318304	+	0.874533i
$872$	7.49952	−	4.32985i	0.253966	−	0.146627i
$873$	16.3737	+	46.4544i	0.554166	+	1.57224i
$874$	1.69087	−	0.976227i	0.0571947	−	0.0330214i
$875$	−2.63582	+	2.19851i	−0.0891068	+	0.0743231i
$876$	0.424510	+	2.48140i	0.0143429	+	0.0838389i
$877$	−7.28308	−	41.3044i	−0.245932	−	1.39475i	−0.818318	−	0.574766i	$-0.805093\pi$
$877$	−7.28308	−	41.3044i	−0.245932	−	1.39475i	0.572386	−	0.819985i	$-0.306018\pi$
$878$	−22.6934	+	19.0420i	−0.765865	+	0.642637i
$879$	14.1004	−	2.41224i	0.475593	−	0.0813628i
$880$	−4.64268	−	12.7557i	−0.156505	−	0.429993i
$881$	7.19606	+	12.4639i	0.242441	+	0.419921i	0.961409	−	0.275123i	$-0.0887185\pi$
$881$	7.19606	+	12.4639i	0.242441	+	0.419921i	−0.718968	+	0.695043i	$0.755385\pi$
$882$	−20.7370	+	3.31344i	−0.698249	+	0.111569i
$883$	0.824123	−	1.42742i	0.0277340	−	0.0480366i	−0.851825	−	0.523826i	$-0.824504\pi$
$883$	0.824123	−	1.42742i	0.0277340	−	0.0480366i	0.879559	+	0.475789i	$0.157838\pi$
$884$	40.1292	+	7.07586i	1.34969	+	0.237987i
$885$	−52.1662	−	9.47270i	−1.75355	−	0.318421i
$886$	4.98297	+	1.81365i	0.167406	+	0.0609309i
$887$	−18.9801	−	6.90818i	−0.637288	−	0.231954i	0.00311226	−	0.999995i	$-0.499009\pi$
$887$	−18.9801	−	6.90818i	−0.637288	−	0.231954i	−0.640400	+	0.768041i	$0.721232\pi$
$888$	8.15018	+	0.0415396i	0.273502	+	0.00139398i
$889$	27.0731	+	9.94427i	0.908003	+	0.333520i
$890$		−	17.7197i		−	0.593967i
$891$	−12.7403	−	37.3563i	−0.426818	−	1.25148i
$892$	0.747592	+	0.431623i	0.0250312	+	0.0144518i
$893$	2.26544	+	0.399459i	0.0758101	+	0.0133674i
$894$	−10.9434	+	6.24400i	−0.366001	+	0.208831i
$895$	−47.6498	−	56.7869i	−1.59276	−	1.89818i
$896$	−0.00779754	+	2.64574i	−0.000260498	+	0.0883880i
$897$	−7.01773	−	19.5912i	−0.234315	−	0.654130i
$898$	2.30241	−	13.0576i	0.0768323	−	0.435738i
$899$	−7.77569	−	13.4679i	−0.259334	−	0.449179i
$900$	−6.74965	−	11.9709i	−0.224988	−	0.399030i
$901$	22.3203	+	12.8866i	0.743597	+	0.429316i
$902$	−8.01142	+	45.4350i	−0.266751	+	1.51282i
$903$	−7.15248	−	4.20656i	−0.238020	−	0.139986i
$904$	−8.95034	−	3.25766i	−0.297684	−	0.108348i
$905$	40.1962	−	7.08768i	1.33617	−	0.235603i
$906$	9.54064	+	3.52768i	0.316967	+	0.117199i
$907$	4.13254	+	3.46761i	0.137219	+	0.115140i	0.708814	−	0.705396i	$-0.249231\pi$
$907$	4.13254	+	3.46761i	0.137219	+	0.115140i	−0.571595	+	0.820536i	$0.693675\pi$
$908$	12.5840	−	21.7961i	0.417615	−	0.723330i
$909$	−27.7944	−	23.8092i	−0.921881	−	0.789702i
$910$	7.67810	−	42.8065i	0.254526	−	1.41902i
$911$	5.33904	−	6.36282i	0.176890	−	0.210810i	−0.670313	−	0.742079i	$-0.733840\pi$
$911$	5.33904	−	6.36282i	0.176890	−	0.210810i	0.847203	+	0.531269i	$0.178285\pi$
