LMFDB - Embedded newform 966.2.j.a.137.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(137,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4, 3]))

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

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

chi := DirichletCharacter("966.137");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.j (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$64$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			137.9
Character	$\chi$	$=$	966.137
Dual form			966.2.j.a.275.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-1.25907 + 1.18943i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.82493 - 3.16086i) q^{5} +(0.495676 - 1.65961i) q^{6} +(-2.63810 - 0.201024i) q^{7} +1.00000i q^{8} +(0.170531 - 2.99515i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.25907 + 1.18943i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.82493 - 3.16086i) q^{5} +(0.495676 - 1.65961i) q^{6} +(-2.63810 - 0.201024i) q^{7} +1.00000i q^{8} +(0.170531 - 2.99515i) q^{9} +(3.16086 + 1.82493i) q^{10} +(1.75782 - 3.04463i) q^{11} +(0.400537 + 1.68510i) q^{12} -6.74736 q^{13} +(2.38518 - 1.14496i) q^{14} +(6.05733 + 1.80914i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.07813 + 1.86737i) q^{17} +(1.34989 + 2.67914i) q^{18} +(2.41351 - 1.39344i) q^{19} -3.64985 q^{20} +(3.56067 - 2.88473i) q^{21} +3.51564i q^{22} +(0.681540 - 4.74716i) q^{23} +(-1.18943 - 1.25907i) q^{24} +(-4.16070 + 7.20655i) q^{25} +(5.84338 - 3.37368i) q^{26} +(3.34780 + 3.97395i) q^{27} +(-1.49314 + 2.18415i) q^{28} +1.51015i q^{29} +(-6.15037 + 1.46190i) q^{30} +(-0.307060 + 0.531843i) q^{31} +(0.866025 + 0.500000i) q^{32} +(1.40814 + 5.92421i) q^{33} -2.15625i q^{34} +(4.17893 + 8.70554i) q^{35} +(-2.50861 - 1.64526i) q^{36} +(2.57728 - 1.48799i) q^{37} +(-1.39344 + 2.41351i) q^{38} +(8.49541 - 8.02548i) q^{39} +(3.16086 - 1.82493i) q^{40} +9.93430i q^{41} +(-1.64127 + 4.27858i) q^{42} +12.8212i q^{43} +(-1.75782 - 3.04463i) q^{44} +(-9.77846 + 4.92690i) q^{45} +(1.78335 + 4.45193i) q^{46} +(-1.90907 + 1.10220i) q^{47} +(1.65961 + 0.495676i) q^{48} +(6.91918 + 1.06064i) q^{49} -8.32141i q^{50} +(-0.863659 - 3.63351i) q^{51} +(-3.37368 + 5.84338i) q^{52} +(4.79840 - 8.31108i) q^{53} +(-4.88625 - 1.76764i) q^{54} -12.8315 q^{55} +(0.201024 - 2.63810i) q^{56} +(-1.38139 + 4.62513i) q^{57} +(-0.755075 - 1.30783i) q^{58} +(-9.84716 - 5.68526i) q^{59} +(4.59543 - 4.34123i) q^{60} +(2.82177 - 1.62915i) q^{61} -0.614119i q^{62} +(-1.05197 + 7.86723i) q^{63} -1.00000 q^{64} +(12.3134 + 21.3275i) q^{65} +(-4.18159 - 4.42644i) q^{66} +(0.232417 + 0.134186i) q^{67} +(1.07813 + 1.86737i) q^{68} +(4.78828 + 6.78766i) q^{69} +(-7.97183 - 5.44975i) q^{70} -12.1776i q^{71} +(2.99515 + 0.170531i) q^{72} +(-5.51937 + 9.55983i) q^{73} +(-1.48799 + 2.57728i) q^{74} +(-3.33303 - 14.0224i) q^{75} -2.78688i q^{76} +(-5.24935 + 7.67869i) q^{77} +(-3.34450 + 11.1980i) q^{78} +(-11.3698 + 6.56436i) q^{79} +(-1.82493 + 3.16086i) q^{80} +(-8.94184 - 1.02153i) q^{81} +(-4.96715 - 8.60336i) q^{82} +0.829779 q^{83} +(-0.717912 - 4.52599i) q^{84} +7.87001 q^{85} +(-6.41062 - 11.1035i) q^{86} +(-1.79621 - 1.90139i) q^{87} +(3.04463 + 1.75782i) q^{88} +(-2.83747 - 4.91465i) q^{89} +(6.00495 - 9.15605i) q^{90} +(17.8002 + 1.35638i) q^{91} +(-3.77039 - 2.96381i) q^{92} +(-0.245977 - 1.03485i) q^{93} +(1.10220 - 1.90907i) q^{94} +(-8.80894 - 5.08585i) q^{95} +(-1.68510 + 0.400537i) q^{96} +11.5037i q^{97} +(-6.52251 + 2.54105i) q^{98} +(-8.81936 - 5.78413i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 64 q^{4} + 8 q^{6} - 4 q^{9}+O(q^{10}) $ 128 * q + 64 * q^4 + 8 * q^6 - 4 * q^9	$ 128 q + 64 q^{4} + 8 q^{6} - 4 q^{9} - 64 q^{16} + 4 q^{24} - 72 q^{25} + 24 q^{27} - 8 q^{36} + 4 q^{39} + 12 q^{46} + 72 q^{49} + 4 q^{54} - 96 q^{55} - 128 q^{64} - 56 q^{69} + 32 q^{70} - 40 q^{73} - 40 q^{75} - 16 q^{78} + 36 q^{81} - 32 q^{82} - 64 q^{85} - 24 q^{87} + 32 q^{93} - 8 q^{94} - 4 q^{96}+O(q^{100}) $ 128 * q + 64 * q^4 + 8 * q^6 - 4 * q^9 - 64 * q^16 + 4 * q^24 - 72 * q^25 + 24 * q^27 - 8 * q^36 + 4 * q^39 + 12 * q^46 + 72 * q^49 + 4 * q^54 - 96 * q^55 - 128 * q^64 - 56 * q^69 + 32 * q^70 - 40 * q^73 - 40 * q^75 - 16 * q^78 + 36 * q^81 - 32 * q^82 - 64 * q^85 - 24 * q^87 + 32 * q^93 - 8 * q^94 - 4 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−1.25907	+	1.18943i	−0.726926	+	0.686716i
$3$	−1.25907	+	1.18943i	−0.726926	+	0.686716i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−1.82493	−	3.16086i	−0.816131	−	1.41358i	−0.908513	−	0.417857i	$-0.862781\pi$
$5$	−1.82493	−	3.16086i	−0.816131	−	1.41358i	0.0923812	−	0.995724i	$-0.470552\pi$
$6$	0.495676	−	1.65961i	0.202359	−	0.677533i
$7$	−2.63810	−	0.201024i	−0.997109	−	0.0759798i
$7$	−2.63810	−	0.201024i	−0.997109	−	0.0759798i
$8$			1.00000i			0.353553i
$9$	0.170531	−	2.99515i	0.0568436	−	0.998383i
$10$	3.16086	+	1.82493i	0.999553	+	0.577092i
$11$	1.75782	−	3.04463i	0.530002	−	0.917991i	−0.469385	−	0.882993i	$-0.655524\pi$
$11$	1.75782	−	3.04463i	0.530002	−	0.917991i	0.999387	−	0.0349972i	$-0.0111422\pi$
$12$	0.400537	+	1.68510i	0.115625	+	0.486447i
$13$	−6.74736			−1.87138			−0.935690	−	0.352824i	$-0.885222\pi$
$13$	−6.74736			−1.87138			−0.935690	+	0.352824i	$0.885222\pi$
$14$	2.38518	−	1.14496i	0.637465	−	0.306003i
$15$	6.05733	+	1.80914i	1.56400	+	0.467119i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.07813	+	1.86737i	−0.261484	+	0.452904i	−0.966637	−	0.256152i	$-0.917545\pi$
$17$	−1.07813	+	1.86737i	−0.261484	+	0.452904i	0.705152	+	0.709056i	$0.250879\pi$
$18$	1.34989	+	2.67914i	0.318172	+	0.631480i
$19$	2.41351	−	1.39344i	0.553697	−	0.319677i	−0.196915	−	0.980421i	$-0.563092\pi$
$19$	2.41351	−	1.39344i	0.553697	−	0.319677i	0.750612	+	0.660744i	$0.229759\pi$
$20$	−3.64985			−0.816131
$21$	3.56067	−	2.88473i	0.777001	−	0.629499i
$22$			3.51564i			0.749536i
$23$	0.681540	−	4.74716i	0.142111	−	0.989851i
$23$	0.681540	−	4.74716i	0.142111	−	0.989851i
$24$	−1.18943	−	1.25907i	−0.242791	−	0.257007i
$25$	−4.16070	+	7.20655i	−0.832141	+	1.44131i
$26$	5.84338	−	3.37368i	1.14598	−	0.661633i
$27$	3.34780	+	3.97395i	0.644284	+	0.764786i
$28$	−1.49314	+	2.18415i	−0.282178	+	0.412766i
$29$			1.51015i			0.280428i	0.990121	+	0.140214i	$0.0447790\pi$
$29$			1.51015i			0.280428i	−0.990121	+	0.140214i	$0.955221\pi$
$30$	−6.15037	+	1.46190i	−1.12290	+	0.266905i
$31$	−0.307060	+	0.531843i	−0.0551496	+	0.0955218i	−0.892282	−	0.451478i	$-0.850897\pi$
$31$	−0.307060	+	0.531843i	−0.0551496	+	0.0955218i	0.837133	+	0.547000i	$0.184230\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	1.40814	+	5.92421i	0.245126	+	1.03127i
$34$		−	2.15625i		−	0.369795i
$35$	4.17893	+	8.70554i	0.706369	+	1.47150i
$36$	−2.50861	−	1.64526i	−0.418102	−	0.274210i
$37$	2.57728	−	1.48799i	0.423702	−	0.244625i	−0.272958	−	0.962026i	$-0.588002\pi$
$37$	2.57728	−	1.48799i	0.423702	−	0.244625i	0.696660	+	0.717401i	$0.254669\pi$
$38$	−1.39344	+	2.41351i	−0.226046	+	0.391523i
$39$	8.49541	−	8.02548i	1.36036	−	1.28511i
$40$	3.16086	−	1.82493i	0.499776	−	0.288546i
$41$			9.93430i			1.55148i	0.631054	+	0.775739i	$0.282622\pi$
$41$			9.93430i			1.55148i	−0.631054	+	0.775739i	$0.717378\pi$
$42$	−1.64127	+	4.27858i	−0.253253	+	0.660199i
$43$			12.8212i			1.95522i	0.210427	+	0.977610i	$0.432515\pi$
$43$			12.8212i			1.95522i	−0.210427	+	0.977610i	$0.567485\pi$
