LMFDB - Embedded newform 378.2.z.a.293.1

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			293.1
Character	$\chi$	$=$	378.293
Dual form			378.2.z.a.209.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.342020 + 0.939693i) q^{2} +(-1.68636 - 0.395229i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(-0.330418 + 1.87389i) q^{5} +(0.948161 - 1.44948i) q^{6} +(2.54679 - 0.716846i) q^{7} +(0.866025 - 0.500000i) q^{8} +(2.68759 + 1.33299i) q^{9} +O(q^{10})$	\(q+(-0.342020 + 0.939693i) q^{2} +(-1.68636 - 0.395229i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(-0.330418 + 1.87389i) q^{5} +(0.948161 - 1.44948i) q^{6} +(2.54679 - 0.716846i) q^{7} +(0.866025 - 0.500000i) q^{8} +(2.68759 + 1.33299i) q^{9} +(-1.64788 - 0.951401i) q^{10} +(-1.99795 + 0.352293i) q^{11} +(1.03778 + 1.38673i) q^{12} +(0.169770 + 0.466440i) q^{13} +(-0.197438 + 2.63837i) q^{14} +(1.29782 - 3.02946i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-2.21416 + 3.83503i) q^{17} +(-2.17181 + 2.06960i) q^{18} +(-3.77699 + 2.18065i) q^{19} +(1.45763 - 1.22310i) q^{20} +(-4.57811 + 0.202293i) q^{21} +(0.352293 - 1.99795i) q^{22} +(-3.43842 + 4.09775i) q^{23} +(-1.65804 + 0.500900i) q^{24} +(1.29616 + 0.471763i) q^{25} -0.496375 q^{26} +(-4.00539 - 3.31011i) q^{27} +(-2.41173 - 1.08791i) q^{28} +(-2.07195 + 5.69263i) q^{29} +(2.40288 + 2.25569i) q^{30} +(-0.836828 + 0.997292i) q^{31} +(-0.984808 - 0.173648i) q^{32} +(3.50849 + 0.195557i) q^{33} +(-2.84647 - 3.39229i) q^{34} +(0.501788 + 5.00927i) q^{35} +(-1.20198 - 2.74868i) q^{36} +(-3.22468 + 5.58532i) q^{37} +(-0.757330 - 4.29503i) q^{38} +(-0.101942 - 0.853681i) q^{39} +(0.650797 + 1.78805i) q^{40} +(1.67326 - 0.609017i) q^{41} +(1.37571 - 4.37120i) q^{42} +(-0.194294 - 1.10190i) q^{43} +(1.75697 + 1.01439i) q^{44} +(-3.38592 + 4.59581i) q^{45} +(-2.67462 - 4.63258i) q^{46} +(8.86416 - 7.43791i) q^{47} +(0.0963917 - 1.72937i) q^{48} +(5.97226 - 3.65131i) q^{49} +(-0.886624 + 1.05664i) q^{50} +(5.24957 - 5.59213i) q^{51} +(0.169770 - 0.466440i) q^{52} +6.77888i q^{53} +(4.48041 - 2.63171i) q^{54} -3.86036i q^{55} +(1.84716 - 1.89420i) q^{56} +(7.23120 - 2.18457i) q^{57} +(-4.64068 - 3.89399i) q^{58} +(-0.400404 + 2.27080i) q^{59} +(-2.94149 + 1.48648i) q^{60} +(-3.31870 - 3.95508i) q^{61} +(-0.650936 - 1.12745i) q^{62} +(7.80027 + 1.46826i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-0.930154 + 0.164011i) q^{65} +(-1.38374 + 3.23002i) q^{66} +(9.96015 - 3.62520i) q^{67} +(4.16126 - 1.51457i) q^{68} +(7.41795 - 5.55131i) q^{69} +(-4.87880 - 1.24175i) q^{70} +(-0.688323 - 0.397403i) q^{71} +(2.99402 - 0.189389i) q^{72} +(-11.1538 + 6.43963i) q^{73} +(-4.14557 - 4.94050i) q^{74} +(-1.99933 - 1.30784i) q^{75} +(4.29503 + 0.757330i) q^{76} +(-4.83582 + 2.32944i) q^{77} +(0.837064 + 0.196182i) q^{78} +(-13.3611 - 4.86305i) q^{79} -1.90280 q^{80} +(5.44626 + 7.16507i) q^{81} +1.78065i q^{82} +(10.7214 + 3.90227i) q^{83} +(3.63707 + 2.78779i) q^{84} +(-6.45485 - 5.41626i) q^{85} +(1.10190 + 0.194294i) q^{86} +(5.74394 - 8.78091i) q^{87} +(-1.55413 + 1.30407i) q^{88} +(1.09582 + 1.89801i) q^{89} +(-3.16060 - 4.75358i) q^{90} +(0.766734 + 1.06622i) q^{91} +(5.26797 - 0.928885i) q^{92} +(1.80535 - 1.35105i) q^{93} +(3.95763 + 10.8735i) q^{94} +(-2.83831 - 7.79820i) q^{95} +(1.59211 + 0.682057i) q^{96} +(11.7066 - 2.06420i) q^{97} +(1.38847 + 6.86091i) q^{98} +(-5.83928 - 1.71644i) 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 $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$-1$

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 $

$2$	−0.342020	+	0.939693i	−0.241845	+	0.664463i
$2$	−0.342020	+	0.939693i	−0.241845	+	0.664463i
$3$	−1.68636	−	0.395229i	−0.973618	−	0.228185i
$3$	−1.68636	−	0.395229i	−0.973618	−	0.228185i
$4$	−0.766044	−	0.642788i	−0.383022	−	0.321394i
$5$	−0.330418	+	1.87389i	−0.147768	+	0.838031i	0.817336	+	0.576162i	$0.195450\pi$
$5$	−0.330418	+	1.87389i	−0.147768	+	0.838031i	−0.965103	+	0.261870i	$0.915661\pi$
$6$	0.948161	−	1.44948i	0.387085	−	0.591748i
$7$	2.54679	−	0.716846i	0.962596	−	0.270942i
$7$	2.54679	−	0.716846i	0.962596	−	0.270942i
$8$	0.866025	−	0.500000i	0.306186	−	0.176777i
$9$	2.68759	+	1.33299i	0.895863	+	0.444331i
$10$	−1.64788	−	0.951401i	−0.521104	−	0.300860i
$11$	−1.99795	+	0.352293i	−0.602405	+	0.106220i	−0.466530	−	0.884506i	$-0.654496\pi$
$11$	−1.99795	+	0.352293i	−0.602405	+	0.106220i	−0.135876	+	0.990726i	$0.543385\pi$
$12$	1.03778	+	1.38673i	0.299580	+	0.400315i
$13$	0.169770	+	0.466440i	0.0470858	+	0.129367i	0.961007	−	0.276525i	$-0.0891830\pi$
$13$	0.169770	+	0.466440i	0.0470858	+	0.129367i	−0.913921	+	0.405892i	$0.866961\pi$
$14$	−0.197438	+	2.63837i	−0.0527676	+	0.705135i
$15$	1.29782	−	3.02946i	0.335096	−	0.782204i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	−2.21416	+	3.83503i	−0.537012	+	0.930132i	0.462051	+	0.886853i	$0.347114\pi$
$17$	−2.21416	+	3.83503i	−0.537012	+	0.930132i	−0.999063	+	0.0432790i	$0.986220\pi$
$18$	−2.17181	+	2.06960i	−0.511901	+	0.487809i
$19$	−3.77699	+	2.18065i	−0.866501	+	0.500274i	−0.866184	−	0.499726i	$-0.833434\pi$
$19$	−3.77699	+	2.18065i	−0.866501	+	0.500274i	−0.000316777		1.00000i	$0.500101\pi$
$20$	1.45763	−	1.22310i	0.325936	−	0.273493i
$21$	−4.57811	+	0.202293i	−0.999025	+	0.0441439i
$22$	0.352293	−	1.99795i	0.0751091	−	0.425965i
$23$	−3.43842	+	4.09775i	−0.716961	+	0.854441i	−0.994332	−	0.106322i	$-0.966093\pi$
$23$	−3.43842	+	4.09775i	−0.716961	+	0.854441i	0.277371	+	0.960763i	$0.410537\pi$
$24$	−1.65804	+	0.500900i	−0.338446	+	0.102246i
$25$	1.29616	+	0.471763i	0.259231	+	0.0943525i
$26$	−0.496375			−0.0973471
$27$	−4.00539	−	3.31011i	−0.770838	−	0.637031i
$28$	−2.41173	−	1.08791i	−0.455775	−	0.205595i
$29$	−2.07195	+	5.69263i	−0.384751	+	1.05710i	0.584580	+	0.811336i	$0.301260\pi$
$29$	−2.07195	+	5.69263i	−0.384751	+	1.05710i	−0.969331	+	0.245759i	$0.920963\pi$
$30$	2.40288	+	2.25569i	0.438704	+	0.411830i
$31$	−0.836828	+	0.997292i	−0.150299	+	0.179119i	−0.835940	−	0.548820i	$-0.815077\pi$
$31$	−0.836828	+	0.997292i	−0.150299	+	0.179119i	0.685642	+	0.727939i	$0.259522\pi$
$32$	−0.984808	−	0.173648i	−0.174091	−	0.0306970i
$33$	3.50849	+	0.195557i	0.610750	+	0.0340421i
$34$	−2.84647	−	3.39229i	−0.488165	−	0.581772i
$35$	0.501788	+	5.00927i	0.0848177	+	0.846722i
$36$	−1.20198	−	2.74868i	−0.200330	−	0.458113i
$37$	−3.22468	+	5.58532i	−0.530135	+	0.918220i	0.469247	+	0.883067i	$0.344525\pi$
$37$	−3.22468	+	5.58532i	−0.530135	+	0.918220i	−0.999382	+	0.0351536i	$0.988808\pi$
$38$	−0.757330	−	4.29503i	−0.122855	−	0.696746i
$39$	−0.101942	−	0.853681i	−0.0163239	−	0.136698i
$40$	0.650797	+	1.78805i	0.102900	+	0.282715i
$41$	1.67326	−	0.609017i	0.261319	−	0.0951125i	−0.208038	−	0.978121i	$-0.566708\pi$
$41$	1.67326	−	0.609017i	0.261319	−	0.0951125i	0.469357	+	0.883008i	$0.344486\pi$
$42$	1.37571	−	4.37120i	0.212277	−	0.674491i
$43$	−0.194294	−	1.10190i	−0.0296296	−	0.168038i	0.966402	−	0.257034i	$-0.0827452\pi$
$43$	−0.194294	−	1.10190i	−0.0296296	−	0.168038i	−0.996032	+	0.0889962i	$0.971634\pi$
$44$	1.75697	+	1.01439i	0.264873	+	0.152925i
$45$	−3.38592	+	4.59581i	−0.504742	+	0.685103i
$46$	−2.67462	−	4.63258i	−0.394351	−	0.683036i
$47$	8.86416	−	7.43791i	1.29297	−	1.08493i	0.301657	−	0.953417i	$-0.402460\pi$
$47$	8.86416	−	7.43791i	1.29297	−	1.08493i	0.991314	−	0.131515i	$-0.0419840\pi$
$48$	0.0963917	−	1.72937i	0.0139129	−	0.249613i
$49$	5.97226	−	3.65131i	0.853181	−	0.521616i
$50$	−0.886624	+	1.05664i	−0.125388	+	0.149431i
$51$	5.24957	−	5.59213i	0.735087	−	0.783055i
$52$	0.169770	−	0.466440i	0.0235429	−	0.0646835i
$53$			6.77888i			0.931151i	0.885008	+	0.465576i	$0.154153\pi$
$53$			6.77888i			0.931151i	−0.885008	+	0.465576i	$0.845847\pi$
$54$	4.48041	−	2.63171i	0.609707	−	0.358131i
$55$		−	3.86036i		−	0.520530i
$56$	1.84716	−	1.89420i	0.246837	−	0.253123i
$57$	7.23120	−	2.18457i	0.957796	−	0.289353i
$58$	−4.64068	−	3.89399i	−0.609351	−	0.511306i
$59$	−0.400404	+	2.27080i	−0.0521282	+	0.295633i	−0.999715	−	0.0238642i	$-0.992403\pi$
$59$	−0.400404	+	2.27080i	−0.0521282	+	0.295633i	0.947587	+	0.319498i	$0.103514\pi$
$60$	−2.94149	+	1.48648i	−0.379744	+	0.191904i
$61$	−3.31870	−	3.95508i	−0.424916	−	0.506396i	0.510532	−	0.859859i	$-0.329448\pi$
$61$	−3.31870	−	3.95508i	−0.424916	−	0.506396i	−0.935449	+	0.353463i	$0.885004\pi$
$62$	−0.650936	−	1.12745i	−0.0826690	−	0.143187i
$63$	7.80027	+	1.46826i	0.982742	+	0.184984i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	−0.930154	+	0.164011i	−0.115371	+	0.0203431i
$66$	−1.38374	+	3.23002i	−0.170327	+	0.397588i
$67$	9.96015	−	3.62520i	1.21683	−	0.442888i	0.347759	−	0.937584i	$-0.386943\pi$
$67$	9.96015	−	3.62520i	1.21683	−	0.442888i	0.869066	+	0.494695i	$0.164720\pi$
$68$	4.16126	−	1.51457i	0.504626	−	0.183669i
$69$	7.41795	−	5.55131i	0.893017	−	0.668299i
$70$	−4.87880	−	1.24175i	−0.583128	−	0.148417i
$71$	−0.688323	−	0.397403i	−0.0816889	−	0.0471631i	0.458599	−	0.888643i	$-0.348351\pi$
$71$	−0.688323	−	0.397403i	−0.0816889	−	0.0471631i	−0.540288	+	0.841480i	$0.681685\pi$
$72$	2.99402	−	0.189389i	0.352848	−	0.0223198i
$73$	−11.1538	+	6.43963i	−1.30545	+	0.753701i	−0.981333	−	0.192316i	$-0.938400\pi$
$73$	−11.1538	+	6.43963i	−1.30545	+	0.753701i	−0.324116	+	0.946017i	$0.605067\pi$