$912$	0.267055	−	1.47068i	0.00884309	−	0.0486989i
$913$	20.2522	−	55.6425i	0.670251	−	1.84150i
$914$	−38.3557	+	6.76314i	−1.26869	+	0.223705i
$915$	28.4488	+	0.144997i	0.940487	+	0.00479345i
$916$	−6.07917	−	16.7024i	−0.200861	−	0.551862i
$917$	−3.98560	+	22.2203i	−0.131616	+	0.733779i
$918$	−30.1475	−	26.0925i	−0.995015	−	0.861182i
$919$	16.5571	+	28.6778i	0.546169	+	0.945992i	0.998532	+	0.0541584i	$0.0172476\pi$
$919$	16.5571	+	28.6778i	0.546169	+	0.945992i	−0.452364	+	0.891834i	$0.649419\pi$
$920$	−1.21605	+	6.89659i	−0.0400921	+	0.227374i
$921$	6.99300	+	0.0356417i	0.230427	+	0.00117443i
$922$	−0.717518	+	1.97136i	−0.0236302	+	0.0649234i
$923$	−3.85345	−	21.8540i	−0.126838	−	0.719333i
$924$	−15.4984	+	12.7936i	−0.509858	+	0.420880i
$925$	16.5126	+	13.8557i	0.542930	+	0.455573i
$926$			11.2842i			0.370822i
$927$	−9.79100	+	26.0706i	−0.321579	+	0.856270i
$928$	9.19898			0.301971
$929$	40.8859	−	14.8813i	1.34142	−	0.488238i	0.431163	−	0.902274i	$-0.358103\pi$
$929$	40.8859	−	14.8813i	1.34142	−	0.488238i	0.910261	+	0.414036i	$0.135881\pi$
$930$	3.14324	−	8.50093i	0.103071	−	0.278756i
$931$	−2.03260	−	5.68863i	−0.0666158	−	0.186437i
$932$	−5.33808	+	14.6663i	−0.174855	+	0.480409i
$933$	40.8989	−	6.99684i	1.33897	−	0.229066i
$934$	−11.5904	+	13.8129i	−0.379250	+	0.451972i
$935$		−	104.158i		−	3.40632i
$936$	−14.9144	−	5.60120i	−0.487491	−	0.183081i
$937$	27.5502	+	15.9061i	0.900025	+	0.519630i	0.877208	−	0.480110i	$-0.159403\pi$
$937$	27.5502	+	15.9061i	0.900025	+	0.519630i	0.0228166	+	0.999740i	$0.492737\pi$
$938$	−13.4831	+	2.33648i	−0.440238	+	0.0762888i
$939$	8.31676	−	45.8005i	0.271407	−	1.49464i
$940$	−6.32059	+	5.30360i	−0.206155	+	0.172984i
$941$	−1.22480	−	6.94619i	−0.0399274	−	0.226439i	0.958314	−	0.285716i	$-0.0922315\pi$
$941$	−1.22480	−	6.94619i	−0.0399274	−	0.226439i	−0.998242	+	0.0592771i	$0.981120\pi$
$942$	0.113687	−	22.3058i	0.00370414	−	0.726762i
$943$	15.2993	−	18.2330i	0.498215	−	0.593749i
$944$	9.88941			0.321873
$945$	−27.9427	+	32.0935i	−0.908975	+	1.04400i
$946$	−7.94085			−0.258179
$947$	11.7238	−	13.9719i	0.380974	−	0.454027i	−0.541148	−	0.840928i	$-0.682010\pi$
$947$	11.7238	−	13.9719i	0.380974	−	0.454027i	0.922121	+	0.386901i	$0.126454\pi$
$948$	−2.65430	+	1.51447i	−0.0862075	+	0.0491878i
$949$	1.34031	+	7.60128i	0.0435083	+	0.246748i
$950$	3.02833	−	2.54107i	0.0982521	−	0.0824433i
$951$	−23.6994	−	20.0929i	−0.768507	−	0.651557i
$952$	−6.99964	+	19.0564i	−0.226860	+	0.617622i
$953$	−10.5477	−	6.08972i	−0.341674	−	0.197265i	0.319338	−	0.947641i	$-0.396539\pi$
$953$	−10.5477	−	6.08972i	−0.341674	−	0.197265i	−0.661012	+	0.750375i	$0.729873\pi$