$44$	−1.75782	−	3.04463i	−0.265001	−	0.458995i
$45$	−9.77846	+	4.92690i	−1.45769	+	0.734459i
$46$	1.78335	+	4.45193i	0.262940	+	0.656401i
$47$	−1.90907	+	1.10220i	−0.278466	+	0.160772i	−0.632729	−	0.774374i	$-0.718065\pi$
$47$	−1.90907	+	1.10220i	−0.278466	+	0.160772i	0.354263	+	0.935146i	$0.384732\pi$
$48$	1.65961	+	0.495676i	0.239544	+	0.0715447i
$49$	6.91918	+	1.06064i	0.988454	+	0.151520i
$50$		−	8.32141i		−	1.17683i
$51$	−0.863659	−	3.63351i	−0.120936	−	0.508793i
$52$	−3.37368	+	5.84338i	−0.467845	+	0.810331i
$53$	4.79840	−	8.31108i	0.659111	−	1.14161i	−0.321735	−	0.946830i	$-0.604266\pi$
$53$	4.79840	−	8.31108i	0.659111	−	1.14161i	0.980846	−	0.194784i	$-0.0624007\pi$
$54$	−4.88625	−	1.76764i	−0.664935	−	0.240545i
$55$	−12.8315			−1.73021
$56$	0.201024	−	2.63810i	0.0268629	−	0.352531i
$57$	−1.38139	+	4.62513i	−0.182970	+	0.612614i
$58$	−0.755075	−	1.30783i	−0.0991463	−	0.171726i
$59$	−9.84716	−	5.68526i	−1.28199	−	0.740158i	−0.304779	−	0.952423i	$-0.598582\pi$
$59$	−9.84716	−	5.68526i	−1.28199	−	0.740158i	−0.977212	+	0.212266i	$0.931916\pi$
$60$	4.59543	−	4.34123i	0.593267	−	0.560450i
$61$	2.82177	−	1.62915i	0.361291	−	0.208591i	−0.308356	−	0.951271i	$-0.599779\pi$
$61$	2.82177	−	1.62915i	0.361291	−	0.208591i	0.669647	+	0.742680i	$0.266446\pi$
$62$		−	0.614119i		−	0.0779932i
$63$	−1.05197	+	7.86723i	−0.132536	+	0.991178i
$64$	−1.00000			−0.125000
$65$	12.3134	+	21.3275i	1.52729	+	2.64535i
$66$	−4.18159	−	4.42644i	−0.514718	−	0.544858i
$67$	0.232417	+	0.134186i	0.0283942	+	0.0163934i	0.514130	−	0.857712i	$-0.328115\pi$
$67$	0.232417	+	0.134186i	0.0283942	+	0.0163934i	−0.485736	+	0.874106i	$0.661448\pi$
$68$	1.07813	+	1.86737i	0.130742	+	0.226452i
$69$	4.78828	+	6.78766i	0.576442	+	0.817138i
$70$	−7.97183	−	5.44975i	−0.952816	−	0.651370i
$71$		−	12.1776i		−	1.44522i	−0.691259	−	0.722608i	$-0.742943\pi$
$71$		−	12.1776i		−	1.44522i	0.691259	−	0.722608i	$-0.257057\pi$
$72$	2.99515	+	0.170531i	0.352982	+	0.0200972i
$73$	−5.51937	+	9.55983i	−0.645993	+	1.11889i	0.338078	+	0.941118i	$0.390223\pi$
$73$	−5.51937	+	9.55983i	−0.645993	+	1.11889i	−0.984071	+	0.177775i	$0.943110\pi$
$74$	−1.48799	+	2.57728i	−0.172976	+	0.299603i
$75$	−3.33303	−	14.0224i	−0.384865	−	1.61917i
$76$		−	2.78688i		−	0.319677i
$77$	−5.24935	+	7.67869i	−0.598219	+	0.875068i
$78$	−3.34450	+	11.1980i	−0.378691	+	1.26792i
$79$	−11.3698	+	6.56436i	−1.27920	+	0.738548i	−0.976702	−	0.214600i	$-0.931155\pi$
$79$	−11.3698	+	6.56436i	−1.27920	+	0.738548i	−0.302502	+	0.953149i	$0.597822\pi$
$80$	−1.82493	+	3.16086i	−0.204033	+	0.353395i
$81$	−8.94184	−	1.02153i	−0.993538	−	0.113503i
$82$	−4.96715	−	8.60336i	−0.548530	−	0.950082i
$83$	0.829779			0.0910801			0.0455401	−	0.998963i	$-0.485499\pi$
$83$	0.829779			0.0910801			0.0455401	+	0.998963i	$0.485499\pi$
$84$	−0.717912	−	4.52599i	−0.0783306	−	0.493826i
$85$	7.87001			0.853622
$86$	−6.41062	−	11.1035i	−0.691274	−	1.19732i
$87$	−1.79621	−	1.90139i	−0.192574	−	0.203850i
$88$	3.04463	+	1.75782i	0.324559	+	0.187384i
$89$	−2.83747	−	4.91465i	−0.300772	−	0.520952i	0.675539	−	0.737324i	$-0.263911\pi$
$89$	−2.83747	−	4.91465i	−0.300772	−	0.520952i	−0.976311	+	0.216372i	$0.930578\pi$
$90$	6.00495	−	9.15605i	0.632977	−	0.965133i
$91$	17.8002	+	1.35638i	1.86597	+	0.142187i
$92$	−3.77039	−	2.96381i	−0.393090	−	0.308998i
$93$	−0.245977	−	1.03485i	−0.0255067	−	0.107309i
$94$	1.10220	−	1.90907i	0.113683	−	0.196905i
$95$	−8.80894	−	5.08585i	−0.903779	−	0.521797i
$96$	−1.68510	+	0.400537i	−0.171985	+	0.0408796i
$97$			11.5037i			1.16803i	0.811745	+	0.584013i	$0.198518\pi$
$97$			11.5037i			1.16803i	−0.811745	+	0.584013i	$0.801482\pi$
$98$	−6.52251	+	2.54105i	−0.658873	+	0.256684i
$99$	−8.81936	−	5.78413i	−0.886379	−	0.581327i
$100$	4.16070	+	7.20655i	0.416070	+	0.720655i
$101$	11.6864	+	6.74717i	1.16284	+	0.671368i	0.951984	−	0.306148i	$-0.0990403\pi$
$101$	11.6864	+	6.74717i	1.16284	+	0.671368i	0.210860	+	0.977516i	$0.432374\pi$
$102$	2.56471	+	2.71488i	0.253944	+	0.268813i
$103$	6.01843	−	3.47474i	0.593013	−	0.342376i	−0.173275	−	0.984874i	$-0.555435\pi$
$103$	6.01843	−	3.47474i	0.593013	−	0.342376i	0.766288	+	0.642497i	$0.222102\pi$
$104$		−	6.74736i		−	0.661633i
$105$	−15.6162	−	5.99038i	−1.52398	−	0.584601i
$106$			9.59680i			0.932124i
$107$	−2.19545	−	3.80263i	−0.212242	−	0.367614i	0.740174	−	0.672416i	$-0.234743\pi$
$107$	−2.19545	−	3.80263i	−0.212242	−	0.367614i	−0.952416	+	0.304802i	$0.901410\pi$
$108$	5.11544	−	0.912305i	0.492233	−	0.0877866i
$109$	−6.06338	−	3.50069i	−0.580766	−	0.335306i	0.180671	−	0.983543i	$-0.442173\pi$
$109$	−6.06338	−	3.50069i	−0.580766	−	0.335306i	−0.761438	+	0.648238i	$0.775506\pi$
$110$	11.1124	−	6.41577i	1.05953	−	0.611720i
$111$	−1.47513	+	4.93898i	−0.140013	+	0.468787i
$112$	1.14496	+	2.38518i	0.108189	+	0.225378i
$113$	3.52659			0.331753			0.165877	−	0.986146i	$-0.446955\pi$
$113$	3.52659			0.331753			0.165877	+	0.986146i	$0.446955\pi$
$114$	−1.11625	−	4.69618i	−0.104546	−	0.439837i
$115$	−16.2489	+	6.50895i	−1.51522	+	0.606963i
$116$	1.30783	+	0.755075i	0.121429	+	0.0701070i
$117$	−1.15063	+	20.2093i	−0.106376	+	1.86835i
$118$	11.3705			1.04674
$119$	3.21960	−	4.70959i	0.295140	−	0.431727i
$120$	−1.80914	+	6.05733i	−0.165152	+	0.552956i
$121$	−0.679850	−	1.17753i	−0.0618045	−	0.107049i
$122$	−1.62915	+	2.82177i	−0.147496	+	0.255471i
$123$	−11.8161	−	12.5080i	−1.06542	−	1.12781i
$124$	0.307060	+	0.531843i	0.0275748	+	0.0477609i
$125$	12.1226			1.08428
$126$	−3.02258	−	7.33921i	−0.269273	−	0.653829i
$127$	0.881650			0.0782338			0.0391169	−	0.999235i	$-0.487546\pi$
$127$	0.881650			0.0782338			0.0391169	+	0.999235i	$0.487546\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−15.2499	−	16.1429i	−1.34268	−	1.42130i
$130$	−21.3275	−	12.3134i	−1.87054	−	1.07996i
$131$	−6.02426	+	3.47811i	−0.526342	+	0.303884i	−0.739526	−	0.673128i	$-0.764950\pi$
$131$	−6.02426	+	3.47811i	−0.526342	+	0.303884i	0.213183	+	0.977012i	$0.431617\pi$
$132$	5.83459	+	1.74262i	0.507835	+	0.151675i
$133$	−6.64720	+	3.19087i	−0.576385	+	0.276683i
$134$	−0.268372			−0.0231838
$135$	6.45162	−	17.8341i	0.555267	−	1.53491i
$136$	−1.86737	−	1.07813i	−0.160126	−	0.0924486i
$137$	−1.99228	+	3.45073i	−0.170212	+	0.294816i	−0.938494	−	0.345296i	$-0.887779\pi$
$137$	−1.99228	+	3.45073i	−0.170212	+	0.294816i	0.768282	+	0.640112i	$0.221112\pi$
$138$	−7.54061	−	3.48414i	−0.641899	−	0.296590i
$139$	22.5504			1.91270			0.956349	−	0.292226i	$-0.0943961\pi$
$139$	22.5504			1.91270			0.956349	+	0.292226i	$0.0943961\pi$
$140$	9.62868	+	0.733706i	0.813772	+	0.0620095i
$141$	1.09267	−	3.65844i	0.0920193	−	0.308096i
$142$	6.08880	+	10.5461i	0.510961	+	0.885010i
$143$	−11.8606	+	20.5432i	−0.991835	+	1.71791i
$144$	−2.67914	+	1.34989i	−0.223262	+	0.112491i
$145$	4.77338	−	2.75591i	0.396408	−	0.228866i
$146$		−	11.0387i		−	0.913572i
$147$	−9.97331	+	6.89443i	−0.822585	+	0.568643i
$148$		−	2.97599i		−	0.244625i
$149$	6.41224	+	11.1063i	0.525311	+	0.909866i	0.999565	+	0.0294779i	$0.00938447\pi$
$149$	6.41224	+	11.1063i	0.525311	+	0.909866i	−0.474254	+	0.880388i	$0.657282\pi$
$150$	9.89770	+	10.4773i	0.808144	+	0.855465i
$151$	−8.61975	+	14.9299i	−0.701466	+	1.21497i	0.266486	+	0.963839i	$0.414137\pi$
$151$	−8.61975	+	14.9299i	−0.701466	+	1.21497i	−0.967952	+	0.251135i	$0.919196\pi$
$152$	1.39344	+	2.41351i	0.113023	+	0.195761i