$74$	−4.14557	−	4.94050i	−0.481913	−	0.574322i
$75$	−1.99933	−	1.30784i	−0.230862	−	0.151016i
$76$	4.29503	+	0.757330i	0.492674	+	0.0868717i
$77$	−4.83582	+	2.32944i	−0.551093	+	0.265464i
$78$	0.837064	+	0.196182i	0.0947788	+	0.0222132i
$79$	−13.3611	−	4.86305i	−1.50324	−	0.547135i	−0.546345	−	0.837561i	$-0.683981\pi$
$79$	−13.3611	−	4.86305i	−1.50324	−	0.547135i	−0.956898	+	0.290425i	$0.906203\pi$
$80$	−1.90280			−0.212740
$81$	5.44626	+	7.16507i	0.605141	+	0.796119i
$82$			1.78065i			0.196640i
$83$	10.7214	+	3.90227i	1.17683	+	0.428329i	0.855080	−	0.518497i	$-0.173508\pi$
$83$	10.7214	+	3.90227i	1.17683	+	0.428329i	0.321746	+	0.946826i	$0.395730\pi$
$84$	3.63707	+	2.78779i	0.396836	+	0.304172i
$85$	−6.45485	−	5.41626i	−0.700127	−	0.587476i
$86$	1.10190	+	0.194294i	0.118821	+	0.0209513i
$87$	5.74394	−	8.78091i	0.615815	−	0.941412i
$88$	−1.55413	+	1.30407i	−0.165671	+	0.139014i
$89$	1.09582	+	1.89801i	0.116156	+	0.201188i	0.918241	−	0.396021i	$-0.129609\pi$
$89$	1.09582	+	1.89801i	0.116156	+	0.201188i	−0.802085	+	0.597210i	$0.796276\pi$
$90$	−3.16060	−	4.75358i	−0.333157	−	0.501071i
$91$	0.766734	+	1.06622i	0.0803756	+	0.111771i
$92$	5.26797	−	0.928885i	0.549224	−	0.0968430i
$93$	1.80535	−	1.35105i	0.187206	−	0.140097i
$94$	3.95763	+	10.8735i	0.408199	+	1.12152i
$95$	−2.83831	−	7.79820i	−0.291205	−	0.800079i
$96$	1.59211	+	0.682057i	0.162494	+	0.0696121i
$97$	11.7066	−	2.06420i	1.18863	−	0.209587i	0.455852	−	0.890056i	$-0.349335\pi$
$97$	11.7066	−	2.06420i	1.18863	−	0.209587i	0.732777	+	0.680468i	$0.238224\pi$
$98$	1.38847	+	6.86091i	0.140257	+	0.693057i
$99$	−5.83928	−	1.71644i	−0.586870	−	0.172508i
$100$	−0.689671	−	1.19455i	−0.0689671	−	0.119455i
$101$	−3.49695	+	2.93429i	−0.347960	+	0.291973i	−0.799970	−	0.600040i	$-0.795151\pi$
$101$	−3.49695	+	2.93429i	−0.347960	+	0.291973i	0.452010	+	0.892013i	$0.350707\pi$
$102$	3.45943	+	6.84561i	0.342534	+	0.677816i
$103$	15.2014	+	2.68041i	1.49783	+	0.264109i	0.861679	−	0.507453i	$-0.169413\pi$
$103$	15.2014	+	2.68041i	1.49783	+	0.264109i	0.636155	+	0.771562i	$0.280524\pi$
$104$	0.380245	+	0.319064i	0.0372861	+	0.0312868i
$105$	1.13361	−	8.64574i	0.110629	−	0.843737i
$106$	−6.37007	−	2.31851i	−0.618716	−	0.225194i
$107$		−	0.763804i		−	0.0738397i	−0.999318	−	0.0369198i	$-0.988245\pi$
$107$		−	0.763804i		−	0.0738397i	0.999318	−	0.0369198i	$-0.0117546\pi$
$108$	0.940611	+	5.11031i	0.0905103	+	0.491740i
$109$	8.80680			0.843538			0.421769	−	0.906703i	$-0.361409\pi$
$109$	8.80680			0.843538			0.421769	+	0.906703i	$0.361409\pi$
$110$	3.62755	+	1.32032i	0.345873	+	0.125888i
$111$	7.64544	−	8.14434i	0.725673	−	0.773027i
$112$	1.14820	+	2.38362i	0.108495	+	0.225231i
$113$	0.769126	+	0.135618i	0.0723533	+	0.0127578i	0.209708	−	0.977764i	$-0.432749\pi$
$113$	0.769126	+	0.135618i	0.0723533	+	0.0127578i	−0.137354	+	0.990522i	$0.543860\pi$
$114$	−0.420392	+	7.54227i	−0.0393733	+	0.706398i
$115$	−6.54264	−	7.79722i	−0.610105	−	0.727094i
$116$	5.24636	−	3.02899i	0.487112	−	0.281234i
$117$	−0.165488	+	1.47990i	−0.0152994	+	0.136817i
$118$	−1.99691	−	1.15292i	−0.183831	−	0.106135i
$119$	−2.88986	+	11.3542i	−0.264913	+	1.04084i
$120$	−0.390786	−	3.27250i	−0.0356737	−	0.298737i
$121$	−6.46891	+	2.35449i	−0.588083	+	0.214045i
$122$	4.85162	−	1.76585i	0.439245	−	0.159872i
$123$	−3.06241	+	0.365699i	−0.276128	+	0.0329739i
$124$	1.28209	−	0.226068i	0.115135	−	0.0203015i
$125$	−6.06931	+	10.5124i	−0.542856	+	0.940254i
$126$	−4.04756	+	6.82768i	−0.360586	+	0.608258i
$127$	6.13165	+	10.6203i	0.544096	+	0.942402i	0.998663	+	0.0516893i	$0.0164605\pi$
$127$	6.13165	+	10.6203i	0.544096	+	0.942402i	−0.454567	+	0.890712i	$0.650206\pi$
$128$	0.642788	+	0.766044i	0.0568149	+	0.0677094i
$129$	−0.107852	+	1.93498i	−0.00949586	+	0.170365i
$130$	0.164011	−	0.930154i	0.0143847	−	0.0815799i
$131$	−14.5722	−	12.2275i	−1.27318	−	1.06832i	−0.994146	−	0.108041i	$-0.965542\pi$
$131$	−14.5722	−	12.2275i	−1.27318	−	1.06832i	−0.279031	−	0.960282i	$-0.590013\pi$
$132$	−2.56196	−	2.40502i	−0.222990	−	0.209330i
$133$	−8.05600	+	8.26116i	−0.698544	+	0.716333i
$134$			10.5994i			0.915646i
$135$	7.52625	−	6.41196i	0.647757	−	0.551854i
$136$			4.42832i			0.379725i
$137$	5.12957	−	14.0934i	0.438249	−	1.20408i	−0.502381	−	0.864646i	$-0.667542\pi$
$137$	5.12957	−	14.0934i	0.438249	−	1.20408i	0.940630	−	0.339433i	$-0.110235\pi$
$138$	2.67943	+	8.86925i	0.228088	+	0.755001i
$139$	12.5817	−	14.9942i	1.06716	−	1.27180i	0.106430	−	0.994320i	$-0.466058\pi$
$139$	12.5817	−	14.9942i	1.06716	−	1.27180i	0.960733	−	0.277475i	$-0.0894976\pi$
$140$	2.83551	−	4.15987i	0.239644	−	0.351573i
$141$	−17.8878	+	9.03960i	−1.50642	+	0.761271i
$142$	0.608857	−	0.510892i	0.0510942	−	0.0428731i
$143$	−0.503516	−	0.872115i	−0.0421061	−	0.0729300i
$144$	−0.846046	+	2.87823i	−0.0705038	+	0.239852i
$145$	−9.98279	−	5.76357i	−0.829026	−	0.478638i
$146$	−2.23646	−	12.6836i	−0.185091	−	1.04970i
$147$	−11.5145	+	3.79700i	−0.949697	+	0.313171i
$148$	6.06042	−	2.20581i	0.498164	−	0.181317i
$149$	−0.494859	−	1.35962i	−0.0405405	−	0.111384i	0.917771	−	0.397111i	$-0.129987\pi$
$149$	−0.494859	−	1.35962i	−0.0405405	−	0.111384i	−0.958311	+	0.285727i	$0.907765\pi$
$150$	1.91278	−	1.43145i	0.156178	−	0.116877i
$151$	3.73449	+	21.1793i	0.303908	+	1.72355i	0.628600	+	0.777729i	$0.283628\pi$
$151$	3.73449	+	21.1793i	0.303908	+	1.72355i	−0.324692	+	0.945820i	$0.605261\pi$
$152$	−2.18065	+	3.77699i	−0.176874	+	0.306354i
$153$	−11.0628	+	7.35554i	−0.894376	+	0.594660i
$154$	−0.535008	−	5.34090i	−0.0431122	−	0.430382i
$155$	−1.59232	−	1.89765i	−0.127898	−	0.152423i
$156$	−0.470643	+	0.719485i	−0.0376816	+	0.0576049i
$157$	2.86792	+	0.505692i	0.228885	+	0.0403586i	0.286914	−	0.957956i	$-0.407371\pi$
$157$	2.86792	+	0.505692i	0.228885	+	0.0403586i	−0.0580292	+	0.998315i	$0.518482\pi$
$158$	9.13954	−	10.8921i	0.727103	−	0.866527i
$159$	2.67921	−	11.4316i	0.212475	−	0.906585i
$160$	0.650797	−	1.78805i	0.0514500	−	0.141358i
$161$	−5.81948	+	12.9009i	−0.458639	+	1.01674i
$162$	−8.59569	+	2.66722i	−0.675341	+	0.209556i
$163$	−7.96674			−0.624003			−0.312002	−	0.950082i	$-0.600999\pi$
$163$	−7.96674			−0.624003			−0.312002	+	0.950082i	$0.600999\pi$
$164$	−1.67326	−	0.609017i	−0.130660	−	0.0475562i
$165$	−1.52572	+	6.50993i	−0.118777	+	0.506798i
$166$	−7.33386	+	8.74015i	−0.569218	+	0.678368i
$167$	2.62148	−	14.8671i	0.202856	−	1.15045i	−0.697922	−	0.716174i	$-0.745892\pi$
$167$	2.62148	−	14.8671i	0.202856	−	1.15045i	0.900778	−	0.434280i	$-0.142997\pi$
$168$	−3.86361	+	2.46425i	−0.298084	+	0.190121i
$169$	9.76983	−	8.19786i	0.751526	−	0.630605i
$170$	7.29731	−	4.21311i	0.559678	−	0.323130i
$171$	−13.0578	+	0.825982i	−0.998553	+	0.0631644i
$172$	−0.559447	+	0.968991i	−0.0426575	+	0.0738849i
$173$	−2.11780	−	12.0106i	−0.161013	−	0.913151i	−0.953080	−	0.302717i	$-0.902106\pi$
$173$	−2.11780	−	12.0106i	−0.161013	−	0.913151i	0.792067	−	0.610434i	$-0.209005\pi$
$174$	6.28682	+	8.40078i	0.476602	+	0.636862i
$175$	3.63922	+	0.272335i	0.275099	+	0.0205866i
$176$	−0.693882	−	1.90642i	−0.0523033	−	0.143702i
$177$	1.57271	−	3.67113i	0.118212	−	0.275939i
$178$	−2.15833	+	0.380573i	−0.161774	+	0.0285251i
$179$	−21.6760	−	12.5146i	−1.62014	−	0.935388i	−0.986881	−	0.161447i	$-0.948384\pi$
$179$	−21.6760	−	12.5146i	−1.62014	−	0.935388i	−0.633258	−	0.773941i	$-0.718283\pi$
$180$	5.54789	−	1.34417i	0.413516	−	0.100189i
$181$	−11.4967	+	6.63764i	−0.854545	+	0.493372i	−0.862182	−	0.506599i	$-0.830902\pi$
$181$	−11.4967	+	6.63764i	−0.854545	+	0.493372i	0.00763694	+	0.999971i	$0.497569\pi$
$182$	−1.26416	+	0.355824i	−0.0937059	+	0.0263754i
$183$	4.03335	+	7.98131i	0.298154	+	0.589996i
$184$	−0.928885	+	5.26797i	−0.0684783	+	0.388360i
$185$	−9.40080	−	7.88821i	−0.691161	−	0.579953i
$186$	0.652107	+	2.15856i	0.0478148	+	0.158273i
$187$	3.07273	−	8.44225i	0.224700	−	0.617358i
$188$	−11.5713			−0.843927
$189$	−12.5737	−	5.55890i	−0.914604	−	0.404351i
$190$	8.29868			0.602049
$191$	6.40341	−	17.5932i	0.463334	−	1.27300i	−0.459629	−	0.888111i	$-0.652018\pi$
$191$	6.40341	−	17.5932i	0.463334	−	1.27300i	0.922963	−	0.384889i	$-0.125760\pi$
$192$	−1.18546	+	1.26281i	−0.0855529	+	0.0911356i
$193$	7.98609	+	6.70113i	0.574851	+	0.482358i	0.883252	−	0.468899i	$-0.155349\pi$
$193$	7.98609	+	6.70113i	0.574851	+	0.482358i	−0.308400	+	0.951257i	$0.599794\pi$
$194$	−2.06420	+	11.7066i	−0.148201	+	0.840488i
$195$	1.63339	+	0.0910423i	0.116970	+	0.00651967i
$196$	−6.92204	−	1.04183i	−0.494431	−	0.0744166i
$197$	20.2464	−	11.6892i	1.44249	−	0.832824i	0.444477	−	0.895790i	$-0.353389\pi$
$197$	20.2464	−	11.6892i	1.44249	−	0.832824i	0.998016	+	0.0629664i	$0.0200561\pi$
$198$	3.61007	−	4.90007i	0.256557	−	0.348233i
$199$	−2.99021	−	1.72640i	−0.211971	−	0.122381i	0.390256	−	0.920706i	$-0.372386\pi$
$199$	−2.99021	−	1.72640i	−0.211971	−	0.122381i	−0.602227	+	0.798325i	$0.705720\pi$
$200$	1.35839	−	0.239520i	0.0960524	−	0.0169366i
$201$	−18.2291	+	2.17684i	−1.28578	+	0.153542i
$202$	−1.56130	−	4.28965i	−0.109853	−	0.301818i
$203$	−1.19608	+	15.9832i	−0.0839481	+	1.12180i
$204$	−7.61596	+	0.909461i	−0.533224	+	0.0636750i
$205$	0.588358	+	3.33674i	0.0410927	+	0.233048i
$206$	−7.71793	+	13.3678i	−0.537734	+	0.931382i
$207$	−14.7033	+	6.42969i	−1.02195	+	0.446894i