$954$	−7.65273	−	6.55549i	−0.247766	−	0.212242i
$955$		−	59.6843i		−	1.93134i
$956$	−1.75056	+	2.08623i	−0.0566170	+	0.0674735i
$957$	44.6407	+	53.7547i	1.44303	+	1.73764i
$958$	4.64930	−	12.7738i	0.150212	−	0.412704i
$959$	−0.0471842	+	16.0098i	−0.00152366	+	0.516984i
$960$	3.42515	+	4.12444i	0.110546	+	0.133116i
$961$	−26.4449	+	9.62514i	−0.853060	+	0.310488i
$962$	24.9889			0.805673
$963$	9.93813	+	5.87366i	0.320252	+	0.189276i
$964$			2.48798i			0.0801325i
$965$	−44.4639	−	37.3097i	−1.43134	−	1.20104i
$966$	10.2245	−	1.71817i	0.328968	−	0.0552813i
$967$	3.11258	+	17.6523i	0.100094	+	0.567661i	0.993067	+	0.117551i	$0.0375042\pi$
$967$	3.11258	+	17.6523i	0.100094	+	0.567661i	−0.892973	+	0.450110i	$0.851385\pi$
$968$	−2.81558	+	7.73574i	−0.0904961	+	0.248636i
$969$	5.78519	−	9.90333i	0.185847	−	0.318141i
$970$	8.82484	−	50.0481i	0.283348	−	1.60695i
$971$	−20.0342	−	34.7002i	−0.642927	−	1.11358i	−0.984776	−	0.173828i	$-0.944386\pi$
$971$	−20.0342	−	34.7002i	−0.642927	−	1.11358i	0.341849	−	0.939755i	$-0.388947\pi$
$972$	9.71254	+	12.1929i	0.311530	+	0.391087i
$973$	−3.68558	+	4.36610i	−0.118154	+	0.139971i
$974$	1.14098	+	3.13482i	0.0365593	+	0.100446i
$975$	−20.8813	−	36.5970i	−0.668737	−	1.17204i
$976$	−5.22585	+	0.921459i	−0.167275	+	0.0294952i
$977$	7.18083	−	19.7292i	0.229735	−	0.631192i	−0.770244	−	0.637750i	$-0.779865\pi$
$977$	7.18083	−	19.7292i	0.229735	−	0.631192i	0.999978	+	0.00655827i	$0.00208758\pi$
$978$	−1.26421	−	1.07183i	−0.0404250	−	0.0342732i
$979$	−16.1375	+	19.2319i	−0.515757	+	0.614655i
$980$	20.3164	+	7.53047i	0.648983	+	0.240552i
$981$	−25.9777	−	0.264812i	−0.829405	−	0.00845480i
$982$	−20.2912	+	35.1453i	−0.647517	+	1.12153i
$983$	31.7128	+	26.6102i	1.01148	+	0.848735i	0.988533	−	0.151002i	$-0.0482500\pi$
$983$	31.7128	+	26.6102i	1.01148	+	0.848735i	0.0229492	+	0.999737i	$0.492694\pi$
$984$	−3.07264	−	17.9606i	−0.0979522	−	0.572564i
$985$	−36.4580	+	6.42853i	−1.16165	+	0.204830i
$986$	66.3284	+	24.1416i	2.11233	+	0.768825i
$987$	10.5294	+	6.19264i	0.335156	+	0.197114i
$988$	0.795803	−	4.51322i	0.0253179	−	0.143585i
$989$	3.54783	+	2.04834i	0.112814	+	0.0651335i
$990$	−7.47988	+	40.0300i	−0.237726	+	1.27224i
$991$	26.1434	+	45.2816i	0.830471	+	1.43842i	0.897665	+	0.440679i	$0.145262\pi$
$991$	26.1434	+	45.2816i	0.830471	+	1.43842i	−0.0671934	+	0.997740i	$0.521404\pi$
$992$	−0.293562	+	1.66487i	−0.00932059	+	0.0528597i
$993$	−30.2802	+	35.7153i	−0.960914	+	1.13339i
$994$	11.0559	+	0.0325839i	0.350670	+	0.00103350i
$995$	49.3040	+	58.7582i	1.56304	+	1.86276i
$996$	−0.119195	+	23.3863i	−0.00377683	+	0.741023i