$153$	5.40920	+	3.54760i	0.437308	+	0.286806i
$154$	0.706726	−	9.27461i	0.0569496	−	0.747370i
$155$	2.24144			0.180037
$156$	−2.70256	−	11.3700i	−0.216378	−	0.910327i
$157$	13.4766	+	7.78072i	1.07555	+	0.620969i	0.929692	−	0.368337i	$-0.120073\pi$
$157$	13.4766	+	7.78072i	1.07555	+	0.620969i	0.145857	+	0.989306i	$0.453406\pi$
$158$	6.56436	−	11.3698i	0.522233	−	0.904533i
$159$	3.84387	+	16.1716i	0.304839	+	1.28249i
$160$		−	3.64985i		−	0.288546i
$161$	−2.75226	+	12.3865i	−0.216909	+	0.976192i
$162$	8.25462	−	3.58625i	0.648545	−	0.281762i
$163$	−9.09525	−	15.7534i	−0.712395	−	1.23390i	−0.963956	−	0.266063i	$-0.914277\pi$
$163$	−9.09525	−	15.7534i	−0.712395	−	1.23390i	0.251561	−	0.967841i	$-0.419056\pi$
$164$	8.60336	+	4.96715i	0.671809	+	0.387869i
$165$	16.1559	−	15.2622i	1.25773	−	1.18816i
$166$	−0.718610	+	0.414890i	−0.0557749	+	0.0322017i
$167$		−	5.88063i		−	0.455057i	−0.973771	−	0.227529i	$-0.926935\pi$
$167$		−	5.88063i		−	0.455057i	0.973771	−	0.227529i	$-0.0730645\pi$
$168$	2.88473	+	3.56067i	0.222561	+	0.274712i
$169$	32.5268			2.50206
$170$	−6.81563	+	3.93500i	−0.522735	+	0.301801i
$171$	−3.76198	−	7.46644i	−0.287686	−	0.570973i
$172$	11.1035	+	6.41062i	0.846635	+	0.488805i
$173$	−8.40219	+	4.85101i	−0.638807	+	0.368815i	−0.784155	−	0.620565i	$-0.786903\pi$
$173$	−8.40219	+	4.85101i	−0.638807	+	0.368815i	0.145348	+	0.989381i	$0.453570\pi$
$174$	2.50626	+	0.748546i	0.189999	+	0.0567471i
$175$	12.4251	−	18.1752i	0.939246	−	1.37392i
$176$	−3.51564			−0.265001
$177$	19.1605	−	4.55431i	1.44019	−	0.342323i
$178$	4.91465	+	2.83747i	0.368369	+	0.212678i
$179$	10.3477	+	5.97426i	0.773426	+	0.446538i	0.834095	−	0.551620i	$-0.185990\pi$
$179$	10.3477	+	5.97426i	0.773426	+	0.446538i	−0.0606696	+	0.998158i	$0.519324\pi$
$180$	−0.622412	+	10.9318i	−0.0463918	+	0.814812i
$181$		−	15.0848i		−	1.12125i	−0.828071	−	0.560624i	$-0.810561\pi$
$181$		−	15.0848i		−	1.12125i	0.828071	−	0.560624i	$-0.189439\pi$
$182$	−16.0936	+	7.72545i	−1.19294	+	0.572649i
$183$	−1.61506	+	5.40751i	−0.119389	+	0.399734i
$184$	4.74716	+	0.681540i	0.349965	+	0.0502438i
$185$	−9.40668	−	5.43095i	−0.691593	−	0.399292i
$186$	0.730450	+	0.773221i	0.0535592	+	0.0566953i
$187$	3.79030	+	6.56500i	0.277174	+	0.480080i
$188$			2.20440i			0.160772i
$189$	−8.03298	−	11.1567i	−0.584313	−	0.811528i
$190$	10.1717			0.737932
$191$	6.01000	+	10.4096i	0.434868	+	0.753214i	0.997285	−	0.0736402i	$-0.0234616\pi$
$191$	6.01000	+	10.4096i	0.434868	+	0.753214i	−0.562417	+	0.826854i	$0.690128\pi$
$192$	1.25907	−	1.18943i	0.0908658	−	0.0858394i
$193$	2.69725	−	4.67177i	0.194152	−	0.336281i	−0.752470	−	0.658626i	$-0.771138\pi$
$193$	2.69725	−	4.67177i	0.194152	−	0.336281i	0.946622	+	0.322345i	$0.104471\pi$
$194$	−5.75186	−	9.96251i	−0.412959	−	0.715267i
$195$	−40.8709	−	12.2069i	−2.92683	−	0.874157i
$196$	4.37813	−	5.46186i	0.312724	−	0.390133i
$197$			18.1653i			1.29423i	0.762394	+	0.647113i	$0.224024\pi$
$197$			18.1653i			1.29423i	−0.762394	+	0.647113i	$0.775976\pi$
$198$	10.5299	+	0.599524i	0.748324	+	0.0426063i
$199$	3.19727	+	1.84594i	0.226648	+	0.130855i	0.609025	−	0.793151i	$-0.291561\pi$
$199$	3.19727	+	1.84594i	0.226648	+	0.130855i	−0.382377	+	0.924007i	$0.624894\pi$
$200$	−7.20655	−	4.16070i	−0.509580	−	0.294206i
$201$	−0.452234	+	0.107493i	−0.0318981	+	0.00758195i
$202$	−13.4943			−0.949458
$203$	0.303576	−	3.98393i	0.0213069	−	0.279617i
$204$	−3.57854	−	1.06880i	−0.250548	−	0.0748313i
$205$	31.4010	−	18.1294i	2.19314	−	1.26621i
$206$	−3.47474	+	6.01843i	−0.242097	+	0.419324i
$207$	−14.1022	−	2.85085i	−0.980172	−	0.198148i
$208$	3.37368	+	5.84338i	0.233922	+	0.405166i
$209$		−	9.79765i		−	0.677718i
$210$	16.5192	−	2.62027i	1.13993	−	0.180816i
$211$	11.0719			0.762220			0.381110	−	0.924530i	$-0.375542\pi$
$211$	11.0719			0.762220			0.381110	+	0.924530i	$0.375542\pi$
$212$	−4.79840	−	8.31108i	−0.329556	−	0.570807i
$213$	14.4844	+	15.3325i	0.992452	+	1.05056i
$214$	3.80263	+	2.19545i	0.259942	+	0.150078i
$215$	40.5262	−	23.3978i	2.76386	−	1.59572i
$216$	−3.97395	+	3.34780i	−0.270393	+	0.227789i
$217$	0.916968	−	1.34133i	0.0622479	−	0.0910555i
$218$	7.00139			0.474194
$219$	−4.42142	−	18.6014i	−0.298772	−	1.25697i
$220$	−6.41577	+	11.1124i	−0.432551	+	0.749201i
$221$	7.27451	−	12.5998i	0.489336	−	0.847555i
$222$	−1.19199	−	5.01484i	−0.0800012	−	0.336574i
$223$	2.45274			0.164247			0.0821237	−	0.996622i	$-0.473830\pi$
$223$	2.45274			0.164247			0.0821237	+	0.996622i	$0.473830\pi$
$224$	−2.18415	−	1.49314i	−0.145935	−	0.0997648i
$225$	20.8752	+	13.6909i	1.39168	+	0.912725i
$226$	−3.05411	+	1.76329i	−0.203157	+	0.117293i
$227$	10.4950	−	18.1778i	0.696575	−	1.20650i	−0.273071	−	0.961994i	$-0.588039\pi$
$227$	10.4950	−	18.1778i	0.696575	−	1.20650i	0.969647	−	0.244510i	$-0.0786272\pi$
$228$	3.31479	+	3.50889i	0.219527	+	0.232382i
$229$	2.44746	−	1.41304i	0.161732	−	0.0933763i	−0.416949	−	0.908930i	$-0.636901\pi$
$229$	2.44746	−	1.41304i	0.161732	−	0.0933763i	0.578682	+	0.815553i	$0.303567\pi$
$230$	10.8175	−	13.7614i	0.713282	−	0.907397i
$231$	−2.52392	−	15.9117i	−0.166062	−	1.04692i
$232$	−1.51015			−0.0991463
$233$	−6.63013	+	3.82791i	−0.434354	+	0.250775i	−0.701200	−	0.712965i	$-0.747352\pi$
$233$	−6.63013	+	3.82791i	−0.434354	+	0.250775i	0.266846	+	0.963739i	$0.414019\pi$
$234$	−9.10819	−	18.0771i	−0.595421	−	1.18174i
$235$	6.96780	+	4.02286i	0.454529	+	0.262423i
$236$	−9.84716	+	5.68526i	−0.640995	+	0.370079i
$237$	6.50760	−	21.7886i	0.422714	−	1.41532i
$238$	−0.433458	+	5.68842i	−0.0280969	+	0.368726i
$239$			3.33073i			0.215447i	0.994181	+	0.107723i	$0.0343561\pi$
$239$			3.33073i			0.215447i	−0.994181	+	0.107723i	$0.965644\pi$
$240$	−1.46190	−	6.15037i	−0.0943652	−	0.397005i
$241$	−22.1440	−	12.7849i	−1.42642	−	0.823545i	−0.429586	−	0.903026i	$-0.641340\pi$
$241$	−22.1440	−	12.7849i	−1.42642	−	0.823545i	−0.996836	+	0.0794810i	$0.974674\pi$
$242$	1.17753	+	0.679850i	0.0756948	+	0.0437024i
$243$	12.4735	−	9.34948i	0.800173	−	0.599769i
$244$		−	3.25830i		−	0.208591i
$245$	−9.27444	−	23.8062i	−0.592522	−	1.52092i
$246$	16.4871	+	4.92420i	1.05118	+	0.313955i
$247$	−16.2848	+	9.40203i	−1.03618	+	0.598237i
$248$	−0.531843	−	0.307060i	−0.0337721	−	0.0194983i
$249$	−1.04475	+	0.986961i	−0.0662085	+	0.0625461i
$250$	−10.4985	+	6.06132i	−0.663985	+	0.383352i
$251$	−20.5145			−1.29486			−0.647432	−	0.762123i	$-0.724157\pi$
$251$	−20.5145			−1.29486			−0.647432	+	0.762123i	$0.724157\pi$
$252$	6.28724	+	4.84465i	0.396059	+	0.305184i
$253$	−13.2553	−	10.4197i	−0.833355	−	0.655079i
$254$	−0.763532	+	0.440825i	−0.0479082	+	0.0276598i
$255$	−9.90891	+	9.36079i	−0.620520	+	0.586196i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−14.8875	+	8.59530i	−0.928657	+	0.536160i	−0.886386	−	0.462946i	$-0.846792\pi$
$257$	−14.8875	+	8.59530i	−0.928657	+	0.536160i	−0.0422701	+	0.999106i	$0.513459\pi$
$258$	21.2782	+	6.35518i	1.32473	+	0.395656i
$259$	−7.09825	+	3.40738i	−0.441064	+	0.211725i
$260$	24.6268			1.52729
$261$	4.52313	+	0.257527i	0.279975	+	0.0159405i
$262$	3.47811	−	6.02426i	0.214878	−	0.372180i
$263$	6.34012	−	10.9814i	0.390949	−	0.677143i	−0.601626	−	0.798778i	$-0.705480\pi$
$263$	6.34012	−	10.9814i	0.390949	−	0.677143i	0.992575	+	0.121635i	$0.0388136\pi$
$264$	−5.92421	+	1.40814i	−0.364610	+	0.0866651i
$265$	−35.0269			−2.15169
$266$	4.16121	−	6.08697i	0.255140	−	0.373216i