$208$	−0.429873	+	0.248187i	−0.0298063	+	0.0172087i
$209$	6.77802	−	5.68743i	0.468845	−	0.393408i
$210$	7.73661	+	4.02227i	0.533877	+	0.277563i
$211$	−3.21452	+	18.2305i	−0.221297	+	1.25504i	0.648343	+	0.761349i	$0.275462\pi$
$211$	−3.21452	+	18.2305i	−0.221297	+	1.25504i	−0.869639	+	0.493687i	$0.835649\pi$
$212$	4.35738	−	5.19293i	0.299266	−	0.356652i
$213$	1.00369	+	0.942208i	0.0687718	+	0.0645590i
$214$	0.717741	+	0.261236i	0.0490637	+	0.0178577i
$215$	2.12904			0.145199
$216$	−5.12383	−	0.863943i	−0.348632	−	0.0587839i
$217$	−1.41632	+	3.13977i	−0.0961459	+	0.213141i
$218$	−3.01210	+	8.27568i	−0.204005	+	0.560500i
$219$	21.3543	−	6.45121i	1.44299	−	0.435933i
$220$	−2.48139	+	2.95721i	−0.167295	+	0.199375i
$221$	−2.16471	−	0.381697i	−0.145614	−	0.0256757i
$222$	5.03828	+	9.96989i	0.338147	+	0.669135i
$223$	9.20664	+	10.9720i	0.616522	+	0.734743i	0.980468	−	0.196677i	$-0.0630152\pi$
$223$	9.20664	+	10.9720i	0.616522	+	0.734743i	−0.363946	+	0.931420i	$0.618571\pi$
$224$	−2.63258	+	0.263710i	−0.175896	+	0.0176199i
$225$	2.85468	+	2.99567i	0.190312	+	0.199711i
$226$	−0.390496	+	0.676358i	−0.0259754	+	0.0449907i
$227$	3.76382	+	21.3457i	0.249813	+	1.41676i	0.809044	+	0.587749i	$0.199986\pi$
$227$	3.76382	+	21.3457i	0.249813	+	1.41676i	−0.559230	+	0.829012i	$0.688903\pi$
$228$	−6.94363	−	2.97465i	−0.459853	−	0.197001i
$229$	−4.13750	−	11.3677i	−0.273414	−	0.751199i	−0.998071	−	0.0620886i	$-0.980224\pi$
$229$	−4.13750	−	11.3677i	−0.273414	−	0.751199i	0.724657	−	0.689110i	$-0.241998\pi$
$230$	9.56470	−	3.48127i	0.630678	−	0.229548i
$231$	9.07558	−	2.01701i	0.597129	−	0.132709i
$232$	1.05196	+	5.96594i	0.0690643	+	0.391683i
$233$	6.96562	+	4.02160i	0.456333	+	0.263464i	0.710501	−	0.703696i	$-0.248468\pi$
$233$	6.96562	+	4.02160i	0.456333	+	0.263464i	−0.254168	+	0.967160i	$0.581802\pi$
$234$	−1.33405	−	0.661663i	−0.0872096	−	0.0432543i
$235$	11.0090	+	19.0681i	0.718147	+	1.24387i
$236$	1.76637	−	1.48216i	0.114981	−	0.0964805i
$237$	20.6096	+	13.4815i	1.33874	+	0.875719i
$238$	−9.68110	−	6.59896i	−0.627532	−	0.427747i
$239$	−11.3847	+	13.5678i	−0.736416	+	0.877627i	−0.996115	−	0.0880631i	$-0.971932\pi$
$239$	−11.3847	+	13.5678i	−0.736416	+	0.877627i	0.259699	+	0.965690i	$0.416377\pi$
$240$	3.20880	+	0.752042i	0.207127	+	0.0485441i
$241$	5.68505	−	15.6195i	0.366206	−	1.00614i	−0.610585	−	0.791950i	$-0.709066\pi$
$241$	5.68505	−	15.6195i	0.366206	−	1.00614i	0.976791	−	0.214193i	$-0.0687120\pi$
$242$		−	6.88408i		−	0.442525i
$243$	−6.35250	−	14.2354i	−0.407513	−	0.913199i
$244$			5.16299i			0.330526i
$245$	4.86883	+	12.3979i	0.311058	+	0.792070i
$246$	0.703763	−	3.00280i	0.0448703	−	0.191452i
$247$	−1.65836	−	1.39153i	−0.105519	−	0.0885408i
$248$	−0.226068	+	1.28209i	−0.0143553	+	0.0814131i
$249$	−16.5378	−	10.8180i	−1.04804	−	0.685563i
$250$	−7.80256	−	9.29873i	−0.493477	−	0.588103i
$251$	−8.39153	−	14.5346i	−0.529669	−	0.917413i	−0.999401	−	0.0346043i	$-0.988983\pi$
$251$	−8.39153	−	14.5346i	−0.529669	−	0.917413i	0.469732	−	0.882809i	$-0.344350\pi$
$252$	−5.03157	−	6.13867i	−0.316959	−	0.386700i
$253$	5.42620	−	9.39845i	0.341142	−	0.590876i
$254$	−12.0770	+	2.12950i	−0.757778	+	0.133617i
$255$	8.74451	+	11.6849i	0.547603	+	0.731736i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−15.3784	+	5.59727i	−0.959277	+	0.349148i	−0.773750	−	0.633491i	$-0.781621\pi$
$257$	−15.3784	+	5.59727i	−0.959277	+	0.349148i	−0.185527	+	0.982639i	$0.559399\pi$
$258$	−1.78140	−	0.763150i	−0.110905	−	0.0475116i
$259$	−4.20878	+	16.5362i	−0.261521	+	1.02751i
$260$	0.817964	+	0.472252i	0.0507280	+	0.0292878i
$261$	−13.1568	+	12.5376i	−0.814385	+	0.776056i
$262$	16.4741	−	9.51132i	1.01777	−	0.587611i
$263$	−13.9625	−	16.6399i	−0.860964	−	1.02606i	−0.999363	−	0.0356809i	$-0.988640\pi$
$263$	−13.9625	−	16.6399i	−0.860964	−	1.02606i	0.138399	−	0.990377i	$-0.455804\pi$
$264$	3.13622	−	1.58489i	0.193021	−	0.0975432i
$265$	−12.7029	−	2.23987i	−0.780334	−	0.137594i
$266$	−5.00764	−	10.3957i	−0.307038	−	0.637398i
$267$	−1.09779	−	3.63381i	−0.0671834	−	0.222386i
$268$	−9.96015	−	3.62520i	−0.608413	−	0.221444i
$269$	31.8076			1.93935			0.969673	−	0.244407i	$-0.0785934\pi$
$269$	31.8076			1.93935			0.969673	+	0.244407i	$0.0785934\pi$
$270$	3.45115	+	9.26539i	0.210030	+	0.563873i
$271$			6.10915i			0.371104i	0.982634	+	0.185552i	$0.0594074\pi$
$271$			6.10915i			0.371104i	−0.982634	+	0.185552i	$0.940593\pi$
$272$	−4.16126	−	1.51457i	−0.252313	−	0.0918345i
$273$	−0.871584	−	2.10107i	−0.0527506	−	0.127162i
$274$	11.4890	+	9.64045i	0.694078	+	0.582401i
$275$	−2.75586	−	0.485932i	−0.166185	−	0.0293028i
$276$	−9.25079	−	0.515622i	−0.556832	−	0.0310368i
$277$	18.8180	−	15.7902i	1.13066	−	0.948739i	0.131569	−	0.991307i	$-0.457998\pi$
$277$	18.8180	−	15.7902i	1.13066	−	0.948739i	0.999094	+	0.0425681i	$0.0135539\pi$
$278$	9.78680	+	16.9512i	0.586973	+	1.01667i
$279$	−3.57843	+	1.56483i	−0.214235	+	0.0936837i
$280$	2.93920	+	4.08726i	0.175651	+	0.244261i
$281$	13.3983	−	2.36248i	0.799276	−	0.140934i	0.240930	−	0.970542i	$-0.422547\pi$
$281$	13.3983	−	2.36248i	0.799276	−	0.140934i	0.558345	+	0.829609i	$0.311436\pi$
$282$	−2.37645	−	19.9008i	−0.141516	−	1.18507i
$283$	7.62554	+	20.9510i	0.453291	+	1.24541i	0.930394	+	0.366560i	$0.119464\pi$
$283$	7.62554	+	20.9510i	0.453291	+	1.24541i	−0.477103	+	0.878847i	$0.658313\pi$
$284$	0.271840	+	0.746874i	0.0161307	+	0.0443188i
$285$	1.70433	+	14.2723i	0.100956	+	0.845420i
$286$	0.991733	−	0.174869i	0.0586424	−	0.0103402i
$287$	3.82487	−	2.75051i	0.225775	−	0.162357i
$288$	−2.41529	−	1.77944i	−0.142322	−	0.104854i
$289$	−1.30499	−	2.26031i	−0.0767643	−	0.132960i
$290$	8.83030	−	7.40950i	0.518533	−	0.435101i
$291$	−20.5574	−	1.14583i	−1.20509	−	0.0671698i
$292$	12.6836	+	2.23646i	0.742251	+	0.130879i
$293$	8.21733	+	6.89516i	0.480061	+	0.402819i	0.850449	−	0.526058i	$-0.176331\pi$
$293$	8.21733	+	6.89516i	0.480061	+	0.402819i	−0.370387	+	0.928877i	$0.620775\pi$
$294$	0.370169	−	12.1187i	0.0215887	−	0.706777i
$295$	−4.12295	−	1.50063i	−0.240047	−	0.0873700i
$296$			6.44937i			0.374862i
$297$	9.16871	+	5.20237i	0.532023	+	0.301872i
$298$	1.44687			0.0838151
$299$	−2.49510	−	0.908141i	−0.144295	−	0.0525191i
$300$	0.690912	+	2.28701i	0.0398898	+	0.132040i
$301$	−1.28472	−	2.66702i	−0.0740498	−	0.153724i
$302$	−21.1793	−	3.73449i	−1.21873	−	0.214895i
$303$	7.05682	−	3.56616i	0.405404	−	0.204871i
$304$	−2.80338	−	3.34094i	−0.160785	−	0.191616i
$305$	8.50796	−	4.91207i	0.487164	−	0.281264i
$306$	−3.12824	−	12.9114i	−0.178830	−	0.738095i
$307$	3.02853	+	1.74852i	0.172847	+	0.0997934i	0.583928	−	0.811806i	$-0.301515\pi$
$307$	3.02853	+	1.74852i	0.172847	+	0.0997934i	−0.411081	+	0.911599i	$0.634848\pi$
$308$	5.20179	+	1.32395i	0.296400	+	0.0754392i
$309$	−24.5755	−	10.5281i	−1.39805	−	0.598925i
$310$	2.32781	−	0.847255i	0.132211	−	0.0481208i
$311$	−17.7719	+	6.46844i	−1.00775	+	0.366792i	−0.792569	−	0.609782i	$-0.791257\pi$
$311$	−17.7719	+	6.46844i	−1.00775	+	0.366792i	−0.215183	+	0.976574i	$0.569035\pi$
$312$	−0.515125	−	0.688338i	−0.0291632	−	0.0389695i
$313$	22.2608	−	3.92518i	1.25826	−	0.221864i	0.495533	−	0.868589i	$-0.334973\pi$
$313$	22.2608	−	3.92518i	1.25826	−	0.221864i	0.762723	+	0.646725i	$0.223862\pi$
$314$	−1.45608	+	2.52201i	−0.0821714	+	0.142325i
$315$	−5.32872	+	14.1317i	−0.300239	+	0.796234i
$316$	7.10930	+	12.3137i	0.399929	+	0.692698i
$317$	14.3036	+	17.0464i	0.803373	+	0.957423i	0.999733	−	0.0231093i	$-0.00735656\pi$
$317$	14.3036	+	17.0464i	0.803373	+	0.957423i	−0.196360	+	0.980532i	$0.562912\pi$
$318$	9.82585	+	6.42747i	0.551006	+	0.360435i
$319$	2.13418	−	12.1035i	0.119491	−	0.677669i
$320$	1.45763	+	1.22310i	0.0814841	+	0.0683733i
$321$	−0.301877	+	1.28804i	−0.0168491	+	0.0718916i
$322$	−10.1325	−	9.88090i	−0.564664	−	0.550641i
$323$		−	19.3132i		−	1.07461i
$324$	0.433536	−	8.98955i	0.0240853	−	0.499420i
$325$			0.684670i			0.0379787i
$326$	2.72479	−	7.48629i	0.150912	−	0.414627i
$327$	−14.8514	−	3.48070i	−0.821284	−	0.192483i
$328$	1.14458	−	1.36405i	0.0631987	−	0.0753173i
$329$	17.2433	−	25.2970i	0.950654	−	1.39467i
$330$	−5.59551	−	3.66024i	−0.308023	−	0.201490i
$331$	4.66208	−	3.91195i	0.256251	−	0.215020i	−0.505607	−	0.862764i	$-0.668732\pi$
$331$	4.66208	−	3.91195i	0.256251	−	0.215020i	0.761858	+	0.647744i	$0.224287\pi$
$332$	−5.70473	−	9.88088i	−0.313088	−	0.542284i
$333$	−16.1118	+	10.7126i	−0.882922	+	0.587044i
$334$	13.0739	+	7.54824i	0.715374	+	0.413021i
$335$	3.50222	+	19.8621i	0.191347	+	1.08518i
$336$	−0.994200	−	4.47343i	−0.0542380	−	0.244046i
$337$	−0.0898958	+	0.0327194i	−0.00489694	+	0.00178234i	−0.344467	−	0.938798i	$-0.611941\pi$
$337$	−0.0898958	+	0.0327194i	−0.00489694	+	0.00178234i	0.339571	+	0.940581i	$0.389718\pi$
$338$	4.36199	+	11.9845i	0.237261	+	0.651870i
$339$	−1.24342	−	0.532681i	−0.0675333	−	0.0289312i
$340$	1.46320	+	8.29820i	0.0793530	+	0.450033i
$341$	1.32060	−	2.28735i	0.0715146	−	0.123867i
$342$	3.68985	−	12.5528i	0.199524	−	0.678777i
$343$	12.5927	−	13.5803i	0.679940	−	0.733268i
$344$	−0.719212	−	0.857123i	−0.0387773	−	0.0462130i
$345$	7.95154	+	15.7347i	0.428096	+	0.847129i
$346$	12.0106	+	2.11780i	0.645696	+	0.113854i
$347$	−2.74848	+	3.27551i	−0.147546	+	0.175839i	−0.834755	−	0.550621i	$-0.814391\pi$