$997$	46.6333	+	8.22270i	1.47689	+	0.260416i	0.853335	−	0.521363i	$-0.174576\pi$
$997$	46.6333	+	8.22270i	1.47689	+	0.260416i	0.623556	+	0.781779i	$0.285687\pi$
$998$	14.7151	+	8.49577i	0.465799	+	0.268929i
$999$	−20.9857	−	12.5478i	−0.663957	−	0.396993i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.bf.a.101.22	yes	144
7.5	odd	6		378.2.ba.a.47.10	✓	144
27.23	odd	18		378.2.ba.a.185.10	yes	144
189.131	even	18	inner	378.2.bf.a.131.22	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.ba.a.47.10	✓	144	7.5	odd	6
378.2.ba.a.185.10	yes	144	27.23	odd	18
378.2.bf.a.101.22	yes	144	1.1	even	1	trivial
378.2.bf.a.131.22	yes	144	189.131	even	18	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.bf (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.642788 - 0.766044i) q^{2} +(1.49557 + 0.873659i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(2.37114 - 1.98962i) q^{5} +(1.63059 - 0.584093i) q^{6} +(0.451749 + 2.60690i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(1.47344 + 2.61323i) q^{9} +O(q^{10})\)	\(q+(0.642788 - 0.766044i) q^{2} +(1.49557 + 0.873659i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(2.37114 - 1.98962i) q^{5} +(1.63059 - 0.584093i) q^{6} +(0.451749 + 2.60690i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(1.47344 + 2.61323i) q^{9} -3.09530i q^{10} +(-2.81892 + 3.35945i) q^{11} +(0.600684 - 1.62455i) q^{12} +(1.81629 - 4.99023i) q^{13} +(2.28738 + 1.32962i) q^{14} +(5.28444 - 0.904044i) q^{15} +(-0.939693 + 0.342020i) q^{16} -7.67316 q^{17} +(2.94896 + 0.551033i) q^{18} +0.862980i q^{19} +(-2.37114 - 1.98962i) q^{20} +(-1.60192 + 4.29347i) q^{21} +(0.761526 + 4.31883i) q^{22} +(0.773805 - 2.12601i) q^{23} +(-0.858369 - 1.50439i) q^{24} +(0.795461 - 4.51129i) q^{25} +(-2.65524 - 4.59902i) q^{26} +(-0.0794470 + 5.19555i) q^{27} +(2.48885 - 0.897569i) q^{28} +(-3.14624 - 8.64421i) q^{29} +(2.70424 - 4.62923i) q^{30} +(1.66487 - 0.293562i) q^{31} +(-0.342020 + 0.939693i) q^{32} +(-7.15089 + 2.56151i) q^{33} +(-4.93221 + 5.87798i) q^{34} +(6.25790 + 5.28251i) q^{35} +(2.31767 - 1.90484i) q^{36} +(-2.35278 + 4.07514i) q^{37} +(0.661081 + 0.554713i) q^{38} +(7.07615 - 5.87639i) q^{39} +(-3.04828 + 0.537493i) q^{40} +(9.88578 + 3.59813i) q^{41} +(2.25929 + 3.98693i) q^{42} +(-0.314429 + 1.78322i) q^{43} +(3.79791 + 2.19273i) q^{44} +(8.69306 + 3.26474i) q^{45} +(-1.13123 - 1.95934i) q^{46} +(0.462883 - 2.62514i) q^{47} +(-1.70418 - 0.309457i) q^{48} +(-6.59185 + 2.35533i) q^{49} +(-2.94453 - 3.50916i) q^{50} +(-11.4757 - 6.70373i) q^{51} +(-5.22981 - 0.922157i) q^{52} +(-2.90888 - 1.67944i) q^{53} +(3.92895 + 3.40049i) q^{54} +13.5743i q^{55} +(0.912224 - 2.48352i) q^{56} +(-0.753951 + 1.29064i) q^{57} +(-8.64421 - 3.14624i) q^{58} +(-9.29301 - 3.38238i) q^{59} +(-1.80794 - 5.04718i) q^{60} +(5.22585 + 0.921459i) q^{61} +(0.845277 - 1.46406i) q^{62} +(-6.14681 + 5.02163i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-5.62197 - 15.4462i) q^{65} +(-2.63427 + 7.12441i) q^{66} +(-3.96204 + 3.32455i) q^{67} +(1.33243 + 7.55659i) q^{68} +(3.01469 - 2.50355i) q^{69} +(8.06913 - 1.39830i) q^{70} +(3.61889 - 2.08937i) q^{71} +(0.0305798 - 2.99984i) q^{72} +(-1.25873 + 0.726726i) q^{73} +(1.60940 + 4.42179i) q^{74} +(5.13099 - 6.05197i) q^{75} +(0.849870 - 0.149855i) q^{76} +(-10.0312 - 5.83100i) q^{77} +(0.0468797 - 9.19792i) q^{78} +(-1.35158 - 1.13411i) q^{79} +(-1.54765 + 2.68061i) q^{80} +(-4.65795 + 7.70087i) q^{81} +(9.11078 - 5.26011i) q^{82} +(-12.6880 + 4.61804i) q^{83} +(4.50641 + 0.832032i) q^{84} +(-18.1941 + 15.2667i) q^{85} +(1.16391 + 1.38710i) q^{86} +(2.84669 - 15.6767i) q^{87} +(4.12098 - 1.49991i) q^{88} +5.72472 q^{89} +(8.08873 - 4.56074i) q^{90} +(13.8295 + 2.48057i) q^{91} +(-2.22808 - 0.392871i) q^{92} +(2.74640 + 1.01549i) q^{93} +(-1.71344 - 2.04200i) q^{94} +(1.71700 + 2.04624i) q^{95} +(-1.33249 + 1.10656i) q^{96} +(16.1691 + 2.85104i) q^{97} +(-2.43287 + 6.56362i) q^{98} +(-12.9325 - 2.41653i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 18 q^{6} - 12 q^{9}+O(q^{10}) \) 144 * q + 18 * q^6 - 12 * q^9	\( 144 q + 18 q^{6} - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 6 q^{21} - 6 q^{23} - 6 q^{29} - 18 q^{30} - 54 q^{35} + 6 q^{36} - 6 q^{39} + 24 q^{42} - 54 q^{47} + 18 q^{49} + 12 q^{50} + 18 q^{51} + 90 q^{53} - 54 q^{54} - 12 q^{56} - 6 q^{57} - 90 q^{59} - 36 q^{60} - 24 q^{63} + 72 q^{64} - 84 q^{65} - 36 q^{69} - 18 q^{70} - 72 q^{71} + 12 q^{72} + 18 q^{74} - 90 q^{75} - 78 q^{77} - 60 q^{78} + 36 q^{79} - 6 q^{84} - 72 q^{85} + 24 q^{86} + 90 q^{87} - 18 q^{91} - 42 q^{92} - 12 q^{93} + 78 q^{95} - 36 q^{98} - 108 q^{99}+O(q^{100}) \) 144 * q + 18 * q^6 - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 6 * q^21 - 6 * q^23 - 6 * q^29 - 18 * q^30 - 54 * q^35 + 6 * q^36 - 6 * q^39 + 24 * q^42 - 54 * q^47 + 18 * q^49 + 12 * q^50 + 18 * q^51 + 90 * q^53 - 54 * q^54 - 12 * q^56 - 6 * q^57 - 90 * q^59 - 36 * q^60 - 24 * q^63 + 72 * q^64 - 84 * q^65 - 36 * q^69 - 18 * q^70 - 72 * q^71 + 12 * q^72 + 18 * q^74 - 90 * q^75 - 78 * q^77 - 60 * q^78 + 36 * q^79 - 6 * q^84 - 72 * q^85 + 24 * q^86 + 90 * q^87 - 18 * q^91 - 42 * q^92 - 12 * q^93 + 78 * q^95 - 36 * q^98 - 108 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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