$267$	9.41820	+	2.81294i	0.576385	+	0.172149i
$268$	0.232417	−	0.134186i	0.0141971	−	0.00819670i
$269$	3.78604	+	2.18587i	0.230839	+	0.133275i	0.610959	−	0.791662i	$-0.290784\pi$
$269$	3.78604	+	2.18587i	0.230839	+	0.133275i	−0.380120	+	0.924937i	$0.624117\pi$
$270$	3.32978	+	18.6706i	0.202644	+	1.13626i
$271$	7.88328	+	13.6542i	0.478875	+	0.829436i	0.999707	−	0.0242233i	$-0.00771126\pi$
$271$	7.88328	+	13.6542i	0.478875	+	0.829436i	−0.520831	+	0.853660i	$0.674378\pi$
$272$	2.15625			0.130742
$273$	−24.0251	+	19.4643i	−1.45406	+	1.17803i
$274$		−	3.98456i		−	0.240716i
$275$	14.6275	+	25.3356i	0.882073	+	1.52780i
$276$	8.27243	−	0.752946i	0.497942	−	0.0453220i
$277$	3.18675	−	5.51961i	0.191473	−	0.331641i	−0.754266	−	0.656569i	$-0.772007\pi$
$277$	3.18675	−	5.51961i	0.191473	−	0.331641i	0.945739	+	0.324928i	$0.105340\pi$
$278$	−19.5292	+	11.2752i	−1.17128	+	0.676241i
$279$	1.54059	+	1.01039i	0.0922325	+	0.0604902i
$280$	−8.70554	+	4.17893i	−0.520255	+	0.249739i
$281$	−15.8916			−0.948016			−0.474008	−	0.880520i	$-0.657193\pi$
$281$	−15.8916			−0.948016			−0.474008	+	0.880520i	$0.657193\pi$
$282$	0.882943	+	3.71464i	0.0525785	+	0.221204i
$283$	−19.4489	−	11.2288i	−1.15612	−	0.667486i	−0.205748	−	0.978605i	$-0.565963\pi$
$283$	−19.4489	−	11.2288i	−1.15612	−	0.667486i	−0.950371	+	0.311119i	$0.899296\pi$
$284$	−10.5461	−	6.08880i	−0.625796	−	0.361304i
$285$	17.1403	−	4.07414i	1.01531	−	0.241331i
$286$		−	23.7212i		−	1.40267i
$287$	1.99703	−	26.2077i	0.117881	−	1.54699i
$288$	1.64526	−	2.50861i	0.0969478	−	0.147821i
$289$	6.17528	+	10.6959i	0.363252	+	0.629171i
$290$	−2.75591	+	4.77338i	−0.161833	+	0.280303i
$291$	−13.6828	−	14.4840i	−0.802101	−	0.849068i
$292$	5.51937	+	9.55983i	0.322997	+	0.559447i
$293$	−15.3692			−0.897876			−0.448938	−	0.893563i	$-0.648198\pi$
$293$	−15.3692			−0.897876			−0.448938	+	0.893563i	$0.648198\pi$
$294$	5.18993	−	10.9574i	0.302683	−	0.639049i
$295$			41.5007i			2.41626i
$296$	1.48799	+	2.57728i	0.0864878	+	0.149801i
$297$	17.9840	−	3.20733i	1.04354	−	0.186108i
$298$	−11.1063	−	6.41224i	−0.643372	−	0.371451i
$299$	−4.59859	+	32.0308i	−0.265943	+	1.85239i
$300$	−13.8103	−	4.12473i	−0.797338	−	0.238141i
$301$	2.57737	−	33.8237i	0.148557	−	1.94957i
$302$		−	17.2395i		−	0.992022i
$303$	−22.7393	+	5.40497i	−1.30634	+	0.310508i
$304$	−2.41351	−	1.39344i	−0.138424	−	0.0799192i
$305$	−10.2990	−	5.94615i	−0.589721	−	0.340476i
$306$	−6.45830	−	0.367708i	−0.369197	−	0.0210204i
$307$	15.6396			0.892601			0.446301	−	0.894883i	$-0.352741\pi$
$307$	15.6396			0.892601			0.446301	+	0.894883i	$0.352741\pi$
$308$	4.02526	+	8.38541i	0.229361	+	0.477803i
$309$	−3.44469	+	11.5334i	−0.195962	+	0.656114i
$310$	−1.94115	+	1.12072i	−0.110250	+	0.0636527i
$311$	10.0473	+	5.80080i	0.569729	+	0.328933i	0.757041	−	0.653367i	$-0.226644\pi$
$311$	10.0473	+	5.80080i	0.569729	+	0.328933i	−0.187312	+	0.982300i	$0.559978\pi$
$312$	8.02548	+	8.49541i	0.454353	+	0.480958i
$313$	−10.7305	+	6.19525i	−0.606523	+	0.350176i	−0.771603	−	0.636104i	$-0.780545\pi$
$313$	−10.7305	+	6.19525i	−0.606523	+	0.350176i	0.165080	+	0.986280i	$0.447212\pi$
$314$	−15.5614			−0.878183
$315$	26.7870	−	11.0320i	1.50928	−	0.621581i
$316$			13.1287i			0.738548i
$317$	−18.6279	+	10.7548i	−1.04625	+	0.604052i	−0.921597	−	0.388149i	$-0.873115\pi$
$317$	−18.6279	+	10.7548i	−1.04625	+	0.604052i	−0.124652	+	0.992201i	$0.539781\pi$
$318$	−11.4147	−	12.0831i	−0.640104	−	0.677585i
$319$	4.59785	+	2.65457i	0.257430	+	0.148627i
$320$	1.82493	+	3.16086i	0.102016	+	0.176698i
$321$	7.28718	+	2.17646i	0.406731	+	0.121478i
$322$	−3.80971	−	12.1031i	−0.212307	−	0.674482i
$323$			6.00922i			0.334362i
$324$	−5.35559	+	7.23309i	−0.297533	+	0.401839i
$325$	28.0738	−	48.6252i	1.55725	−	2.69724i
$326$	15.7534	+	9.09525i	0.872502	+	0.503739i
$327$	11.7981	−	2.80431i	0.652434	−	0.155079i
$328$	−9.93430			−0.548530
$329$	5.25788	−	2.52395i	0.289876	−	0.139150i
$330$	−6.36029	+	21.2954i	−0.350123	+	1.17227i
$331$	−2.04592	−	3.54363i	−0.112454	−	0.194776i	0.804305	−	0.594216i	$-0.202538\pi$
$331$	−2.04592	−	3.54363i	−0.112454	−	0.194776i	−0.916759	+	0.399441i	$0.869204\pi$
$332$	0.414890	−	0.718610i	0.0227700	−	0.0394388i
$333$	−4.01726	−	7.97308i	−0.220144	−	0.436922i
$334$	2.94032	+	5.09278i	0.160887	+	0.278664i
$335$		−	0.979517i		−	0.0535167i
$336$	−4.27858	−	1.64127i	−0.233416	−	0.0895384i
$337$			14.4965i			0.789672i	0.918752	+	0.394836i	$0.129199\pi$
$337$			14.4965i			0.789672i	−0.918752	+	0.394836i	$0.870801\pi$
$338$	−28.1690	+	16.2634i	−1.53219	+	0.884612i
$339$	−4.44023	+	4.19462i	−0.241160	+	0.227820i
$340$	3.93500	−	6.81563i	0.213406	−	0.369629i
$341$	1.07951	+	1.86977i	0.0584588	+	0.101254i
$342$	6.99119	+	4.58514i	0.378040	+	0.247936i
$343$	−18.0403	−	4.18900i	−0.974084	−	0.226185i
$344$	−12.8212			−0.691274
$345$	12.7166	−	27.5221i	0.684639	−	1.48174i
$346$	4.85101	−	8.40219i	0.260792	−	0.451705i
$347$	13.3840	+	7.72727i	0.718492	+	0.414822i	0.814198	−	0.580588i	$-0.197177\pi$
$347$	13.3840	+	7.72727i	0.718492	+	0.414822i	−0.0957051	+	0.995410i	$0.530511\pi$
$348$	−2.54476	+	0.604871i	−0.136413	+	0.0324245i
$349$	−17.4317			−0.933097			−0.466549	−	0.884496i	$-0.654503\pi$
$349$	−17.4317			−0.933097			−0.466549	+	0.884496i	$0.654503\pi$
$350$	−1.67280	+	21.9527i	−0.0894149	+	1.17342i
$351$	−22.5888	−	26.8136i	−1.20570	−	1.43121i
$352$	3.04463	−	1.75782i	0.162279	−	0.0936920i
$353$	−1.83485	−	1.05935i	−0.0976593	−	0.0563836i	0.450375	−	0.892840i	$-0.351290\pi$
$353$	−1.83485	−	1.05935i	−0.0976593	−	0.0563836i	−0.548034	+	0.836456i	$0.684624\pi$
$354$	−14.3163	+	13.5244i	−0.760904	+	0.718813i
$355$	−38.4917	+	22.2232i	−2.04293	+	1.17949i
$356$	−5.67495			−0.300772
$357$	1.54800	+	9.75919i	0.0819289	+	0.516511i
$358$	−11.9485			−0.631499
$359$	−7.17412	−	12.4259i	−0.378635	−	0.655816i	0.612229	−	0.790681i	$-0.290273\pi$
$359$	−7.17412	−	12.4259i	−0.378635	−	0.655816i	−0.990864	+	0.134865i	$0.956940\pi$
$360$	−4.92690	−	9.77846i	−0.259670	−	0.515370i
$361$	−5.61665	+	9.72833i	−0.295613	+	0.512017i
$362$	7.54242	+	13.0639i	0.396421	+	0.686621i
$363$	2.25657	+	0.673971i	0.118439	+	0.0353743i
$364$	10.0748	−	14.7373i	0.528061	−	0.772442i
$365$	40.2897			2.10886
$366$	−1.30507	−	5.49057i	−0.0682170	−	0.286997i
$367$	0.950286	+	0.548648i	0.0496045	+	0.0286392i	0.524597	−	0.851351i	$-0.324216\pi$
$367$	0.950286	+	0.548648i	0.0496045	+	0.0286392i	−0.474993	+	0.879990i	$0.657549\pi$
$368$	−4.45193	+	1.78335i	−0.232073	+	0.0929634i
$369$	29.7547	+	1.69410i	1.54897	+	0.0881915i
$370$	10.8619			0.564683
$371$	−14.3294	+	20.9609i	−0.743946	+	1.08823i
$372$	−1.01920	−	0.304404i	−0.0528430	−	0.0157826i
$373$	23.4253	−	13.5246i	1.21291	−	0.700277i	0.249522	−	0.968369i	$-0.419727\pi$
$373$	23.4253	−	13.5246i	1.21291	−	0.700277i	0.963393	+	0.268093i	$0.0863933\pi$
$374$	−6.56500	−	3.79030i	−0.339468	−	0.195992i
$375$	−15.2633	+	14.4190i	−0.788194	+	0.744594i
$376$	−1.10220	−	1.90907i	−0.0568416	−	0.0984525i
$377$		−	10.1895i		−	0.524787i
$378$	12.5351	+	5.64547i	0.644736	+	0.290371i
$379$		−	22.1641i		−	1.13849i	−0.822167	−	0.569247i	$-0.807235\pi$
$379$		−	22.1641i		−	1.13849i	0.822167	−	0.569247i	$-0.192765\pi$
$380$	−8.80894	+	5.08585i	−0.451889	+	0.260898i
$381$	−1.11006	+	1.04866i	−0.0568702	+	0.0537244i
$382$	−10.4096	−	6.01000i	−0.532603	−	0.307498i
$383$	−19.3201	−	33.4634i	−0.987210	−	1.70990i	−0.631669	−	0.775238i	$-0.717630\pi$