$347$	−2.74848	+	3.27551i	−0.147546	+	0.175839i	0.687209	+	0.726459i	$0.258835\pi$
$348$	−10.0444	+	3.03444i	−0.538435	+	0.162663i
$349$	−3.88566	+	10.6758i	−0.207994	+	0.571460i	−0.999196	−	0.0400958i	$-0.987234\pi$
$349$	−3.88566	+	10.6758i	−0.207994	+	0.571460i	0.791201	+	0.611556i	$0.209456\pi$
$350$	−1.50060	+	3.32660i	−0.0802103	+	0.177814i
$351$	0.863971	−	2.43023i	0.0461153	−	0.129716i
$352$	2.02877			0.108134
$353$	−6.63619	−	2.41538i	−0.353209	−	0.128558i	0.159321	−	0.987227i	$-0.449069\pi$
$353$	−6.63619	−	2.41538i	−0.353209	−	0.128558i	−0.512530	+	0.858669i	$0.671292\pi$
$354$	2.91184	+	2.73346i	0.154762	+	0.145282i
$355$	0.972126	−	1.15853i	0.0515951	−	0.0614887i
$356$	0.380573	−	2.15833i	0.0201703	−	0.114391i
$357$	9.36086	−	18.0051i	0.495429	−	0.952932i
$358$	19.1735	−	16.0885i	1.01335	−	0.850304i
$359$	4.10550	−	2.37031i	0.216680	−	0.125100i	−0.387732	−	0.921772i	$-0.626741\pi$
$359$	4.10550	−	2.37031i	0.216680	−	0.125100i	0.604412	+	0.796672i	$0.293408\pi$
$360$	−0.634382	+	5.67305i	−0.0334348	+	0.298996i
$361$	0.0104267	−	0.0180596i	0.000548774	−	0.000950505i
$362$	−2.30523	−	13.0736i	−0.121160	−	0.687133i
$363$	11.8395	−	1.41381i	0.621410	−	0.0742058i
$364$	0.0980034	−	1.30962i	0.00513677	−	0.0686429i
$365$	−8.38178	−	23.0287i	−0.438722	−	1.20538i
$366$	−8.87947	+	1.06034i	−0.464137	+	0.0554250i
$367$	27.7686	−	4.89635i	1.44951	−	0.255587i	0.607184	−	0.794561i	$-0.292299\pi$
$367$	27.7686	−	4.89635i	1.44951	−	0.255587i	0.842322	+	0.538974i	$0.181188\pi$
$368$	−4.63258	−	2.67462i	−0.241490	−	0.139424i
$369$	5.30885	+	0.593656i	0.276368	+	0.0309045i
$370$	10.6278	−	6.13594i	0.552511	−	0.318992i
$371$	4.85941	+	17.2644i	0.252288	+	0.896322i
$372$	−2.25141	−	0.125490i	−0.116730	−	0.00650634i
$373$	0.741909	−	4.20757i	0.0384146	−	0.217860i	−0.959558	−	0.281513i	$-0.909164\pi$
$373$	0.741909	−	4.20757i	0.0384146	−	0.217860i	0.997972	+	0.0636527i	$0.0202750\pi$
$374$	6.88218	+	5.77484i	0.355869	+	0.298610i
$375$	14.3898	−	15.3288i	0.743086	−	0.791576i
$376$	3.95763	−	10.8735i	0.204099	−	0.560758i
$377$	−3.00703			−0.154870
$378$	9.52413	−	9.91418i	0.489868	−	0.509931i
$379$	−0.349234			−0.0179389			−0.00896947	−	0.999960i	$-0.502855\pi$
$379$	−0.349234			−0.0179389			−0.00896947	+	0.999960i	$0.502855\pi$
$380$	−2.83831	+	7.79820i	−0.145602	+	0.400039i
$381$	−6.14268	−	20.3330i	−0.314699	−	1.04169i
$382$	14.3421	+	12.0345i	0.733807	+	0.615737i
$383$	−2.57833	+	14.6224i	−0.131747	+	0.747172i	0.845324	+	0.534255i	$0.179408\pi$
$383$	−2.57833	+	14.6224i	−0.131747	+	0.747172i	−0.977070	+	0.212917i	$0.931703\pi$
$384$	−0.781206	−	1.54587i	−0.0398657	−	0.0788874i
$385$	−2.76728	−	9.83151i	−0.141034	−	0.501060i
$386$	−9.02840	+	5.21255i	−0.459534	+	0.265312i
$387$	0.946637	−	3.22044i	0.0481202	−	0.163704i
$388$	−10.2946	−	5.94362i	−0.522631	−	0.301741i
$389$	19.3167	−	3.40606i	0.979397	−	0.172694i	0.339040	−	0.940772i	$-0.389898\pi$
$389$	19.3167	−	3.40606i	0.979397	−	0.172694i	0.640357	+	0.768078i	$0.278787\pi$
$390$	−0.644205	+	1.50375i	−0.0326206	+	0.0761453i
$391$	−8.10181	−	22.2595i	−0.409726	−	1.12571i
$392$	3.34648	−	6.14826i	0.169023	−	0.310534i
$393$	19.7412	+	26.3793i	0.995812	+	1.33066i
$394$	4.05963	+	23.0233i	0.204521	+	1.15990i
$395$	13.5276	−	23.4305i	0.680647	−	1.17892i
$396$	3.36984	+	5.06828i	0.169341	+	0.254691i
$397$	−23.5624	+	13.6038i	−1.18256	+	0.682753i	−0.956606	−	0.291385i	$-0.905884\pi$
$397$	−23.5624	+	13.6038i	−1.18256	+	0.682753i	−0.225956	+	0.974137i	$0.572551\pi$
$398$	2.64500	−	2.21942i	0.132582	−	0.111249i
$399$	16.8503	−	10.7473i	0.843572	−	0.538037i
$400$	−0.239520	+	1.35839i	−0.0119760	+	0.0679193i
$401$	−7.56377	+	9.01415i	−0.377717	+	0.450145i	−0.921092	−	0.389344i	$-0.872702\pi$
$401$	−7.56377	+	9.01415i	−0.377717	+	0.450145i	0.543375	+	0.839490i	$0.317146\pi$
$402$	4.18917	−	17.8743i	0.208937	−	0.891489i
$403$	−0.607245	−	0.221019i	−0.0302490	−	0.0110097i
$404$	4.56495			0.227115
$405$	−15.2261	+	7.83826i	−0.756592	+	0.389486i
$406$	−14.6102	−	6.59052i	−0.725093	−	0.327082i
$407$	4.47510	−	12.2952i	0.221822	−	0.609452i
$408$	1.75020	−	7.46771i	0.0866477	−	0.369707i
$409$	−1.82969	+	2.18054i	−0.0904725	+	0.107821i	−0.809381	−	0.587283i	$-0.800197\pi$
$409$	−1.82969	+	2.18054i	−0.0904725	+	0.107821i	0.718909	+	0.695104i	$0.244642\pi$
$410$	−3.33674	−	0.588358i	−0.164790	−	0.0290569i
$411$	−14.2204	+	21.7391i	−0.701441	+	1.07231i
$412$	−9.92198	−	11.8246i	−0.488821	−	0.582554i
$413$	0.608072	+	6.07028i	0.0299213	+	0.298699i
$414$	−1.01309	−	16.0157i	−0.0497906	−	0.787129i
$415$	−10.8550	+	18.8014i	−0.532850	+	0.922923i
$416$	−0.0861946	−	0.488834i	−0.00422604	−	0.0239670i
$417$	−27.1433	+	20.3130i	−1.32921	+	0.994731i
$418$	3.02622	+	8.31447i	0.148017	+	0.406674i
$419$	−13.3889	+	4.87314i	−0.654088	+	0.238069i	−0.647682	−	0.761911i	$-0.724261\pi$
$419$	−13.3889	+	4.87314i	−0.654088	+	0.238069i	−0.00640640	+	0.999979i	$0.502039\pi$
$420$	−6.42577	+	5.89434i	−0.313546	+	0.287615i
$421$	−0.0927017	−	0.525737i	−0.00451800	−	0.0256229i	0.982465	−	0.186445i	$-0.0596966\pi$
$421$	−0.0927017	−	0.525737i	−0.00451800	−	0.0256229i	−0.986983	+	0.160822i	$0.948585\pi$
$422$	−16.0316	−	9.25584i	−0.780406	−	0.450567i
$423$	33.7379	−	8.17420i	1.64039	−	0.397443i
$424$	3.38944	+	5.87068i	0.164606	+	0.285106i
$425$	−4.67912	+	3.92625i	−0.226971	+	0.190451i
$426$	−1.22867	+	0.620907i	−0.0595292	+	0.0300831i
$427$	−11.2872	−	7.69375i	−0.546227	−	0.372326i
$428$	−0.490964	+	0.585108i	−0.0237316	+	0.0282822i
$429$	0.504422	+	1.66970i	0.0243537	+	0.0806139i
$430$	−0.728173	+	2.00064i	−0.0351156	+	0.0964794i
$431$		−	17.9847i		−	0.866295i	−0.901323	−	0.433147i	$-0.857403\pi$
$431$		−	17.9847i		−	0.866295i	0.901323	−	0.433147i	$-0.142597\pi$
$432$	2.56429	−	4.51934i	0.123375	−	0.217437i
$433$			31.0680i			1.49303i	0.665368	+	0.746515i	$0.268275\pi$
$433$			31.0680i			1.49303i	−0.665368	+	0.746515i	$0.731725\pi$
$434$	−2.46601	−	2.40477i	−0.118372	−	0.115433i
$435$	14.5566	+	13.6649i	0.697936	+	0.655182i
$436$	−6.74640	−	5.66090i	−0.323094	−	0.271108i
$437$	4.05114	−	22.9752i	0.193792	−	1.09905i
$438$	−1.24145	+	22.2730i	−0.0593190	+	1.06424i
$439$	−0.928207	−	1.10619i	−0.0443009	−	0.0527958i	0.743439	−	0.668804i	$-0.233193\pi$
$439$	−0.928207	−	1.10619i	−0.0443009	−	0.0527958i	−0.787740	+	0.616008i	$0.788749\pi$
$440$	−1.93018	−	3.34317i	−0.0920177	−	0.159379i
$441$	20.9182	−	1.85224i	0.996103	−	0.0882018i
$442$	1.09905	−	1.90361i	0.0522766	−	0.0905457i
$443$	−2.55681	+	0.450834i	−0.121478	+	0.0214198i	−0.234056	−	0.972223i	$-0.575200\pi$
$443$	−2.55681	+	0.450834i	−0.121478	+	0.0214198i	0.112579	+	0.993643i	$0.464089\pi$
$444$	−11.0918	+	1.32453i	−0.526395	+	0.0628595i
$445$	−3.91874	+	1.42631i	−0.185766	+	0.0676134i
$446$	−13.4592	+	4.89875i	−0.637312	+	0.231963i
$447$	0.297150	+	2.48838i	0.0140547	+	0.117696i
$448$	0.652588	−	2.56401i	0.0308319	−	0.121138i
$449$	−14.4558	−	8.34606i	−0.682211	−	0.393875i	0.118476	−	0.992957i	$-0.462199\pi$
$449$	−14.4558	−	8.34606i	−0.682211	−	0.393875i	−0.800688	+	0.599082i	$0.795532\pi$
$450$	−3.79137	+	1.65794i	−0.178727	+	0.0781562i
$451$	−3.12854	+	1.80627i	−0.147317	+	0.0850537i
$452$	−0.502012	−	0.598274i	−0.0236126	−	0.0281404i
$453$	2.07300	−	37.1918i	0.0973983	−	1.74742i
$454$	−21.3457	−	3.76382i	−1.00180	−	0.176645i
$455$	−2.25133	+	1.08448i	−0.105544	+	0.0508412i
$456$	5.17012	−	5.50749i	0.242113	−	0.257912i
$457$	−33.4172	−	12.1629i	−1.56319	−	0.568955i	−0.591727	−	0.806138i	$-0.701554\pi$
$457$	−33.4172	−	12.1629i	−1.56319	−	0.568955i	−0.971465	+	0.237183i	$0.923776\pi$
$458$	12.0973			0.565267
$459$	21.5630	−	8.03171i	1.00647	−	0.374888i
$460$			10.1785i			0.474577i
$461$	8.55133	+	3.11243i	0.398275	+	0.144960i	0.533389	−	0.845870i	$-0.320918\pi$
$461$	8.55133	+	3.11243i	0.398275	+	0.144960i	−0.135115	+	0.990830i	$0.543140\pi$
$462$	−1.20866	+	9.21811i	−0.0562321	+	0.428865i
$463$	−25.3764	−	21.2933i	−1.17934	−	0.989585i	−0.999983	−	0.00580123i	$-0.998153\pi$
$463$	−25.3764	−	21.2933i	−1.17934	−	0.989585i	−0.179358	−	0.983784i	$-0.557402\pi$
$464$	−5.96594	−	1.05196i	−0.276962	−	0.0488358i
$465$	1.93521	+	3.82944i	0.0897431	+	0.177586i
$466$	−6.16145	+	5.17007i	−0.285424	+	0.239499i
$467$	10.4311	+	18.0672i	0.482693	+	0.836050i	0.999803	−	0.0198699i	$-0.00632521\pi$
$467$	10.4311	+	18.0672i	0.482693	+	0.836050i	−0.517109	+	0.855919i	$0.672992\pi$
$468$	1.07803	−	1.02730i	0.0498321	−	0.0474868i
$469$	22.7677	−	16.3725i	1.05131	−	0.756012i
$470$	−21.6835	+	3.82338i	−1.00018	+	0.176359i
$471$	−4.63647	−	1.98626i	−0.213637	−	0.0915220i
$472$	0.788642	+	2.16678i	0.0363002	+	0.0997339i
$473$	0.776381	+	2.13309i	0.0356980	+	0.0980795i
$474$	−19.7174	+	14.7557i	−0.905649	+	0.677752i
$475$	−5.92432	+	1.04462i	−0.271826	+	0.0479303i
$476$	9.51212	−	6.84028i	0.435987	−	0.313524i
$477$	−9.03620	+	18.2188i	−0.413739	+	0.834184i
$478$	−8.85574	−	15.3386i	−0.405052	−	0.701571i
$479$	−23.0255	+	19.3207i	−1.05206	+	0.882787i	−0.993309	−	0.115486i	$-0.963158\pi$
$479$	−23.0255	+	19.3207i	−1.05206	+	0.882787i	−0.0587551	+	0.998272i	$0.518713\pi$
$480$	−1.80416	+	2.75807i	−0.0823484	+	0.125888i
$481$	−3.15267	−	0.555901i	−0.143749	−	0.0253469i
$482$	12.7332	+	10.6844i	0.579980	+	0.486661i
$483$	14.9125	−	19.4555i	0.678544	−	0.885257i
$484$	6.46891	+	2.35449i	0.294042	+	0.107022i
$485$			22.6191i			1.02708i
$486$	15.5496	−	1.10061i	0.705342	−	0.0499248i
$487$	10.0338			0.454676			0.227338	−	0.973816i	$-0.426998\pi$
$487$	10.0338			0.454676			0.227338	+	0.973816i	$0.426998\pi$
$488$	−4.85162	−	1.76585i	−0.219623	−	0.0799361i
$489$	13.4348	+	3.14868i	0.607541	+	0.142388i
$490$	−13.3154	+	0.334883i	−0.601529	+	0.0151285i
$491$	25.6047	+	4.51479i	1.15552	+	0.203750i	0.718385	−	0.695645i	$-0.244882\pi$
$491$	25.6047	+	4.51479i	1.15552	+	0.203750i	0.437137	+	0.899395i	$0.355993\pi$
$492$	2.58101	+	1.68834i	0.116361	+	0.0761162i
$493$	−17.2438	−	20.5504i	−0.776623	−	0.925543i
$494$	1.87480	−	1.08242i	0.0843513	−	0.0487002i
$495$	5.14582	−	10.3751i	0.231288	−	0.466324i
$496$	−1.12745	−	0.650936i	−0.0506242	−	0.0292279i
$497$	−2.03789	−	0.518681i	−0.0914118	−	0.0232660i
$498$	15.8219	−	11.8405i	0.708994	−	0.530583i
$499$	−17.2458	+	6.27695i	−0.772028	+	0.280995i	−0.697844	−	0.716250i	$-0.745857\pi$
$499$	−17.2458	+	6.27695i	−0.772028	+	0.280995i	−0.0741834	+	0.997245i	$0.523635\pi$
$500$	11.4066	−	4.15166i	0.510118	−	0.185668i
$501$	−10.2967	+	24.0352i	−0.460021	+	1.07381i
$502$	16.5281	−	2.91435i	0.737685	−	0.130074i
$503$	−0.680482	+	1.17863i	−0.0303412	+	0.0525525i	−0.880797	−	0.473494i	$-0.842993\pi$
$503$	−0.680482	+	1.17863i	−0.0303412	+	0.0525525i	0.850456	+	0.526046i	$0.176326\pi$
$504$	7.48936	−	2.62858i	0.333603	−	0.117086i
$505$	−4.34310	−	7.52246i	−0.193265	−	0.334745i
$506$	6.97579	+	8.31342i	0.310111	+	0.369576i
$507$	−19.7154	+	9.96319i	−0.875594	+	0.442481i
$508$	2.12950	−	12.0770i	0.0944813	−	0.535830i
$509$	24.4040	+	20.4774i	1.08169	+	0.907644i	0.996060	−	0.0886833i	$-0.0282659\pi$
$509$	24.4040	+	20.4774i	1.08169	+	0.907644i	0.0856280	+	0.996327i	$0.472710\pi$
$510$	−13.9710	+	4.22069i	−0.618646	+	0.186895i
$511$	−23.7901	+	24.3959i	−1.05241	+	1.07921i
$512$		−	1.00000i		−	0.0441942i
$513$	22.3465	+	3.76791i	0.986622	+	0.166357i
$514$		−	16.3653i		−	0.721844i
$515$	−10.0456	+	27.6001i	−0.442662	+	1.21621i
$516$	1.32640	−	1.41295i	0.0583915	−	0.0622018i
$517$	−15.0898	+	17.9834i	−0.663651	+	0.790908i
$518$	−14.0995	−	9.61068i	−0.619496	−	0.422269i
$519$	−1.17559	+	21.0912i	−0.0516025	+	0.925801i
$520$	−0.723531	+	0.607115i	−0.0317289	+	0.0266237i
$521$	−8.94852	−	15.4993i	−0.392042	−	0.679036i	0.600677	−	0.799492i	$-0.294898\pi$
$521$	−8.94852	−	15.4993i	−0.392042	−	0.679036i	−0.992719	+	0.120456i	$0.961564\pi$
$522$	−7.28157	−	16.6514i	−0.318706	−	0.728813i
$523$	−26.9434	−	15.5558i	−1.17815	−	0.680206i	−0.222566	−	0.974918i	$-0.571443\pi$
$523$	−26.9434	−	15.5558i	−1.17815	−	0.680206i	−0.955586	+	0.294711i	$0.904776\pi$
$524$	3.30325	+	18.7336i	0.144303	+	0.818383i
$525$	−6.02938	−	1.89758i	−0.263144	−	0.0828171i
$526$	20.4118	−	7.42929i	0.889997	−	0.323932i
$527$	−1.97178	−	5.41743i	−0.0858921	−	0.235987i
$528$	0.416658	+	3.48915i	0.0181327	+	0.151846i
$529$	−0.974921	−	5.52905i	−0.0423879	−	0.240393i
$530$	6.44944	−	11.1708i	0.280146	−	0.485227i
$531$	−4.10308	+	5.56925i	−0.178059	+	0.241685i
$532$	11.4814	−	1.15012i	0.497783	−	0.0498639i
$533$	0.568139	+	0.677082i	0.0246088	+	0.0293277i
$534$	3.79013	+	0.211255i	0.164015	+	0.00914190i
$535$	1.43129	+	0.252375i	0.0618800	+	0.0109111i
$536$	6.81314	−	8.11959i	0.294283	−	0.350713i
$537$	31.6073	+	29.6711i	1.36395	+	1.28040i
$538$	−10.8788	+	29.8894i	−0.469021	+	1.28862i
$539$	−10.6460	+	9.39913i	−0.458554	+	0.404849i
$540$	−9.88698	+	0.0740671i	−0.425468	+	0.00318734i
$541$	3.96036			0.170269			0.0851346	−	0.996369i	$-0.472868\pi$
$541$	3.96036			0.170269			0.0851346	+	0.996369i	$0.472868\pi$
$542$	−5.74072	−	2.08945i	−0.246585	−	0.0897497i
$543$	22.0109	−	6.64958i	0.944580	−	0.285361i
$544$	2.84647	−	3.39229i	0.122041	−	0.145443i
$545$	−2.90993	+	16.5030i	−0.124648	+	0.706911i
$546$	2.27246	−	0.100413i	0.0972522	−	0.00429728i
$547$	−4.11449	+	3.45247i	−0.175923	+	0.147617i	−0.726497	−	0.687169i	$-0.758853\pi$
$547$	−4.11449	+	3.45247i	−0.175923	+	0.147617i	0.550575	+	0.834786i	$0.314409\pi$
$548$	−12.9885	+	7.49894i	−0.554843	+	0.320339i
$549$	−3.64722	−	15.0534i	−0.155660	−	0.642465i
$550$	1.39919	−	2.42346i	0.0596615	−	0.103337i
$551$	−4.58789	−	26.0192i	−0.195451	−	1.10846i
$552$	3.64848	−	8.51655i	0.155290	−	0.362488i
$553$	−37.5140	−	2.80729i	−1.59526	−	0.119378i
$554$	8.40177	+	23.0837i	0.356957	+	0.980731i
$555$	12.7354	+	17.0178i	0.540590	+	0.722365i
$556$	−19.2762	+	3.39892i	−0.817494	+	0.144146i
$557$	22.6883	+	13.0991i	0.961332	+	0.555025i	0.896583	−	0.442876i	$-0.146042\pi$
$557$	22.6883	+	13.0991i	0.961332	+	0.555025i	0.0647493	+	0.997902i	$0.479375\pi$
$558$	−0.246561	−	3.89783i	−0.0104378	−	0.165008i
$559$	0.480983	−	0.277696i	0.0203434	−	0.0117453i
$560$	−4.84604	+	1.36402i	−0.204782	+	0.0576402i
$561$	−8.51833	+	13.0222i	−0.359644	+	0.549798i
$562$	−2.36248	+	13.3983i	−0.0996553	+	0.565173i
$563$	−4.65874	−	3.90915i	−0.196342	−	0.164751i	0.539316	−	0.842103i	$-0.318683\pi$
$563$	−4.65874	−	3.90915i	−0.196342	−	0.164751i	−0.735659	+	0.677352i	$0.763127\pi$
$564$	19.5134	+	4.57333i	0.821662	+	0.192572i
$565$	−0.508267	+	1.39645i	−0.0213829	+	0.0587492i
$566$	−22.2956			−0.937153
$567$	19.0067	+	14.3438i	0.798208	+	0.602382i
$568$	−0.794807			−0.0333493
$569$	−5.26449	+	14.4641i	−0.220699	+	0.606365i	−0.999789	−	0.0205471i	$-0.993459\pi$
$569$	−5.26449	+	14.4641i	−0.220699	+	0.606365i	0.779090	+	0.626912i	$0.215681\pi$
$570$	−13.9945	−	3.27987i	−0.586166	−	0.137379i
$571$	31.4632	+	26.4008i	1.31669	+	1.10484i	0.986995	+	0.160753i	$0.0513921\pi$
$571$	31.4632	+	26.4008i	1.31669	+	1.10484i	0.329700	+	0.944086i	$0.393052\pi$
$572$	−0.174869	+	0.991733i	−0.00731165	+	0.0414664i
$573$	−17.7518	+	27.1376i	−0.741590	+	1.13369i
$574$	1.27645	+	4.53493i	0.0532780	+	0.189284i
$575$	−6.38991	+	3.68921i	−0.266477	+	0.153851i
$576$	2.49820	−	1.66102i	0.104092	−	0.0692093i
$577$	11.9364	+	6.89147i	0.496918	+	0.286896i	0.727440	−	0.686171i	$-0.240710\pi$
$577$	11.9364	+	6.89147i	0.496918	+	0.286896i	−0.230522	+	0.973067i	$0.574043\pi$
$578$	2.57033	−	0.453219i	0.106912	−	0.0188514i
$579$	−10.8189	−	14.4568i	−0.449619	−	0.600805i
$580$	3.94251	+	10.8320i	0.163704	+	0.449773i
$581$	30.1024	+	2.25266i	1.24886	+	0.0934563i
$582$	8.10777	−	18.9257i	0.336078	−	0.784496i
$583$	−2.38815	−	13.5439i	−0.0989072	−	0.560930i
$584$	−6.43963	+	11.1538i	−0.266474	+	0.461546i
$585$	−2.71850	−	0.799093i	−0.112396	−	0.0330384i
$586$	−9.28982	+	5.36348i	−0.383759	+	0.221563i
$587$	−13.2505	+	11.1185i	−0.546905	+	0.458908i	−0.873891	−	0.486121i	$-0.838411\pi$
$587$	−13.2505	+	11.1185i	−0.546905	+	0.458908i	0.326986	+	0.945029i	$0.393967\pi$
$588$	11.2613	+	4.49269i	0.464406	+	0.185275i
$589$	0.985947	−	5.59158i	0.0406253	−	0.230397i
$590$	2.82026	−	3.36106i	0.116108	−	0.138373i
$591$	−38.7625	+	11.7103i	−1.59447	+	0.481696i
$592$	−6.06042	−	2.20581i	−0.249082	−	0.0906584i
$593$	11.2472			0.461866			0.230933	−	0.972970i	$-0.425822\pi$
$593$	11.2472			0.461866			0.230933	+	0.972970i	$0.425822\pi$
$594$	−8.02451	+	6.83646i	−0.329250	+	0.280503i
$595$	−20.3218	−	9.16695i	−0.833111	−	0.375808i
$596$	−0.494859	+	1.35962i	−0.0202702	+	0.0556920i
$597$	4.36024	+	4.09314i	0.178453	+	0.167521i
$598$	1.70675	−	2.03402i	0.0697941	−	0.0831773i
$599$	−0.376139	−	0.0663234i	−0.0153686	−	0.00270990i	0.165959	−	0.986133i	$-0.446928\pi$
$599$	−0.376139	−	0.0663234i	−0.0153686	−	0.00270990i	−0.181327	+	0.983423i	$0.558039\pi$
$600$	−2.38539	−	0.132957i	−0.0973830	−	0.00542795i
$601$	26.6966	+	31.8158i	1.08898	+	1.29779i	0.951622	+	0.307270i	$0.0994155\pi$
$601$	26.6966	+	31.8158i	1.08898	+	1.29779i	0.137354	+	0.990522i	$0.456140\pi$
$602$	2.94558	−	0.295064i	0.120053	−	0.0120259i
$603$	31.6011	+	3.53376i	1.28690	+	0.143906i
$604$	10.7530	−	18.6248i	0.437534	−	0.757832i
$605$	−2.27462	−	12.9000i	−0.0924766	−	0.524461i
$606$	0.937521	+	7.85094i	0.0380842	+	0.318923i
$607$	9.80783	+	26.9468i	0.398087	+	1.09374i	0.963215	+	0.268732i	$0.0866047\pi$
$607$	9.80783	+	26.9468i	0.398087	+	1.09374i	−0.565128	+	0.825004i	$0.691173\pi$
$608$	4.09827	−	1.49165i	0.166207	−	0.0604944i
$609$	8.33403	−	26.4806i	0.337712	−	1.07305i
$610$	1.70594	+	9.67489i	0.0690717	+	0.391725i
$611$	4.97421	+	2.87186i	0.201235	+	0.116183i
$612$	13.2027	+	1.47637i	0.533686	+	0.0596788i
$613$	−17.8923	−	30.9904i	−0.722665	−	1.25169i	−0.959928	−	0.280247i	$-0.909584\pi$
$613$	−17.8923	−	30.9904i	−0.722665	−	1.25169i	0.237263	−	0.971445i	$-0.423750\pi$
$614$	−2.67889	+	2.24786i	−0.108111	+	0.0907160i
$615$	0.326596	−	5.85947i	0.0131696	−	0.236277i
$616$	−3.02323	+	4.43527i	−0.121809	+	0.178702i
$617$	19.5575	−	23.3077i	0.787356	−	0.938335i	−0.211885	−	0.977295i	$-0.567960\pi$
$617$	19.5575	−	23.3077i	0.787356	−	0.938335i	0.999241	+	0.0389601i	$0.0124045\pi$
$618$	18.2985	−	19.4926i	0.736075	−	0.784107i
$619$	−13.2122	+	36.3001i	−0.531042	+	1.45903i	0.326791	+	0.945097i	$0.394033\pi$
$619$	−13.2122	+	36.3001i	−0.531042	+	1.45903i	−0.857833	+	0.513929i	$0.828190\pi$
$620$			2.47721i			0.0994870i
$621$	27.3363	−	5.03155i	1.09697	−	0.201909i
$622$		−	18.9125i		−	0.758320i
$623$	4.15139	+	4.04829i	0.166322	+	0.162191i
$624$	0.823010	−	0.248634i	0.0329468	−	0.00995332i
$625$	−12.4105	−	10.4136i	−0.496418	−	0.416545i