$383$	−19.3201	−	33.4634i	−0.987210	−	1.70990i	−0.355541	−	0.934661i	$-0.615703\pi$
$384$	−0.495676	+	1.65961i	−0.0252949	+	0.0846916i
$385$	33.8510	+	2.57944i	1.72520	+	0.131461i
$386$			5.39449i			0.274572i
$387$	38.4015	+	2.18641i	1.95206	+	0.111142i
$388$	9.96251	+	5.75186i	0.505770	+	0.292006i
$389$	−5.86748	+	10.1628i	−0.297493	+	0.515273i	−0.975562	−	0.219725i	$-0.929484\pi$
$389$	−5.86748	+	10.1628i	−0.297493	+	0.515273i	0.678069	+	0.734999i	$0.262817\pi$
$390$	41.4987	−	9.86395i	2.10137	−	0.499481i
$391$	8.12992	+	6.39073i	0.411148	+	0.323193i
$392$	−1.06064	+	6.91918i	−0.0535705	+	0.349471i
$393$	3.44803	−	11.5446i	0.173930	−	0.582349i
$394$	−9.08266	−	15.7316i	−0.457578	−	0.792548i
$395$	41.4981	+	23.9589i	2.08800	+	1.20551i
$396$	−9.41888	+	4.74572i	−0.473317	+	0.238482i
$397$	4.01876	+	6.96070i	0.201696	+	0.349347i	0.949075	−	0.315050i	$-0.102021\pi$
$397$	4.01876	+	6.96070i	0.201696	+	0.349347i	−0.747379	+	0.664398i	$0.768688\pi$
$398$	−3.69189			−0.185058
$399$	4.57401	−	11.9239i	0.228987	−	0.596941i
$400$	8.32141			0.416070
$401$	−2.42695	−	4.20360i	−0.121196	−	0.209918i	0.799043	−	0.601273i	$-0.205340\pi$
$401$	−2.42695	−	4.20360i	−0.121196	−	0.209918i	−0.920240	+	0.391355i	$0.872006\pi$
$402$	0.337900	−	0.319208i	0.0168529	−	0.0159207i
$403$	2.07184	−	3.58853i	0.103206	−	0.178758i
$404$	11.6864	−	6.74717i	0.581422	−	0.335684i
$405$	13.0893	+	30.1281i	0.650411	+	1.49708i
$406$	1.72906	+	3.60198i	0.0858119	+	0.178763i
$407$		−	10.4625i		−	0.518606i
$408$	3.63351	−	0.863659i	0.179886	−	0.0427575i
$409$	1.50388	−	2.60479i	0.0743619	−	0.128799i	−0.826447	−	0.563015i	$-0.809641\pi$
$409$	1.50388	−	2.60479i	0.0743619	−	0.128799i	0.900809	+	0.434216i	$0.142975\pi$
$410$	−18.1294	+	31.4010i	−0.895345	+	1.55078i
$411$	−1.59596	−	6.71439i	−0.0787230	−	0.331196i
$412$		−	6.94948i		−	0.342376i
$413$	24.8349	+	16.9778i	1.22205	+	0.835424i
$414$	13.6383	−	4.58220i	0.670286	−	0.225203i
$415$	−1.51429	−	2.62282i	−0.0743333	−	0.128749i
$416$	−5.84338	−	3.37368i	−0.286495	−	0.165408i
$417$	−28.3926	+	26.8220i	−1.39039	+	1.31348i
$418$	4.89883	+	8.48502i	0.239609	+	0.415016i
$419$	−0.907912			−0.0443544			−0.0221772	−	0.999754i	$-0.507060\pi$
$419$	−0.907912			−0.0443544			−0.0221772	+	0.999754i	$0.507060\pi$
$420$	−12.9959	+	10.5288i	−0.634135	+	0.513754i
$421$			38.6819i			1.88524i	0.333870	+	0.942619i	$0.391645\pi$
$421$			38.6819i			1.88524i	−0.333870	+	0.942619i	$0.608355\pi$
$422$	−9.58853	+	5.53594i	−0.466762	+	0.269485i
$423$	2.97570	+	5.90590i	0.144683	+	0.287154i
$424$	8.31108	+	4.79840i	0.403622	+	0.233031i
$425$	−8.97154	−	15.5392i	−0.435184	−	0.753760i
$426$	−20.2101	−	6.03615i	−0.979181	−	0.292452i
$427$	−7.77162	+	3.73062i	−0.376095	+	0.180537i
$428$	−4.39090			−0.212242
$429$	−9.50123	−	39.9727i	−0.458724	−	1.92990i
$430$	−23.3978	+	40.5262i	−1.12834	+	1.95434i
$431$	−3.02822	+	5.24503i	−0.145864	+	0.252644i	−0.929695	−	0.368330i	$-0.879930\pi$
$431$	−3.02822	+	5.24503i	−0.145864	+	0.252644i	0.783831	+	0.620974i	$0.213263\pi$
$432$	1.76764	−	4.88625i	0.0850456	−	0.235090i
$433$			18.8956i			0.908066i	0.890985	+	0.454033i	$0.150015\pi$
$433$			18.8956i			0.908066i	−0.890985	+	0.454033i	$0.849985\pi$
$434$	−0.123453	+	1.62011i	−0.00592591	+	0.0777678i
$435$	−2.73208	+	9.14748i	−0.130993	+	0.438588i
$436$	−6.06338	+	3.50069i	−0.290383	+	0.167653i
$437$	−4.96998	−	12.4070i	−0.237746	−	0.593507i
$438$	13.1298	+	13.8986i	0.627364	+	0.664100i
$439$	−8.99736	−	15.5839i	−0.429421	−	0.743778i	0.567401	−	0.823441i	$-0.307949\pi$
$439$	−8.99736	−	15.5839i	−0.429421	−	0.743778i	−0.996822	+	0.0796631i	$0.974616\pi$
$440$		−	12.8315i		−	0.611720i
$441$	4.35672	−	20.5431i	0.207463	−	0.978243i
$442$			14.5490i			0.692026i
$443$	12.4623	−	7.19509i	0.592100	−	0.341849i	−0.173827	−	0.984776i	$-0.555613\pi$
$443$	12.4623	−	7.19509i	0.592100	−	0.341849i	0.765927	+	0.642927i	$0.222280\pi$
$444$	3.53972	+	3.74698i	0.167987	+	0.177824i
$445$	−10.3564	+	17.9377i	−0.490938	+	0.850330i
$446$	−2.12413	+	1.22637i	−0.100581	+	0.0580702i
$447$	−21.2836	−	6.35679i	−1.00668	−	0.300666i
$448$	2.63810	+	0.201024i	0.124639	+	0.00949748i
$449$			12.1289i			0.572398i	0.958170	+	0.286199i	$0.0923919\pi$
$449$			12.1289i			0.572398i	−0.958170	+	0.286199i	$0.907608\pi$
$450$	−24.9239	−	1.41906i	−1.17492	−	0.0668949i
$451$	30.2463	+	17.4627i	1.42424	+	0.822286i
$452$	1.76329	−	3.05411i	0.0829384	−	0.143653i
$453$	−6.90506	−	29.0503i	−0.324428	−	1.36490i
$454$			20.9899i			0.985106i
$455$	−28.1967	−	58.7394i	−1.32188	−	2.75374i
$456$	−4.62513	−	1.38139i	−0.216592	−	0.0646895i
$457$	−9.58146	+	5.53186i	−0.448202	+	0.258769i	−0.707070	−	0.707143i	$-0.749984\pi$
$457$	−9.58146	+	5.53186i	−0.448202	+	0.258769i	0.258869	+	0.965913i	$0.416650\pi$
$458$	−1.41304	+	2.44746i	−0.0660270	+	0.114362i
$459$	−11.0302	+	1.96716i	−0.514845	+	0.0918193i
$460$	−2.48752	+	17.3264i	−0.115981	+	0.807848i
$461$			17.9880i			0.837785i	0.908036	+	0.418892i	$0.137582\pi$
$461$			17.9880i			0.837785i	−0.908036	+	0.418892i	$0.862418\pi$
$462$	10.1416	+	12.5180i	0.471832	+	0.582391i
$463$	−25.9625			−1.20658			−0.603290	−	0.797522i	$-0.706144\pi$
$463$	−25.9625			−1.20658			−0.603290	+	0.797522i	$0.706144\pi$
$464$	1.30783	−	0.755075i	0.0607144	−	0.0350535i
$465$	−2.82214	+	2.66603i	−0.130874	+	0.123634i
$466$	3.82791	−	6.63013i	0.177324	−	0.307135i
$467$	1.87901	+	3.25455i	0.0869504	+	0.150602i	0.906221	−	0.422805i	$-0.138955\pi$
$467$	1.87901	+	3.25455i	0.0869504	+	0.150602i	−0.819270	+	0.573408i	$0.805621\pi$
$468$	16.9265	+	11.1011i	0.782427	+	0.513151i
$469$	−0.586165	−	0.400717i	−0.0270666	−	0.0185034i
$470$	−8.04573			−0.371122
$471$	−26.2226	+	6.23293i	−1.20827	+	0.287198i
$472$	5.68526	−	9.84716i	0.261685	−	0.453252i
$473$	39.0359	+	22.5374i	1.79487	+	1.03627i
$474$	5.25854	+	22.1232i	0.241533	+	1.01615i
$475$			23.1908i			1.06407i
$476$	−2.46883	−	5.14305i	−0.113158	−	0.235731i
$477$	−24.0746	−	15.7892i	−1.10230	−	0.722939i
$478$	−1.66536	−	2.88449i	−0.0761720	−	0.131934i
$479$	−8.55062	+	14.8101i	−0.390688	+	0.676691i	−0.992540	−	0.121916i	$-0.961096\pi$
$479$	−8.55062	+	14.8101i	−0.390688	+	0.676691i	0.601853	+	0.798607i	$0.294429\pi$
$480$	4.34123	+	4.59543i	0.198149	+	0.209752i
$481$	−17.3898	+	10.0400i	−0.792908	+	0.457785i
$482$	25.5697			1.16467
$483$	−11.2675	−	18.8691i	−0.512689	−	0.858574i
$484$	−1.35970			−0.0618045
$485$	36.3617	−	20.9934i	1.65110	−	0.953262i
$486$	−6.12760	+	14.3336i	−0.277954	+	0.650186i
$487$	−11.5497	+	20.0047i	−0.523368	+	0.906500i	0.476262	+	0.879304i	$0.341991\pi$
$487$	−11.5497	+	20.0047i	−0.523368	+	0.906500i	−0.999630	+	0.0271970i	$0.991342\pi$
$488$	1.62915	+	2.82177i	0.0737481	+	0.127736i
$489$	30.1891	+	9.01660i	1.36520	+	0.407745i
$490$	19.9350	+	15.9795i	0.900571	+	0.721882i
$491$			11.3656i			0.512921i	0.966555	+	0.256461i	$0.0825564\pi$
$491$			11.3656i			0.512921i	−0.966555	+	0.256461i	$0.917444\pi$
$492$	−16.7403	+	3.97905i	−0.754712	+	0.179390i
$493$	−2.82001	−	1.62813i	−0.127007	−	0.0733275i
$494$	9.40203	−	16.2848i	0.423017	−	0.732688i
$495$	−2.18817	+	38.4324i	−0.0983511	+	1.72741i
$496$	0.614119			0.0275748
$497$	−2.44799	+	32.1258i	−0.109807	+	1.44104i
$498$	0.411302	−	1.37711i	0.0184309	−	0.0617098i
$499$	6.99273	+	12.1118i	0.313037	+	0.542197i	0.979018	−	0.203772i	$-0.0653201\pi$