$626$	−3.92518	+	22.2608i	−0.156882	+	0.889721i
$627$	−13.6780	+	6.91216i	−0.546246	+	0.276045i
$628$	−1.87190	−	2.23085i	−0.0746970	−	0.0890204i
$629$	−14.2799	−	24.7336i	−0.569378	−	0.986191i
$630$	−11.4570	−	9.84070i	−0.456456	−	0.392063i
$631$	2.10759	−	3.65045i	0.0839017	−	0.145322i	−0.821021	−	0.570898i	$-0.806595\pi$
$631$	2.10759	−	3.65045i	0.0839017	−	0.145322i	0.904923	+	0.425576i	$0.139928\pi$
$632$	−14.0026	+	2.46903i	−0.556993	+	0.0982129i
$633$	12.6260	−	29.4726i	0.501839	−	1.17143i
$634$	−20.9105	+	7.61081i	−0.830463	+	0.302264i
$635$	−21.9274	+	7.98092i	−0.870162	+	0.316713i
$636$	−9.40049	+	7.03496i	−0.372754	+	0.278954i
$637$	2.71703	+	2.16582i	0.107653	+	0.0858128i
$638$	10.6437	+	6.14513i	0.421387	+	0.243288i
$639$	−1.32019	−	1.98558i	−0.0522260	−	0.0785485i
$640$	−1.64788	+	0.951401i	−0.0651380	+	0.0376074i
$641$	−22.0082	−	26.2284i	−0.869272	−	1.03596i	−0.999013	−	0.0444106i	$-0.985859\pi$
$641$	−22.0082	−	26.2284i	−0.869272	−	1.03596i	0.129741	−	0.991548i	$-0.458585\pi$
$642$	−1.10712	−	0.724209i	−0.0436945	−	0.0285822i
$643$	−37.1207	−	6.54538i	−1.46390	−	0.258125i	−0.615774	−	0.787923i	$-0.711157\pi$
$643$	−37.1207	−	6.54538i	−1.46390	−	0.258125i	−0.848124	+	0.529798i	$0.822268\pi$
$644$	12.7505	−	6.14200i	0.502442	−	0.242029i
$645$	−3.59031	−	0.841456i	−0.141368	−	0.0331323i
$646$	18.1484	+	6.60549i	0.714041	+	0.259890i
$647$	45.8507			1.80258			0.901289	−	0.433217i	$-0.142622\pi$
$647$	45.8507			1.80258			0.901289	+	0.433217i	$0.142622\pi$
$648$	8.29914	+	3.48200i	0.326021	+	0.136786i
$649$		−	4.67802i		−	0.183628i
$650$	−0.643380	−	0.234171i	−0.0252354	−	0.00918495i
$651$	3.62934	−	4.73500i	0.142245	−	0.185579i
$652$	6.10288	+	5.12092i	0.239007	+	0.200551i
$653$	25.9923	+	4.58314i	1.01716	+	0.179352i	0.657279	−	0.753647i	$-0.271707\pi$
$653$	25.9923	+	4.58314i	1.01716	+	0.179352i	0.359878	+	0.932999i	$0.382818\pi$
$654$	8.35026	−	12.7653i	0.326521	−	0.499162i
$655$	27.7280	−	23.2665i	1.08342	−	0.909099i
$656$	0.890323	+	1.54209i	0.0347613	+	0.0602083i
$657$	−38.5607	+	2.43919i	−1.50440	+	0.0951620i
$658$	17.8739	+	24.8555i	0.696796	+	0.968968i
$659$	2.42142	−	0.426962i	0.0943251	−	0.0166321i	−0.126286	−	0.991994i	$-0.540306\pi$
$659$	2.42142	−	0.426962i	0.0943251	−	0.0166321i	0.220611	+	0.975362i	$0.429195\pi$
$660$	5.35328	−	4.00618i	0.208376	−	0.155940i
$661$	−10.1041	−	27.7609i	−0.393006	−	1.07977i	−0.965622	−	0.259950i	$-0.916294\pi$
$661$	−10.1041	−	27.7609i	−0.393006	−	1.07977i	0.572616	−	0.819823i	$-0.305928\pi$
$662$	2.08150	+	5.71889i	0.0809000	+	0.222271i
$663$	3.49961	+	1.49923i	0.135914	+	0.0582253i
$664$	11.2361	−	1.98123i	0.436046	−	0.0768867i
$665$	−12.8187	−	17.8257i	−0.497088	−	0.691253i
$666$	−4.55595	−	18.8041i	−0.176539	−	0.728642i
$667$	−16.2028	−	28.0640i	−0.627374	−	1.08664i
$668$	−11.5646	+	9.70383i	−0.447447	+	0.375452i
$669$	−11.1892	−	22.1415i	−0.432599	−	0.856040i
$670$	−19.8621	−	3.50222i	−0.767340	−	0.135303i
$671$	8.02396	+	6.73290i	0.309761	+	0.259921i
$672$	4.54368	+	0.595761i	0.175276	+	0.0229820i
$673$	−44.8508	−	16.3243i	−1.72887	−	0.629257i	−0.730321	−	0.683104i	$-0.760630\pi$
$673$	−44.8508	−	16.3243i	−1.72887	−	0.629257i	−0.998549	+	0.0538463i	$0.982852\pi$
$674$		−	0.0956651i		−	0.00368488i
$675$	−3.63003	−	6.18002i	−0.139720	−	0.237869i
$676$	−12.7536			−0.490524
$677$	−31.2210	−	11.3635i	−1.19992	−	0.436735i	−0.336724	−	0.941604i	$-0.609319\pi$
$677$	−31.2210	−	11.3635i	−1.19992	−	0.436735i	−0.863196	+	0.504868i	$0.831541\pi$
$678$	0.925831	−	0.986246i	0.0355563	−	0.0378765i
$679$	28.3346	−	13.6489i	1.08738	−	0.523798i
$680$	−8.29820	−	1.46320i	−0.318221	−	0.0561110i
$681$	2.08929	−	37.4839i	0.0800616	−	1.43639i
$682$	1.69773	+	2.02328i	0.0650096	+	0.0774754i
$683$	−30.4976	+	17.6078i	−1.16696	+	0.673743i	−0.952962	−	0.303091i	$-0.901981\pi$
$683$	−30.4976	+	17.6078i	−1.16696	+	0.673743i	−0.213996	+	0.976835i	$0.568648\pi$
$684$	10.5338	+	7.76064i	0.402769	+	0.296735i
$685$	24.7146	+	14.2690i	0.944297	+	0.545190i
$686$	8.45437	+	16.4780i	0.322789	+	0.629132i
$687$	2.48446	+	20.8052i	0.0947881	+	0.793769i
$688$	1.05142	−	0.382685i	0.0400849	−	0.0145897i
$689$	−3.16194	+	1.15085i	−0.120460	+	0.0438440i
$690$	−17.5054	+	2.09041i	−0.666419	+	0.0795805i
$691$	−16.2186	+	2.85977i	−0.616983	+	0.108791i	−0.473400	−	0.880847i	$-0.656974\pi$
$691$	−16.2186	+	2.85977i	−0.616983	+	0.108791i	−0.143583	+	0.989638i	$0.545862\pi$
$692$	−6.09796	+	10.5620i	−0.231810	+	0.401506i
$693$	−16.1018	−	0.185538i	−0.611658	−	0.00704800i
$694$	−2.13794	−	3.70301i	−0.0811550	−	0.140565i
$695$	23.9404	+	28.5311i	0.908112	+	1.08225i
$696$	0.583939	−	10.4765i	0.0221341	−	0.397109i
$697$	−1.36926	+	7.76547i	−0.0518645	+	0.294138i
$698$	−8.70295	−	7.30264i	−0.329412	−	0.276409i
$699$	−10.1571	−	9.53486i	−0.384175	−	0.360642i
$700$	−2.61275	−	2.54787i	−0.0987527	−	0.0963003i
$701$			3.65448i			0.138028i	0.997616	+	0.0690140i	$0.0219853\pi$
$701$			3.65448i			0.138028i	−0.997616	+	0.0690140i	$0.978015\pi$
$702$	1.98818	+	1.64305i	0.0750389	+	0.0620131i
$703$		−	28.1276i		−	1.06085i
$704$	−0.693882	+	1.90642i	−0.0261516	+	0.0718511i
$705$	−11.0288	−	36.5067i	−0.415369	−	1.37492i
$706$	4.53942	−	5.40987i	0.170843	−	0.203603i
$707$	−6.80256	+	9.97979i	−0.255837	+	0.375329i
$708$	−3.56452	+	1.80133i	−0.133963	+	0.0676982i
$709$	19.4206	−	16.2958i	0.729356	−	0.612002i	−0.200600	−	0.979673i	$-0.564289\pi$
$709$	19.4206	−	16.2958i	0.729356	−	0.612002i	0.929956	+	0.367671i	$0.119845\pi$
$710$	0.756180	+	1.30974i	0.0283789	+	0.0491537i
$711$	−29.4268	−	30.8801i	−1.10359	−	1.15809i
$712$	1.89801	+	1.09582i	0.0711308	+	0.0410674i
$713$	−1.20929	−	6.85823i	−0.0452883	−	0.256843i
$714$	13.7177	+	14.9544i	0.513371	+	0.559656i
$715$	1.80062	−	0.655373i	0.0673395	−	0.0245096i
$716$	8.56052	+	23.5198i	0.319922	+	0.878977i
$717$	24.5611	−	18.3805i	0.917249	−	0.686433i
$718$	0.823201	+	4.66861i	0.0307216	+	0.174231i
$719$	21.1534	−	36.6388i	0.788889	−	1.36640i	−0.137759	−	0.990466i	$-0.543990\pi$
$719$	21.1534	−	36.6388i	0.788889	−	1.36640i	0.926648	−	0.375931i	$-0.122677\pi$
$720$	−5.11395	−	2.53642i	−0.190586	−	0.0945268i
$721$	40.6361	−	4.07059i	1.51337	−	0.151597i
$722$	0.0134043	+	0.0159747i	0.000498857	+	0.000594515i
$723$	−15.7603	+	24.0932i	−0.586132	+	0.896036i
$724$	13.0736	+	2.30523i	0.485876	+	0.0856731i
$725$	−5.37115	+	6.40108i	−0.199479	+	0.237730i
$726$	−2.72078	+	11.6090i	−0.100978	+	0.430850i
$727$	−10.6152	+	29.1649i	−0.393695	+	1.08167i	0.571607	+	0.820528i	$0.306320\pi$
$727$	−10.6152	+	29.1649i	−0.393695	+	1.08167i	−0.965301	+	0.261139i	$0.915902\pi$
$728$	1.19712	+	0.540010i	0.0443683	+	0.0200141i
$729$	5.08634	+	26.5166i	0.188383	+	0.982096i
$730$	24.5067			0.907033
$731$	4.65601	+	1.69465i	0.172209	+	0.0626788i
$732$	2.04056	−	8.70663i	0.0754213	−	0.321806i
$733$	−0.256296	+	0.305441i	−0.00946650	+	0.0112817i	−0.770757	−	0.637129i	$-0.780122\pi$
$733$	−0.256296	+	0.305441i	−0.00946650	+	0.0112817i	0.761290	+	0.648411i	$0.224566\pi$
$734$	−4.89635	+	27.7686i	−0.180727	+	1.02496i
$735$	−3.31058	−	22.8315i	−0.122113	−	0.842152i
$736$	4.09775	−	3.43842i	0.151045	−	0.126742i
$737$	−18.6228	+	10.7519i	−0.685979	+	0.396050i
$738$	−2.37359	+	4.78565i	−0.0873730	+	0.176162i
$739$	−4.15414	+	7.19518i	−0.152812	+	0.264679i	−0.932260	−	0.361788i	$-0.882166\pi$
$739$	−4.15414	+	7.19518i	−0.152812	+	0.264679i	0.779448	+	0.626467i	$0.215500\pi$
$740$	2.13099	+	12.0854i	0.0783367	+	0.444270i
$741$	2.24661	+	3.00204i	0.0825313	+	0.110283i
$742$	−17.8852	−	1.33841i	−0.656587	−	0.0491346i
$743$	−3.52841	−	9.69423i	−0.129445	−	0.355647i	0.857992	−	0.513664i	$-0.171712\pi$
$743$	−3.52841	−	9.69423i	−0.129445	−	0.355647i	−0.987436	+	0.158017i	$0.949490\pi$
$744$	0.887951	−	2.07272i	0.0325539	−	0.0759895i
$745$	2.71129	−	0.478073i	0.0993339	−	0.0175152i
$746$	3.70008	+	2.13624i	0.135469	+	0.0782133i
$747$	23.6130	+	24.7792i	0.863954	+	0.906624i
$748$	−7.78042	+	4.49203i	−0.284480	+	0.164245i
$749$	−0.547530	−	1.94525i	−0.0200063	−	0.0710778i
$750$	9.48276	+	18.7648i	0.346262	+	0.685192i
$751$	1.51945	−	8.61720i	0.0554454	−	0.314446i	−0.944454	−	0.328644i	$-0.893408\pi$
$751$	1.51945	−	8.61720i	0.0554454	−	0.314446i	0.999899	+	0.0141978i	$0.00451946\pi$
$752$	8.86416	+	7.43791i	0.323243	+	0.271233i
$753$	8.40663	+	27.8270i	0.306355	+	1.01407i
$754$	1.02846	−	2.82568i	0.0374544	−	0.102905i
$755$	−40.9218			−1.48930
$756$	6.05884	+	12.3406i	0.220358	+	0.448823i
$757$	−26.4096			−0.959873			−0.479937	−	0.877303i	$-0.659340\pi$
$757$	−26.4096			−0.959873			−0.479937	+	0.877303i	$0.659340\pi$
$758$	0.119445	−	0.328172i	0.00433844	−	0.0119198i
$759$	−12.8650	+	13.7045i	−0.466971	+	0.497443i
$760$	−6.35715	−	5.33429i	−0.230598	−	0.193495i
$761$	−3.53758	+	20.0626i	−0.128237	+	0.727268i	0.851095	+	0.525011i	$0.175939\pi$
$761$	−3.53758	+	20.0626i	−0.128237	+	0.727268i	−0.979332	+	0.202257i	$0.935172\pi$
$762$	21.2077	+	1.18208i	0.768275	+	0.0428223i
$763$	22.4291	−	6.31312i	0.811986	−	0.228550i
$764$	−16.2140	+	9.36115i	−0.586602	+	0.338675i
$765$	−10.1282	−	23.1610i	−0.366184	−	0.837386i
$766$	−12.8588	−	7.42401i	−0.464606	−	0.268240i
$767$	−1.12717	+	0.198750i	−0.0406997	+	0.00717646i
$768$	1.71983	−	0.205374i	0.0620591	−	0.00741080i
$769$	−17.9627	−	49.3521i	−0.647751	−	1.77968i	−0.625879	−	0.779920i	$-0.715260\pi$
$769$	−17.9627	−	49.3521i	−0.647751	−	1.77968i	−0.0218717	−	0.999761i	$-0.506963\pi$
$770$	10.1851	+	0.762182i	0.367044	+	0.0274671i
$771$	28.1456	−	3.36101i	1.01364	−	0.121044i
$772$	−1.81030	−	10.2667i	−0.0651541	−	0.369507i
$773$	5.43457	−	9.41295i	0.195468	−	0.338560i	−0.751586	−	0.659635i	$-0.770711\pi$
$773$	5.43457	−	9.41295i	0.195468	−	0.338560i	0.947054	+	0.321075i	$0.104044\pi$
$774$	2.70245	+	1.99100i	0.0971376	+	0.0715651i
$775$	−1.55515	+	0.897864i	−0.0558625	+	0.0322522i
$776$	9.10615	−	7.64096i	0.326892	−	0.274295i
$777$	13.6331	−	26.2225i	0.489084	−	0.940728i
$778$	−3.40606	+	19.3167i	−0.122113	+	0.692538i
$779$	−4.99184	+	5.94904i	−0.178851	+	0.213146i
$780$	−1.19273	−	1.11967i	−0.0427066	−	0.0400905i
$781$	1.51524	+	0.551502i	0.0542195	+	0.0197343i
$782$	23.6881			0.847085
$783$	27.1422	−	15.9429i	0.969984	−	0.569751i
$784$	4.63291	+	5.24749i	0.165461	+	0.187410i
$785$	−1.89523	+	5.20709i	−0.0676435	+	0.185849i
$786$	−31.5403	+	9.52843i	−1.12501	+	0.339868i
$787$	−19.0399	+	22.6909i	−0.678700	+	0.808843i	−0.989940	−	0.141488i	$-0.954811\pi$
$787$	−19.0399	+	22.6909i	−0.678700	+	0.808843i	0.311240	+	0.950331i	$0.399256\pi$
$788$	−23.0233	−	4.05963i	−0.820171	−	0.144618i
$789$	16.9692	+	33.5791i	0.604119	+	1.19545i
$790$	17.3907	+	20.7255i	0.618735	+	0.737379i
$791$	2.05602	−	0.205955i	0.0731036	−	0.00732293i
$792$	−5.91518	+	1.43316i	−0.210187	+	0.0509252i
$793$	1.28139	−	2.21943i	0.0455034	−	0.0788142i
$794$	−4.72453	−	26.7942i	−0.167667	−	0.950889i
$795$	20.5364	+	8.79777i	0.728350	+	0.312025i
$796$	1.18093	+	3.24457i	0.0418569	+	0.115001i
$797$	51.6750	−	18.8081i	1.83042	−	0.666219i	0.837648	−	0.546210i	$-0.183930\pi$
$797$	51.6750	−	18.8081i	1.83042	−	0.666219i	0.992773	−	0.120008i	$-0.0382921\pi$
$798$	4.33599	+	19.5099i	0.153493	+	0.690644i
$799$	8.89800	+	50.4631i	0.314789	+	1.78526i
$800$	−1.19455	−	0.689671i	−0.0422335	−	0.0243835i
$801$	0.415071	+	6.56178i	0.0146658	+	0.231849i
$802$	−5.88357	−	10.1906i	−0.207756	−	0.359844i
$803$	20.0161	−	16.7955i	0.706351	−	0.592699i
$804$	15.3636	+	10.0499i	0.541831	+	0.354433i
$805$	−22.2521	−	15.1678i	−0.784284	−	0.534595i
$806$	0.415380	−	0.495031i	0.0146311	−	0.0174367i
$807$	−53.6390	−	12.5713i	−1.88818	−	0.442530i
$808$	−1.56130	+	4.28965i	−0.0549265	+	0.150909i
$809$		−	16.0462i		−	0.564153i	−0.959392	−	0.282077i	$-0.908977\pi$
$809$		−	16.0462i		−	0.564153i	0.959392	−	0.282077i	$-0.0910233\pi$
$810$	−2.15791	−	16.9887i	−0.0758213	−	0.596923i
$811$		−	23.7701i		−	0.834680i	−0.908750	−	0.417340i	$-0.862962\pi$
$811$		−	23.7701i		−	0.834680i	0.908750	−	0.417340i	$-0.137038\pi$
$812$	11.1901	−	11.4750i	0.392694	−	0.402694i
$813$	2.41451	−	10.3022i	0.0846806	−	0.361314i
$814$	10.0232	+	8.41043i	0.351312	+	0.294786i
$815$	2.63236	−	14.9288i	0.0922074	−	0.522934i
$816$	6.41875	+	4.19876i	0.224701	+	0.146986i
$817$	3.13669	+	3.73816i	0.109739	+	0.130782i
$818$	−1.42325	−	2.46514i	−0.0497627	−	0.0861916i
$819$	0.639397	+	3.88762i	0.0223424	+	0.135845i
$820$	1.69411	−	2.93428i	0.0591609	−	0.102470i
$821$	−1.23364	+	0.217524i	−0.0430544	+	0.00759165i	−0.195134	−	0.980777i	$-0.562514\pi$
$821$	−1.23364	+	0.217524i	−0.0430544	+	0.00759165i	0.152079	+	0.988368i	$0.451403\pi$
$822$	−15.5644	−	20.7980i	−0.542871	−	0.725414i
$823$	13.3481	−	4.85831i	0.465285	−	0.169350i	−0.0987301	−	0.995114i	$-0.531478\pi$
$823$	13.3481	−	4.85831i	0.465285	−	0.169350i	0.564015	+	0.825764i	$0.309256\pi$
$824$	14.5050	−	5.27937i	0.505304	−	0.183916i
$825$	4.45530	+	1.90865i	0.155114	+	0.0664506i
$826$	−5.91217	−	1.50476i	−0.205711	−	0.0523573i
$827$	−13.5158	−	7.80332i	−0.469989	−	0.271348i	0.246246	−	0.969207i	$-0.420803\pi$
$827$	−13.5158	−	7.80332i	−0.469989	−	0.271348i	−0.716235	+	0.697859i	$0.754136\pi$
$828$	15.3963	+	4.52570i	0.535060	+	0.157279i
$829$	35.9525	−	20.7572i	1.24868	−	0.720928i	0.277837	−	0.960628i	$-0.410383\pi$
$829$	35.9525	−	20.7572i	1.24868	−	0.720928i	0.970847	+	0.239701i	$0.0770493\pi$
$830$	−13.9549	−	16.6308i	−0.484381	−	0.577263i
$831$	−37.9745	+	19.1904i	−1.31732	+	0.665708i
$832$	0.488834	+	0.0861946i	0.0169473	+	0.00298826i
$833$	0.779361	+	30.9884i	0.0270032	+	1.07368i
$834$	−9.80441	−	32.4538i	−0.339499	−	1.12378i
$835$	26.9933	+	9.82474i	0.934140	+	0.339999i
$836$	−8.84807			−0.306017
$837$	6.65297	−	1.22456i	0.229960	−	0.0423268i
$838$		−	14.2481i		−	0.492193i
$839$	1.70742	+	0.621451i	0.0589468	+	0.0214549i	0.371325	−	0.928503i	$-0.378903\pi$
$839$	1.70742	+	0.621451i	0.0589468	+	0.0214549i	−0.312378	+	0.949958i	$0.601126\pi$
$840$	−3.34113	−	8.05423i	−0.115280	−	0.277897i
$841$	−5.89783	−	4.94886i	−0.203373	−	0.170650i
$842$	0.525737	+	0.0927017i	0.0181181	+	0.00319471i
$843$	−23.5280	−	1.31141i	−0.810348	−	0.0451673i
$844$	14.1808	−	11.8991i	0.488122	−	0.409583i
$845$	12.1338	+	21.0164i	0.417416	+	0.722985i
$846$	−3.85781	+	34.4990i	−0.132634	+	1.18610i
$847$	−14.7871	+	10.6336i	−0.508092	+	0.365375i
$848$	−6.67590	+	1.17714i	−0.229251	+	0.0404232i
$849$	−4.57893	−	38.3446i	−0.157149	−	1.31598i
$850$	−2.08911	−	5.73979i	−0.0716560	−	0.196873i
$851$	−11.7994	−	32.4186i	−0.404479	−	1.11130i
$852$	−0.163233	−	1.36693i	−0.00559226	−	0.0468304i
$853$	−15.8824	+	2.80050i	−0.543804	+	0.0958874i	−0.438801	−	0.898584i	$-0.644597\pi$
$853$	−15.8824	+	2.80050i	−0.543804	+	0.0958874i	−0.105004	+	0.994472i	$0.533485\pi$
$854$	11.0902	−	7.97510i	0.379499	−	0.272902i
$855$	2.76672	−	24.7418i	0.0946199	−	0.846152i
$856$	−0.381902	−	0.661473i	−0.0130531	−	0.0226087i
$857$	−1.91701	+	1.60856i	−0.0654838	+	0.0549474i	−0.674942	−	0.737871i	$-0.735831\pi$
$857$	−1.91701	+	1.60856i	−0.0654838	+	0.0549474i	0.609458	+	0.792818i	$0.291387\pi$
$858$	−1.74153	−	0.0970696i	−0.0594548	−	0.00331390i
$859$	53.7925	+	9.48507i	1.83538	+	0.323627i	0.980698	−	0.195529i	$-0.0626425\pi$
$859$	53.7925	+	9.48507i	1.83538	+	0.323627i	0.854680	+	0.519156i	$0.173754\pi$
$860$	−1.63094	−	1.36852i	−0.0556145	−	0.0466661i
$861$	−7.53717	+	3.12663i	−0.256866	+	0.106555i
$862$	16.9001	+	6.15114i	0.575621	+	0.209509i
$863$		−	6.24755i		−	0.212669i	−0.994330	−	0.106335i	$-0.966089\pi$
$863$		−	6.24755i		−	0.212669i	0.994330	−	0.106335i	$-0.0339115\pi$
$864$	3.36975	+	3.95535i	0.114641	+	0.134564i
$865$	23.2064			0.789042
$866$	−29.1943	−	10.6259i	−0.992064	−	0.361082i
$867$	1.30734	+	4.32746i	0.0443996	+	0.146968i
$868$	3.10317	−	1.49481i	0.105328	−	0.0507372i
$869$	28.4081	+	5.00911i	0.963678	+	0.169922i
$870$	−17.8195	+	9.00506i	−0.604136	+	0.305300i
$871$	3.38187	+	4.03036i	0.114590	+	0.136563i
$872$	7.62691	−	4.40340i	0.258280	−	0.149118i
$873$	34.2142	+	10.0571i	1.15797	+	0.340383i
$874$	20.2040	+	11.6648i	0.683411	+	0.394567i
$875$	−7.92152	+	31.1235i	−0.267796	+	1.05217i
$876$	−20.5051	−	8.78438i	−0.692804	−	0.296797i
$877$	38.5326	−	14.0247i	1.30115	−	0.473581i	0.403781	−	0.914856i	$-0.367696\pi$
$877$	38.5326	−	14.0247i	1.30115	−	0.473581i	0.897372	+	0.441275i	$0.145474\pi$
$878$	1.35695	−	0.493889i	0.0457948	−	0.0166679i
$879$	−11.1322	−	14.8754i	−0.375479	−	0.501735i
$880$	3.80171	−	0.670344i	0.128156	−	0.0225973i
$881$	−16.5925	+	28.7390i	−0.559015	+	0.968243i	0.438564	+	0.898700i	$0.355487\pi$
$881$	−16.5925	+	28.7390i	−0.559015	+	0.968243i	−0.997579	+	0.0695428i	$0.977846\pi$
$882$	−5.41390	+	20.2901i	−0.182295	+	0.683205i
$883$	−12.9120	−	22.3642i	−0.434523	−	0.752616i	0.562733	−	0.826639i	$-0.309750\pi$
$883$	−12.9120	−	22.3642i	−0.434523	−	0.752616i	−0.997257	+	0.0740221i	$0.976416\pi$
$884$	1.41291	+	1.68385i	0.0475214	+	0.0566339i
$885$	6.35966	+	4.16010i	0.213778	+	0.139840i
$886$	0.450834	−	2.55681i	0.0151461	−	0.0858976i
$887$	41.3566	+	34.7023i	1.38862	+	1.16519i	0.965896	+	0.258932i	$0.0833705\pi$
$887$	41.3566	+	34.7023i	1.38862	+	1.16519i	0.422724	+	0.906258i	$0.361074\pi$
$888$	2.54898	−	10.8759i	0.0855380	−	0.364972i
$889$	23.2292	+	22.6523i	0.779081	+	0.759733i
$890$		−	4.17024i		−	0.139787i
$891$	−13.4056	−	12.3968i	−0.449104	−	0.415308i
$892$		−	14.3230i		−	0.479569i
$893$	−17.2604	+	47.4225i	−0.577597	+	1.58693i
$894$	−2.43994	−	0.571845i	−0.0816038	−	0.0191254i
$895$	30.6133	−	36.4835i	1.02329	−	1.21951i
$896$	2.18618	+	1.49017i	0.0730351	+	0.0497832i
$897$	3.84870	+	2.51758i	0.128504	+	0.0840596i
$898$	12.7869	−	10.7295i	0.426704	−	0.358048i
$899$	−3.94336	−	6.83009i	−0.131518	−	0.227796i
$900$	−0.261233	−	4.12977i	−0.00870776	−	0.137659i
$901$	−25.9972	−	15.0095i	−0.866094	−	0.500040i
$902$	−0.627309	−	3.55765i	−0.0208871	−	0.118457i
$903$	1.11241	+	5.00530i	0.0370185	+	0.166566i
$904$	0.733892	−	0.267115i	0.0244089	−	0.00888411i
$905$	−8.63951	−	23.7368i	−0.287187	−	0.789040i
$906$	34.2399	+	14.6683i	1.13754	+	0.487323i
$907$	5.42411	+	30.7616i	0.180105	+	1.02142i	0.932085	+	0.362239i	$0.117987\pi$
$907$	5.42411	+	30.7616i	0.180105	+	1.02142i	−0.751981	+	0.659185i	$0.770901\pi$
$908$	10.8375	−	18.7711i	0.359654	−	0.622939i
$909$	−13.3098	+	3.22476i	−0.441457	+	0.106958i
$910$	−0.249075	−	2.48648i	−0.00825676	−	0.0824259i
$911$	−18.5275	−	22.0802i	−0.613842	−	0.731549i	0.366156	−	0.930553i	$-0.380674\pi$
$911$	−18.5275	−	22.0802i	−0.613842	−	0.731549i	−0.979999	+	0.199005i	$0.936229\pi$
$912$	3.40706	+	6.74199i	0.112819	+	0.223250i