$499$	6.99273	+	12.1118i	0.313037	+	0.542197i	−0.665981	+	0.745969i	$0.731987\pi$
$500$	6.06132	−	10.4985i	0.271071	−	0.469508i
$501$	6.99458	+	7.40415i	0.312495	+	0.330793i
$502$	17.7661	−	10.2572i	0.792939	−	0.457803i
$503$	−23.1200			−1.03087			−0.515435	−	0.856929i	$-0.672370\pi$
$503$	−23.1200			−1.03087			−0.515435	+	0.856929i	$0.672370\pi$
$504$	−7.86723	−	1.05197i	−0.350434	−	0.0468586i
$505$		−	49.2523i		−	2.19170i
$506$	16.6893	+	2.39605i	0.741929	+	0.106517i
$507$	−40.9536	+	38.6882i	−1.81881	+	1.71820i
$508$	0.440825	−	0.763532i	0.0195585	−	0.0338762i
$509$	−26.5832	+	15.3478i	−1.17828	+	0.680280i	−0.955616	−	0.294616i	$-0.904808\pi$
$509$	−26.5832	+	15.3478i	−1.17828	+	0.680280i	−0.222663	+	0.974895i	$0.571475\pi$
$510$	3.90098	−	13.0611i	0.172738	−	0.578357i
$511$	16.4824	−	24.1103i	0.729139	−	1.06658i
$512$		−	1.00000i		−	0.0441942i
$513$	13.6174	+	4.92620i	0.601223	+	0.217497i
$514$	8.59530	−	14.8875i	0.379122	−	0.656659i
$515$	−21.9664	−	12.6823i	−0.967954	−	0.558848i
$516$	−21.6051	+	5.13537i	−0.951111	+	0.226072i
$517$			7.74987i			0.340839i
$518$	4.44357	−	6.50001i	0.195239	−	0.285594i
$519$	4.80906	−	16.1016i	0.211094	−	0.706780i
$520$	−21.3275	+	12.3134i	−0.935271	+	0.539979i
$521$	−1.18962	+	2.06048i	−0.0521181	+	0.0902712i	−0.890907	−	0.454185i	$-0.849931\pi$
$521$	−1.18962	+	2.06048i	−0.0521181	+	0.0902712i	0.838789	+	0.544456i	$0.183264\pi$
$522$	−4.04591	+	2.03854i	−0.177085	+	0.0892244i
$523$	−18.5892	+	10.7325i	−0.812849	+	0.469298i	−0.847944	−	0.530086i	$-0.822160\pi$
$523$	−18.5892	+	10.7325i	−0.812849	+	0.469298i	0.0350956	+	0.999384i	$0.488826\pi$
$524$			6.95622i			0.303884i
$525$	5.97404	+	37.6626i	0.260728	+	1.64373i
$526$			12.6802i			0.552885i
$527$	−0.662099	−	1.14679i	−0.0288415	−	0.0499549i
$528$	4.42644	−	4.18159i	0.192636	−	0.181980i
$529$	−22.0710	−	6.47075i	−0.959609	−	0.281337i
$530$	30.3342	−	17.5134i	1.31763	−	0.760736i
$531$	−18.7074	+	28.5242i	−0.811834	+	1.23784i
$532$	−0.560229	+	7.35208i	−0.0242890	+	0.318753i
$533$		−	67.0303i		−	2.90340i
$534$	−9.56287	+	2.27303i	−0.413826	+	0.0983634i
$535$	−8.01306	+	13.8790i	−0.346435	+	0.600043i
$536$	−0.134186	+	0.232417i	−0.00579595	+	0.0100389i
$537$	−20.1345	+	4.78582i	−0.868868	+	0.206524i
$538$	−4.37174			−0.188479
$539$	15.3919	−	19.2019i	0.662977	−	0.827086i
$540$	−12.2190	−	14.5043i	−0.525820	−	0.624166i
$541$	8.38261	+	14.5191i	0.360397	+	0.624225i	0.988026	−	0.154287i	$-0.0493080\pi$
$541$	8.38261	+	14.5191i	0.360397	+	0.624225i	−0.627629	+	0.778512i	$0.715975\pi$
$542$	−13.6542	−	7.88328i	−0.586500	−	0.338616i
$543$	17.9423	+	18.9929i	0.769978	+	0.815064i
$544$	−1.86737	+	1.07813i	−0.0800629	+	0.0462243i
$545$			25.5540i			1.09461i
$546$	11.0742	−	28.8691i	0.473932	−	1.23548i
$547$	−12.8053			−0.547514			−0.273757	−	0.961799i	$-0.588266\pi$
$547$	−12.8053			−0.547514			−0.273757	+	0.961799i	$0.588266\pi$
$548$	1.99228	+	3.45073i	0.0851059	+	0.147408i
$549$	−4.39835	−	8.72944i	−0.187717	−	0.372564i
$550$	−25.3356	−	14.6275i	−1.08031	−	0.623720i
$551$	2.10430	+	3.64476i	0.0896464	+	0.155272i
$552$	−6.78766	+	4.78828i	−0.288902	+	0.203803i
$553$	31.3143	−	15.0319i	1.33162	−	0.639220i
$554$			6.37349i			0.270784i
$555$	18.3034	−	4.35059i	0.776937	−	0.184672i
$556$	11.2752	−	19.5292i	0.478175	−	0.828223i
$557$	−2.32435	+	4.02589i	−0.0984858	+	0.170582i	−0.911058	−	0.412278i	$-0.864733\pi$
$557$	−2.32435	+	4.02589i	−0.0984858	+	0.170582i	0.812572	+	0.582860i	$0.198067\pi$
$558$	−1.83938	−	0.104726i	−0.0778671	−	0.00443342i
$559$		−	86.5094i		−	3.65896i
$560$	5.44975	−	7.97183i	0.230294	−	0.336871i
$561$	−12.5809	−	3.75753i	−0.531164	−	0.158643i
$562$	13.7626	−	7.94582i	0.580539	−	0.335174i
$563$	4.48761	−	7.77277i	0.189130	−	0.327583i	−0.755830	−	0.654768i	$-0.772766\pi$
$563$	4.48761	−	7.77277i	0.189130	−	0.327583i	0.944961	+	0.327184i	$0.106100\pi$
$564$	−2.62197	−	2.77550i	−0.110405	−	0.116870i
$565$	−6.43576	−	11.1471i	−0.270754	−	0.468960i
$566$	22.4577			0.943967
$567$	23.3841	+	4.49242i	0.982042	+	0.188664i
$568$	12.1776			0.510961
$569$	0.885171	+	1.53316i	0.0371083	+	0.0642734i	0.883983	−	0.467519i	$-0.154852\pi$
$569$	0.885171	+	1.53316i	0.0371083	+	0.0642734i	−0.846875	+	0.531792i	$0.821519\pi$
$570$	−12.8069	+	12.0985i	−0.536422	+	0.506749i
$571$	−6.87324	−	3.96827i	−0.287636	−	0.166067i	0.349239	−	0.937034i	$-0.386440\pi$
$571$	−6.87324	−	3.96827i	−0.287636	−	0.166067i	−0.636875	+	0.770967i	$0.719773\pi$
$572$	11.8606	+	20.5432i	0.495918	+	0.858955i
$573$	−19.9485	−	5.95803i	−0.833361	−	0.248900i
$574$	11.3744	+	23.6951i	0.474757	+	0.989013i
$575$	31.3750	+	24.6631i	1.30843	+	1.02852i
$576$	−0.170531	+	2.99515i	−0.00710545	+	0.124798i
$577$	−6.30678	+	10.9237i	−0.262555	+	0.454758i	−0.966920	−	0.255080i	$-0.917898\pi$
$577$	−6.30678	+	10.9237i	−0.262555	+	0.454758i	0.704365	+	0.709838i	$0.251232\pi$
$578$	−10.6959	−	6.17528i	−0.444891	−	0.256858i
$579$	2.16069	+	9.09027i	0.0897953	+	0.377779i
$580$		−	5.51183i		−	0.228866i
$581$	−2.18904	−	0.166805i	−0.0908168	−	0.00692025i
$582$	19.0917	+	5.70212i	0.791376	+	0.236360i
$583$	−16.8694	−	29.2187i	−0.698661	−	1.21012i
$584$	−9.55983	−	5.51937i	−0.395588	−	0.228393i
$585$	65.9788	−	33.2435i	2.72789	−	1.37445i
$586$	13.3101	−	7.68458i	0.549835	−	0.317447i
$587$		−	9.44651i		−	0.389899i	−0.980813	−	0.194950i	$-0.937546\pi$
$587$		−	9.44651i		−	0.389899i	0.980813	−	0.194950i	$-0.0624543\pi$
$588$	0.984094	+	12.0844i	0.0405833	+	0.498350i
$589$			1.71148i			0.0705202i
$590$	−20.7503	−	35.9407i	−0.854278	−	1.47965i
$591$	−21.6063	−	22.8715i	−0.888765	−	0.940807i
$592$	−2.57728	−	1.48799i	−0.105926	−	0.0611561i
$593$	0.193848	−	0.111918i	0.00796040	−	0.00459594i	−0.496015	−	0.868314i	$-0.665204\pi$
$593$	0.193848	−	0.111918i	0.00796040	−	0.00459594i	0.503975	+	0.863718i	$0.331870\pi$
$594$	−13.9709	+	11.7696i	−0.573235	+	0.482914i
$595$	−20.7619	−	1.58206i	−0.851155	−	0.0648580i
$596$	12.8245			0.525311
$597$	−6.22121	+	1.47874i	−0.254617	+	0.0605206i
$598$	−12.0329	−	30.0387i	−0.492061	−	1.22838i
$599$	−17.2808	−	9.97707i	−0.706074	−	0.407652i	0.103532	−	0.994626i	$-0.466986\pi$
$599$	−17.2808	−	9.97707i	−0.706074	−	0.407652i	−0.809606	+	0.586974i	$0.800319\pi$
$600$	14.0224	−	3.33303i	0.572463	−	0.136070i
$601$	−15.2850			−0.623487			−0.311744	−	0.950166i	$-0.600913\pi$
$601$	−15.2850			−0.623487			−0.311744	+	0.950166i	$0.600913\pi$
$602$	14.6798	+	30.5809i	0.598304	+	1.24638i
$603$	0.441541	−	0.673240i	0.0179809	−	0.0274164i
$604$	8.61975	+	14.9299i	0.350733	+	0.607487i
$605$	−2.48135	+	4.29783i	−0.100881	+	0.174731i
$606$	16.9904	−	16.0505i	0.690186	−	0.652007i
$607$	−9.52595	−	16.4994i	−0.386646	−	0.669691i	0.605350	−	0.795960i	$-0.293033\pi$
$607$	−9.52595	−	16.4994i	−0.386646	−	0.669691i	−0.991996	+	0.126268i	$0.959700\pi$
$608$	2.78688			0.113023
$609$	4.35637	+	5.37715i	0.176529	+	0.217893i
$610$	11.8923			0.481505
$611$	12.8811	−	7.43693i	0.521115	−	0.300866i
$612$	5.77691	−	2.91071i	0.233518	−	0.117658i
$613$	−26.4223	−	15.2549i	−1.06719	−	0.616141i	−0.139776	−	0.990183i	$-0.544638\pi$
$613$	−26.4223	−	15.2549i	−1.06719	−	0.616141i	−0.927412	+	0.374042i	$0.877972\pi$
$614$	−13.5443	+	7.81982i	−0.546604	+	0.315582i
$615$	−17.9726	+	60.1753i	−0.724725	+	2.42650i
$616$	−7.67869	−	5.24935i	−0.309383	−	0.211502i
$617$	43.9666			1.77003			0.885014	−	0.465564i	$-0.154148\pi$
$617$	43.9666			1.77003			0.885014	+	0.465564i	$0.154148\pi$
$618$	−2.78352	−	11.7106i	−0.111970	−	0.471069i
$619$	23.1368	+	13.3580i	0.929946	+	0.536905i	0.886795	−	0.462164i	$-0.152927\pi$
$619$	23.1368	+	13.3580i	0.929946	+	0.536905i	0.0431518	+	0.999069i	$0.486260\pi$
$620$	1.12072	−	1.94115i	0.0450093	−	0.0779584i
$621$	21.1466	−	13.1841i	0.848584	−	0.529061i
$622$	−11.6016			−0.465182
$623$	6.49759	+	13.5358i	0.260320	+	0.542299i
$624$	−11.1980	−	3.34450i	−0.448278	−	0.133887i
$625$	−1.31940	−	2.28527i	−0.0527762	−	0.0914110i
$626$	6.19525	−	10.7305i	0.247612	−	0.428877i
$627$	11.6536	+	12.3360i	0.465399	+	0.492651i
$628$	13.4766	−	7.78072i	0.537775	−	0.310484i
$629$			6.41698i			0.255862i
$630$	−17.6823	+	22.9475i	−0.704478	+	0.914249i
$631$			2.16627i			0.0862380i	0.999070	+	0.0431190i	$0.0137295\pi$
$631$			2.16627i			0.0862380i	−0.999070	+	0.0431190i	$0.986271\pi$
$632$	−6.56436	−	11.3698i	−0.261116	−	0.452267i
$633$	−13.9403	+	13.1692i	−0.554078	+	0.523428i
$634$	10.7548	−	18.6279i	0.427129	−	0.739810i
$635$	−1.60895	−	2.78678i	−0.0638491	−	0.110590i
$636$	15.9270	+	4.75691i	0.631545	+	0.188624i
$637$	−46.6862	−	7.15653i	−1.84977	−	0.283552i
$638$	−5.30914			−0.210191
$639$	−36.4737	−	2.07665i	−1.44288	−	0.0821512i
$640$	−3.16086	−	1.82493i	−0.124944	−	0.0721365i
$641$	3.70333	−	6.41435i	0.146273	−	0.253352i	−0.783574	−	0.621298i	$-0.786606\pi$
$641$	3.70333	−	6.41435i	0.146273	−	0.253352i	0.929847	+	0.367946i	$0.119939\pi$
$642$	−7.39911	+	1.75872i	−0.292020	+	0.0694110i
$643$			4.63951i			0.182964i	0.995807	+	0.0914821i	$0.0291604\pi$
$643$			4.63951i			0.182964i	−0.995807	+	0.0914821i	$0.970840\pi$
$644$	9.35088	+	8.57677i	0.368476	+	0.337972i
$645$	−23.1955	+	77.6624i	−0.913320	+	3.05795i
$646$	−3.00461	−	5.20414i	−0.118215	−	0.204754i
$647$	35.3947	+	20.4352i	1.39151	+	0.803389i	0.993483	−	0.113985i	$-0.0363614\pi$
$647$	35.3947	+	20.4352i	1.39151	+	0.803389i	0.398028	+	0.917373i	$0.369695\pi$
$648$	1.02153	−	8.94184i	0.0401295	−	0.351269i
$649$	−34.6190	+	19.9873i	−1.35892	+	0.784570i
$650$			56.1475i			2.20229i
$651$	0.440883	+	2.77950i	0.0172796	+	0.108937i
$652$	−18.1905			−0.712395
$653$	27.1366	−	15.6673i	1.06194	−	0.613109i	0.135969	−	0.990713i	$-0.456585\pi$
$653$	27.1366	−	15.6673i	1.06194	−	0.613109i	0.925967	+	0.377604i	$0.123252\pi$
$654$	−8.81526	+	8.32763i	−0.344704	+	0.325636i
$655$	21.9877	+	12.6946i	0.859129	+	0.496018i
$656$	8.60336	−	4.96715i	0.335905	−	0.193935i
$657$	27.6919	+	18.1616i	1.08036	+	0.708551i
$658$	−3.29148	+	4.81474i	−0.128315	+	0.187698i
$659$	−42.8645			−1.66976			−0.834882	−	0.550429i	$-0.814464\pi$
$659$	−42.8645			−1.66976			−0.834882	+	0.550429i	$0.814464\pi$
$660$	−5.13951	−	21.6225i	−0.200055	−	0.841654i
$661$	−1.40150	−	0.809159i	−0.0545122	−	0.0314726i	0.472496	−	0.881333i	$-0.343353\pi$
$661$	−1.40150	−	0.809159i	−0.0545122	−	0.0314726i	−0.527008	+	0.849860i	$0.676686\pi$
$662$	3.54363	+	2.04592i	0.137727	+	0.0795169i
$663$	5.82741	+	24.5166i	0.226318	+	0.952145i
$664$			0.829779i			0.0322017i
$665$	22.2165	+	15.1878i	0.861520	+	0.588957i
$666$	7.46559	+	4.89627i	0.289286	+	0.189726i
$667$	7.16892	+	1.02923i	0.277582	+	0.0398519i
$668$	−5.09278	−	2.94032i	−0.197046	−	0.113764i
$669$	−3.08818	+	2.91735i	−0.119396	+	0.112791i
$670$	0.489758	+	0.848286i	0.0189210	+	0.0327722i
$671$		−	11.4550i		−	0.442215i
$672$	4.52599	−	0.717912i	0.174594	−	0.0276940i
$673$	−12.4728			−0.480790			−0.240395	−	0.970675i	$-0.577277\pi$
$673$	−12.4728			−0.480790			−0.240395	+	0.970675i	$0.577277\pi$
$674$	−7.24823	−	12.5543i	−0.279191	−	0.483573i
$675$	−42.5676	+	7.59167i	−1.63843	+	0.292203i
$676$	16.2634	−	28.1690i	0.625515	−	1.08342i
$677$	0.664524	+	1.15099i	0.0255397	+	0.0442361i	0.878513	−	0.477719i	$-0.158536\pi$
$677$	0.664524	+	1.15099i	0.0255397	+	0.0442361i	−0.852973	+	0.521955i	$0.825203\pi$
$678$	1.74805	−	5.85276i	0.0671333	−	0.224774i
$679$	2.31252	−	30.3480i	0.0887463	−	1.16465i
$680$			7.87001i			0.301801i
$681$	8.40724	+	35.3702i	0.322166	+	1.35539i
$682$	−1.86977	−	1.07951i	−0.0715971	−	0.0413366i
$683$	−21.9108	−	12.6502i	−0.838393	−	0.484046i	0.0183246	−	0.999832i	$-0.494167\pi$
$683$	−21.9108	−	12.6502i	−0.838393	−	0.484046i	−0.856718	+	0.515786i	$0.827500\pi$
$684$	−8.34712	−	0.475249i	−0.319160	−	0.0181716i
$685$	14.5430			0.555661
$686$	17.7179	−	5.39236i	0.676471	−	0.205881i
$687$	−1.40082	+	4.69019i	−0.0534446	+	0.178942i
$688$	11.1035	−	6.41062i	0.423317	−	0.244402i
$689$	−32.3765	+	56.0778i	−1.23345	+	2.13639i
$690$	2.74814	+	30.1931i	0.104620	+	1.14943i
$691$	−18.2041	−	31.5304i	−0.692517	−	1.19947i	−0.971011	−	0.239036i	$-0.923168\pi$
$691$	−18.2041	−	31.5304i	−0.692517	−	1.19947i	0.278494	−	0.960438i	$-0.410165\pi$
$692$			9.70201i			0.368815i
$693$	22.1036	+	17.0320i	0.839648	+	0.646994i
$694$	−15.4545			−0.586647
$695$	−41.1528	−	71.2787i	−1.56101	−	2.70375i
$696$	1.90139	−	1.79621i	0.0720720	−	0.0680853i
$697$	−18.5510	−	10.7104i	−0.702670	−	0.405687i
$698$	15.0963	−	8.71585i	0.571403	−	0.329900i
$699$	3.79481	−	12.7057i	0.143533	−	0.480573i
$700$	−9.52768	−	19.8480i	−0.360113	−	0.750185i
$701$	−22.8941			−0.864697			−0.432348	−	0.901707i	$-0.642315\pi$
$701$	−22.8941			−0.864697			−0.432348	+	0.901707i	$0.642315\pi$
$702$	32.9693	+	11.9269i	1.24435	+	0.450151i
$703$	4.14686	−	7.18257i	0.156402	−	0.270896i
$704$	−1.75782	+	3.04463i	−0.0662503	+	0.114749i
$705$	−13.5579	+	3.22261i	−0.510619	+	0.121370i
$706$	2.11871			0.0797385
$707$	−29.4737	−	20.1490i	−1.10847	−	0.757780i
$708$	5.63610	−	18.8706i	0.211817	−	0.709201i
$709$	−5.00325	+	2.88863i	−0.187901	+	0.108485i	−0.591000	−	0.806672i	$-0.701267\pi$
$709$	−5.00325	+	2.88863i	−0.187901	+	0.108485i	0.403098	+	0.915157i	$0.367933\pi$
$710$	22.2232	−	38.4917i	0.834022	−	1.44457i
$711$	17.7223	+	35.1737i	0.664640	+	1.31912i
$712$	4.91465	−	2.83747i	0.184184	−	0.106339i
$713$	2.31547	+	1.82013i	0.0867150	+	0.0681645i
$714$	−6.22020	−	7.67771i	−0.232785	−	0.287331i
$715$	86.5790			3.23787
$716$	10.3477	−	5.97426i	0.386713	−	0.223269i
$717$	−3.96165	−	4.19363i	−0.147951	−	0.156614i
$718$	12.4259	+	7.17412i	0.463732	+	0.267736i
$719$	−4.83670	+	2.79247i	−0.180378	+	0.104141i	−0.587470	−	0.809246i	$-0.699876\pi$
$719$	−4.83670	+	2.79247i	−0.180378	+	0.104141i	0.407092	+	0.913387i	$0.366543\pi$
$720$	9.15605	+	6.00495i	0.341226	+	0.223791i
$721$	−16.5757	+	7.95688i	−0.617313	+	0.296330i
$722$		−	11.2333i		−	0.418060i
$723$	43.0876	−	10.2416i	1.60244	−	0.380890i
$724$	−13.0639	−	7.54242i	−0.485514	−	0.280312i
$725$	−10.8830	−	6.28329i	−0.404184	−	0.233356i
$726$	−2.29123	+	0.544610i	−0.0850357	+	0.0202124i
$727$		−	9.41494i		−	0.349181i	−0.984641	−	0.174590i	$-0.944140\pi$
$727$		−	9.41494i		−	0.349181i	0.984641	−	0.174590i	$-0.0558601\pi$
$728$	−1.35638	+	17.8002i	−0.0502707	+	0.659720i
$729$	−4.58449	+	26.6079i	−0.169796	+	0.985479i
$730$	−34.8919	+	20.1449i	−1.29141	+	0.745595i
$731$	−23.9420	−	13.8229i	−0.885527	−	0.511259i
$732$	3.87551	+	4.10244i	0.143243	+	0.151630i
$733$	−30.1401	+	17.4014i	−1.11325	+	0.642735i	−0.939669	−	0.342085i	$-0.888867\pi$
$733$	−30.1401	+	17.4014i	−1.11325	+	0.642735i	−0.173580	+	0.984820i	$0.555534\pi$
$734$	−1.09730			−0.0405019
$735$	39.9929	+	18.9425i	1.47516	+	0.698703i
$736$	2.96381	−	3.77039i	0.109247	−	0.138978i
$737$	0.817093	−	0.471749i	0.0300980	−	0.0173771i
$738$	−26.6154	+	13.4102i	−0.979726	+	0.493637i