$913$	−22.7956	−	4.01947i	−0.754423	−	0.133025i
$914$	22.8587	−	27.2420i	0.756100	−	0.901084i
$915$	−16.2888	+	4.92091i	−0.538492	+	0.162680i
$916$	−4.13750	+	11.3677i	−0.136707	+	0.375599i
$917$	−45.8775	−	20.6949i	−1.51501	−	0.683405i
$918$	0.172373	+	23.0096i	0.00568917	+	0.759429i
$919$	11.7162			0.386481			0.193240	−	0.981151i	$-0.438100\pi$
$919$	11.7162			0.386481			0.193240	+	0.981151i	$0.438100\pi$
$920$	−9.56470	−	3.48127i	−0.315339	−	0.114774i
$921$	−4.41611	−	4.14559i	−0.145516	−	0.136602i
$922$	−5.84945	+	6.97110i	−0.192641	+	0.229581i
$923$	0.0685080	−	0.388528i	0.00225497	−	0.0127886i
$924$	−8.24880	−	4.28855i	−0.271366	−	0.141083i
$925$	−6.81464	+	5.71816i	−0.224064	+	0.188012i
$926$	28.6884	−	16.5633i	0.942760	−	0.544303i
$927$	37.2820	+	27.4671i	1.22450	+	0.902139i
$928$	3.02899	−	5.24636i	0.0994314	−	0.172220i
$929$	−6.24757	−	35.4317i	−0.204976	−	1.16248i	−0.897477	−	0.441061i	$-0.854602\pi$
$929$	−6.24757	−	35.4317i	−0.204976	−	1.16248i	0.692501	−	0.721417i	$-0.256509\pi$
$930$	−4.26038	+	0.508754i	−0.139703	+	0.0166827i
$931$	−14.5950	+	26.8143i	−0.478331	+	0.878805i
$932$	−2.75094	−	7.55814i	−0.0901099	−	0.247575i
$933$	32.5262	−	3.88413i	1.06486	−	0.127161i
$934$	−20.5452	+	3.62268i	−0.672261	+	0.118538i
$935$	14.8046	+	8.54744i	0.484162	+	0.279531i
$936$	0.596633	+	1.36438i	0.0195016	+	0.0445960i
$937$	35.9485	−	20.7549i	1.17439	−	0.678033i	0.219678	−	0.975572i	$-0.429499\pi$
$937$	35.9485	−	20.7549i	1.17439	−	0.678033i	0.954710	+	0.297539i	$0.0961660\pi$
$938$	7.59811	+	26.9944i	0.248087	+	0.881397i
$939$	−39.0910	−	2.17886i	−1.27569	−	0.0711044i
$940$	3.82338	−	21.6835i	0.124705	−	0.707237i
$941$	−9.46632	−	7.94319i	−0.308593	−	0.258940i	0.475317	−	0.879815i	$-0.342333\pi$
$941$	−9.46632	−	7.94319i	−0.308593	−	0.258940i	−0.783910	+	0.620874i	$0.786778\pi$
$942$	3.45224	−	3.67751i	0.112480	−	0.119820i
$943$	−3.25778	+	8.95067i	−0.106088	+	0.291474i
$944$	−2.30583			−0.0750485
$945$	14.5714	−	21.7251i	0.474007	−	0.706717i
$946$	−2.26999			−0.0738036
$947$	12.2265	−	33.5921i	0.397308	−	1.09160i	−0.566282	−	0.824212i	$-0.691619\pi$
$947$	12.2265	−	33.5921i	0.397308	−	1.09160i	0.963590	−	0.267384i	$-0.0861591\pi$
$948$	−7.12209	−	23.5750i	−0.231315	−	0.765681i
$949$	−4.89727	−	4.10930i	−0.158972	−	0.133394i
$950$	1.04462	−	5.92432i	0.0338919	−	0.192210i
$951$	−17.3838	−	34.3995i	−0.563708	−	1.11548i
$952$	3.17442	+	11.2780i	0.102884	+	0.365522i
$953$	1.75036	−	1.01057i	0.0566998	−	0.0327356i	−0.471382	−	0.881929i	$-0.656245\pi$
$953$	1.75036	−	1.01057i	0.0566998	−	0.0327356i	0.528082	+	0.849193i	$0.322911\pi$
$954$	−14.0296	−	14.7225i	−0.454224	−	0.476657i
$955$	30.8520	+	17.8124i	0.998348	+	0.576397i
$956$	17.4424	−	3.07557i	0.564128	−	0.0994709i
$957$	−8.38266	+	19.5674i	−0.270973	+	0.632524i
$958$	−10.2803	−	28.2450i	−0.332143	−	0.912555i
$959$	2.96115	−	39.5700i	0.0956206	−	1.27778i
$960$	−1.97468	−	2.63868i	−0.0637326	−	0.0851629i
$961$	5.08878	+	28.8599i	0.164154	+	0.930965i
$962$	1.60065	−	2.77241i	0.0516071	−	0.0893861i
$963$	1.01814	−	2.05279i	0.0328092	−	0.0661502i
$964$	−14.3950	+	8.31098i	−0.463633	+	0.267679i
$965$	−15.1960	+	12.7509i	−0.489175	+	0.410467i
$966$	13.1818	+	20.6674i	0.424119	+	0.664962i
$967$	−7.31514	+	41.4862i	−0.235239	+	1.33411i	0.606870	+	0.794801i	$0.292425\pi$
$967$	−7.31514	+	41.4862i	−0.235239	+	1.33411i	−0.842110	+	0.539307i	$0.818686\pi$
$968$	−4.42500	+	5.27351i	−0.142225	+	0.169497i
$969$	−7.63312	+	32.5689i	−0.245211	+	1.04626i
$970$	−21.2550	−	7.73617i	−0.682456	−	0.248394i
$971$	4.27752			0.137272			0.0686360	−	0.997642i	$-0.478135\pi$
$971$	4.27752			0.137272			0.0686360	+	0.997642i	$0.478135\pi$
$972$	−4.28402	+	14.9882i	−0.137410	+	0.480748i
$973$	21.2943	−	47.2063i	0.682663	−	1.51336i
$974$	−3.43177	+	9.42870i	−0.109961	+	0.302115i
$975$	0.270601	−	1.15460i	0.00866618	−	0.0369767i
$976$	3.31870	−	3.95508i	0.106229	−	0.126599i
$977$	15.5639	+	2.74433i	0.497932	+	0.0877989i	0.416974	−	0.908919i	$-0.363091\pi$
$977$	15.5639	+	2.74433i	0.497932	+	0.0877989i	0.0809585	+	0.996717i	$0.474202\pi$
$978$	−7.55375	+	11.5476i	−0.241542	+	0.369252i
$979$	−2.85804	−	3.40608i	−0.0913434	−	0.108859i
$980$	4.23945	−	12.6269i	0.135424	−	0.403352i
$981$	23.6691	+	11.7394i	0.755695	+	0.374810i
$982$	−12.9998	+	22.5164i	−0.414841	+	0.718526i
$983$	1.05934	+	6.00783i	0.0337878	+	0.191620i	0.997030	−	0.0770144i	$-0.0245387\pi$
$983$	1.05934	+	6.00783i	0.0337878	+	0.191620i	−0.963242	+	0.268634i	$0.913428\pi$
$984$	−2.46928	+	1.84791i	−0.0787177	+	0.0589092i
$985$	15.2146	+	41.8019i	0.484779	+	1.33192i
$986$	25.2088	−	9.17525i	0.802811	−	0.292199i
$987$	−39.0765	+	35.8447i	−1.24382	+	1.14095i
$988$	0.375920	+	2.13195i	0.0119596	+	0.0678262i
$989$	5.18337	+	2.99262i	0.164821	+	0.0951597i
$990$	7.98938	+	8.38397i	0.253919	+	0.266460i
$991$	24.0757	+	41.7003i	0.764790	+	1.32465i	0.940358	+	0.340187i	$0.110490\pi$
$991$	24.0757	+	41.7003i	0.764790	+	1.32465i	−0.175568	+	0.984467i	$0.556176\pi$
$992$	0.997292	−	0.836828i	0.0316641	−	0.0265693i
$993$	−9.40803	+	4.75435i	−0.298555	+	0.150875i
$994$	1.18440	−	1.73759i	0.0375669	−	0.0551130i
$995$	4.22311	−	5.03291i	0.133882	−	0.159554i
$996$	5.71499	+	18.9174i	0.181087	+	0.599419i
$997$	13.7600	−	37.8054i	0.435785	−	1.19731i	−0.506424	−	0.862285i	$-0.669033\pi$
$997$	13.7600	−	37.8054i	0.435785	−	1.19731i	0.942209	−	0.335025i	$-0.108745\pi$
$998$		−	18.3526i		−	0.580941i
$999$	31.4041	−	11.6973i	0.993583	−	0.370087i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.z.a.293.1	yes	144
7.6	odd	2	inner	378.2.z.a.293.12	yes	144
27.20	odd	18	inner	378.2.z.a.209.12	yes	144
189.20	even	18	inner	378.2.z.a.209.1	✓	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.z.a.209.1	✓	144	189.20	even	18	inner
378.2.z.a.209.12	yes	144	27.20	odd	18	inner
378.2.z.a.293.1	yes	144	1.1	even	1	trivial
378.2.z.a.293.12	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)

\(f(q)\)	\(=\)	\(q+(-0.342020 + 0.939693i) q^{2} +(-1.68636 - 0.395229i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(-0.330418 + 1.87389i) q^{5} +(0.948161 - 1.44948i) q^{6} +(2.54679 - 0.716846i) q^{7} +(0.866025 - 0.500000i) q^{8} +(2.68759 + 1.33299i) q^{9} +O(q^{10})\)	\(q+(-0.342020 + 0.939693i) q^{2} +(-1.68636 - 0.395229i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(-0.330418 + 1.87389i) q^{5} +(0.948161 - 1.44948i) q^{6} +(2.54679 - 0.716846i) q^{7} +(0.866025 - 0.500000i) q^{8} +(2.68759 + 1.33299i) q^{9} +(-1.64788 - 0.951401i) q^{10} +(-1.99795 + 0.352293i) q^{11} +(1.03778 + 1.38673i) q^{12} +(0.169770 + 0.466440i) q^{13} +(-0.197438 + 2.63837i) q^{14} +(1.29782 - 3.02946i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-2.21416 + 3.83503i) q^{17} +(-2.17181 + 2.06960i) q^{18} +(-3.77699 + 2.18065i) q^{19} +(1.45763 - 1.22310i) q^{20} +(-4.57811 + 0.202293i) q^{21} +(0.352293 - 1.99795i) q^{22} +(-3.43842 + 4.09775i) q^{23} +(-1.65804 + 0.500900i) q^{24} +(1.29616 + 0.471763i) q^{25} -0.496375 q^{26} +(-4.00539 - 3.31011i) q^{27} +(-2.41173 - 1.08791i) q^{28} +(-2.07195 + 5.69263i) q^{29} +(2.40288 + 2.25569i) q^{30} +(-0.836828 + 0.997292i) q^{31} +(-0.984808 - 0.173648i) q^{32} +(3.50849 + 0.195557i) q^{33} +(-2.84647 - 3.39229i) q^{34} +(0.501788 + 5.00927i) q^{35} +(-1.20198 - 2.74868i) q^{36} +(-3.22468 + 5.58532i) q^{37} +(-0.757330 - 4.29503i) q^{38} +(-0.101942 - 0.853681i) q^{39} +(0.650797 + 1.78805i) q^{40} +(1.67326 - 0.609017i) q^{41} +(1.37571 - 4.37120i) q^{42} +(-0.194294 - 1.10190i) q^{43} +(1.75697 + 1.01439i) q^{44} +(-3.38592 + 4.59581i) q^{45} +(-2.67462 - 4.63258i) q^{46} +(8.86416 - 7.43791i) q^{47} +(0.0963917 - 1.72937i) q^{48} +(5.97226 - 3.65131i) q^{49} +(-0.886624 + 1.05664i) q^{50} +(5.24957 - 5.59213i) q^{51} +(0.169770 - 0.466440i) q^{52} +6.77888i q^{53} +(4.48041 - 2.63171i) q^{54} -3.86036i q^{55} +(1.84716 - 1.89420i) q^{56} +(7.23120 - 2.18457i) q^{57} +(-4.64068 - 3.89399i) q^{58} +(-0.400404 + 2.27080i) q^{59} +(-2.94149 + 1.48648i) q^{60} +(-3.31870 - 3.95508i) q^{61} +(-0.650936 - 1.12745i) q^{62} +(7.80027 + 1.46826i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-0.930154 + 0.164011i) q^{65} +(-1.38374 + 3.23002i) q^{66} +(9.96015 - 3.62520i) q^{67} +(4.16126 - 1.51457i) q^{68} +(7.41795 - 5.55131i) q^{69} +(-4.87880 - 1.24175i) q^{70} +(-0.688323 - 0.397403i) q^{71} +(2.99402 - 0.189389i) q^{72} +(-11.1538 + 6.43963i) q^{73} +(-4.14557 - 4.94050i) q^{74} +(-1.99933 - 1.30784i) q^{75} +(4.29503 + 0.757330i) q^{76} +(-4.83582 + 2.32944i) q^{77} +(0.837064 + 0.196182i) q^{78} +(-13.3611 - 4.86305i) q^{79} -1.90280 q^{80} +(5.44626 + 7.16507i) q^{81} +1.78065i q^{82} +(10.7214 + 3.90227i) q^{83} +(3.63707 + 2.78779i) q^{84} +(-6.45485 - 5.41626i) q^{85} +(1.10190 + 0.194294i) q^{86} +(5.74394 - 8.78091i) q^{87} +(-1.55413 + 1.30407i) q^{88} +(1.09582 + 1.89801i) q^{89} +(-3.16060 - 4.75358i) q^{90} +(0.766734 + 1.06622i) q^{91} +(5.26797 - 0.928885i) q^{92} +(1.80535 - 1.35105i) q^{93} +(3.95763 + 10.8735i) q^{94} +(-2.83831 - 7.79820i) q^{95} +(1.59211 + 0.682057i) q^{96} +(11.7066 - 2.06420i) q^{97} +(1.38847 + 6.86091i) q^{98} +(-5.83928 - 1.71644i) 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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