$739$	6.96352	−	12.0612i	0.256157	−	0.443677i	−0.709052	−	0.705156i	$-0.750877\pi$
$739$	6.96352	−	12.0612i	0.256157	−	0.443677i	0.965209	+	0.261479i	$0.0842102\pi$
$740$	−9.40668	+	5.43095i	−0.345797	+	0.199646i
$741$	9.32073	−	31.2074i	0.342406	−	1.14643i
$742$	1.92918	−	25.3174i	0.0708226	−	0.929430i
$743$	−49.2524			−1.80689			−0.903447	−	0.428699i	$-0.858972\pi$
$743$	−49.2524			−1.80689			−0.903447	+	0.428699i	$0.858972\pi$
$744$	1.03485	−	0.245977i	0.0379396	−	0.00901797i
$745$	23.4037	−	40.5364i	0.857446	−	1.48514i
$746$	−13.5246	+	23.4253i	−0.495170	+	0.857660i
$747$	0.141503	−	2.48531i	0.00517732	−	0.0909328i
$748$	7.58061			0.277174
$749$	5.02740	+	10.4731i	0.183697	+	0.382677i
$750$	6.00891	−	20.1189i	0.219414	−	0.734637i
$751$	−15.5015	+	8.94977i	−0.565656	+	0.326582i	−0.755413	−	0.655249i	$-0.772564\pi$
$751$	−15.5015	+	8.94977i	−0.565656	+	0.326582i	0.189756	+	0.981831i	$0.439230\pi$
$752$	1.90907	+	1.10220i	0.0696165	+	0.0401931i
$753$	25.8293	−	24.4005i	0.941270	−	0.889203i
$754$	5.09476	+	8.82439i	0.185540	+	0.321365i
$755$	62.9216			2.28995
$756$	−13.6784	+	1.37843i	−0.497480	+	0.0501331i
$757$			16.0774i			0.584343i	0.956366	+	0.292172i	$0.0943778\pi$
$757$			16.0774i			0.584343i	−0.956366	+	0.292172i	$0.905622\pi$
$758$	11.0821	+	19.1947i	0.402518	+	0.697182i
$759$	29.0829	−	2.64709i	1.05564	−	0.0960831i
$760$	5.08585	−	8.80894i	0.184483	−	0.319534i
$761$	3.21303	−	1.85505i	0.116472	−	0.0672454i	−0.440632	−	0.897688i	$-0.645246\pi$
$761$	3.21303	−	1.85505i	0.116472	−	0.0672454i	0.557104	+	0.830442i	$0.311912\pi$
$762$	0.437013	−	1.46320i	0.0158313	−	0.0530060i
$763$	15.2921	+	10.4541i	0.553611	+	0.378463i
$764$	12.0200			0.434868
$765$	1.34208	−	23.5718i	0.0485229	−	0.852242i
$766$	33.4634	+	19.3201i	1.20908	+	0.698063i
$767$	66.4423	+	38.3605i	2.39909	+	1.38512i
$768$	−0.400537	−	1.68510i	−0.0144531	−	0.0608059i
$769$		−	37.0584i		−	1.33636i	−0.744000	−	0.668180i	$-0.767074\pi$
$769$		−	37.0584i		−	1.33636i	0.744000	−	0.668180i	$-0.232926\pi$
$770$	−30.6055	+	14.6916i	−1.10295	+	0.529449i
$771$	8.52097	−	28.5297i	0.306875	−	1.02747i
$772$	−2.69725	−	4.67177i	−0.0970760	−	0.168141i
$773$	5.19340	−	8.99524i	0.186794	−	0.323536i	−0.757386	−	0.652968i	$-0.773524\pi$
$773$	5.19340	−	8.99524i	0.186794	−	0.323536i	0.944180	+	0.329431i	$0.106857\pi$
$774$	−34.3499	+	17.3073i	−1.23468	+	0.622097i
$775$	−2.55517	−	4.42568i	−0.0917844	−	0.158975i
$776$	−11.5037			−0.412959
$777$	4.88438	−	12.7330i	0.175226	−	0.456794i
$778$		−	11.7350i		−	0.420719i
$779$	13.8428	+	23.9765i	0.495972	+	0.859048i
$780$	−31.0070	+	29.2918i	−1.11023	+	1.04881i
$781$	−37.0763	−	21.4060i	−1.32669	−	0.765967i
$782$	−10.2361	−	1.46957i	−0.366041	−	0.0525518i
$783$	−6.00126	+	5.05568i	−0.214467	+	0.180675i
$784$	−2.54105	−	6.52251i	−0.0907516	−	0.232947i
$785$		−	56.7969i		−	2.02717i
$786$	2.78622	+	11.7219i	0.0993812	+	0.418108i
$787$	26.1892	+	15.1203i	0.933544	+	0.538982i	0.887931	−	0.459977i	$-0.152142\pi$
$787$	26.1892	+	15.1203i	0.933544	+	0.538982i	0.0456134	+	0.998959i	$0.485476\pi$
$788$	15.7316	+	9.08266i	0.560416	+	0.323557i
$789$	5.07890	+	21.3675i	0.180814	+	0.760704i
$790$	−47.9179			−1.70484
$791$	−9.30350	−	0.708928i	−0.330795	−	0.0252066i
$792$	5.78413	−	8.81936i	0.205530	−	0.313382i
$793$	−19.0395	+	10.9925i	−0.676112	+	0.390353i
$794$	−6.96070	−	4.01876i	−0.247026	−	0.142620i
$795$	44.1014	−	41.6619i	1.56412	−	1.47760i
$796$	3.19727	−	1.84594i	0.113324	−	0.0654277i
$797$	18.1940			0.644463			0.322231	−	0.946661i	$-0.395567\pi$
$797$	18.1940			0.644463			0.322231	+	0.946661i	$0.395567\pi$
$798$	2.00073	+	12.6134i	0.0708252	+	0.446509i
$799$		−	4.75325i		−	0.168158i
$800$	−7.20655	+	4.16070i	−0.254790	+	0.147103i
$801$	−15.2040	+	7.66056i	−0.537207	+	0.270673i
$802$	4.20360	+	2.42695i	0.148434	+	0.0856986i
$803$	19.4041	+	33.6089i	0.684756	+	1.18603i
$804$	−0.133025	+	0.445392i	−0.00469145	+	0.0157078i
$805$	44.1747	−	13.9049i	1.55695	−	0.490083i
$806$			4.14368i			0.145955i
$807$	−7.36684	+	1.75104i	−0.259325	+	0.0616397i
$808$	−6.74717	+	11.6864i	−0.237364	+	0.411127i
$809$	−35.4679	−	20.4774i	−1.24699	−	0.719947i	−0.276478	−	0.961020i	$-0.589167\pi$
$809$	−35.4679	−	20.4774i	−1.24699	−	0.719947i	−0.970507	+	0.241073i	$0.922501\pi$
$810$	−26.3997	−	19.5471i	−0.927591	−	0.686815i
$811$	26.1535			0.918372			0.459186	−	0.888340i	$-0.348141\pi$
$811$	26.1535			0.918372			0.459186	+	0.888340i	$0.348141\pi$
$812$	−3.29840	−	2.25487i	−0.115751	−	0.0791305i
$813$	−26.1663	−	7.81511i	−0.917694	−	0.274088i
$814$	5.23124	+	9.06078i	0.183355	+	0.317580i
$815$	−33.1963	+	57.4977i	−1.16282	+	2.01406i
$816$	−2.71488	+	2.56471i	−0.0950399	+	0.0897827i
$817$	17.8656	+	30.9441i	0.625039	+	1.08260i
$818$			3.00775i			0.105164i
$819$	7.09804	−	53.0830i	0.248026	−	1.85487i
$820$		−	36.2587i		−	1.26621i
$821$	46.9204	−	27.0895i	1.63753	−	0.945430i	0.655853	−	0.754889i	$-0.272309\pi$
$821$	46.9204	−	27.0895i	1.63753	−	0.945430i	0.981679	−	0.190541i	$-0.0610242\pi$
$822$	4.73934	+	5.01685i	0.165303	+	0.174983i
$823$	−14.6577	+	25.3879i	−0.510937	+	0.884968i	0.488983	+	0.872293i	$0.337368\pi$
$823$	−14.6577	+	25.3879i	−0.510937	+	0.884968i	−0.999920	+	0.0126748i	$0.995965\pi$
$824$	3.47474	+	6.01843i	0.121048	+	0.209662i
$825$	−48.5520	−	14.5010i	−1.69036	−	0.504861i
$826$	−29.9966	−	2.28574i	−1.04372	−	0.0795312i
$827$	23.9108			0.831461			0.415731	−	0.909488i	$-0.363526\pi$
$827$	23.9108			0.831461			0.415731	+	0.909488i	$0.363526\pi$
$828$	−9.52002	+	10.7875i	−0.330844	+	0.374890i
$829$	5.27256	−	9.13234i	0.183124	−	0.317179i	−0.759819	−	0.650135i	$-0.774713\pi$
$829$	5.27256	−	9.13234i	0.183124	−	0.317179i	0.942943	+	0.332955i	$0.108046\pi$
$830$	2.62282	+	1.51429i	0.0910394	+	0.0525616i
$831$	2.55282	+	10.7400i	0.0885563	+	0.372566i
$832$	6.74736			0.233922
$833$	−9.44037	+	11.7772i	−0.327089	+	0.408055i
$834$	11.1777	−	37.4248i	0.387052	−	1.29592i
$835$	−18.5879	+	10.7317i	−0.643260	+	0.371386i
$836$	−8.48502	−	4.89883i	−0.293460	−	0.169429i
$837$	−3.14149	+	0.560264i	−0.108586	+	0.0193656i
$838$	0.786275	−	0.453956i	0.0271614	−	0.0156817i
$839$	30.5023			1.05306			0.526529	−	0.850157i	$-0.323493\pi$
$839$	30.5023			1.05306			0.526529	+	0.850157i	$0.323493\pi$
$840$	5.99038	−	15.6162i	0.206688	−	0.538809i
$841$	26.7194			0.921360
$842$	−19.3409	−	33.4995i	−0.666532	−	1.15447i
$843$	20.0087	−	18.9019i	0.689138	−	0.651017i
$844$	5.53594	−	9.58853i	0.190555	−	0.330051i
$845$	−59.3590	−	102.813i	−2.04201	−	3.53687i
$846$	−5.52998	−	3.62681i	−0.190125	−	0.124692i
$847$	1.55680	+	3.24312i	0.0534924	+	0.111435i
$848$	−9.59680			−0.329556
$849$	37.8435	−	8.99513i	1.29879	−	0.308712i
$850$	15.5392	+	8.97154i	0.532989	+	0.307721i
$851$	−5.30722	−	13.2489i	−0.181929	−	0.454166i
$852$	20.5205	−	4.87757i	0.703021	−	0.167103i
$853$	−9.09182			−0.311298			−0.155649	−	0.987812i	$-0.549747\pi$
$853$	−9.09182			−0.311298			−0.155649	+	0.987812i	$0.549747\pi$
$854$	4.86511	−	7.11662i	0.166481	−	0.243526i
$855$	−16.7351	+	25.5168i	−0.572327	+	0.872657i
$856$	3.80263	−	2.19545i	0.129971	−	0.0750389i
$857$	−1.85779	−	1.07260i	−0.0634609	−	0.0366392i	0.467934	−	0.883764i	$-0.344999\pi$
$857$	−1.85779	−	1.07260i	−0.0634609	−	0.0366392i	−0.531395	+	0.847124i	$0.678332\pi$
$858$	28.2147	+	29.8668i	0.963233	+	1.01964i
$859$	−4.96533	−	8.60020i	−0.169415	−	0.293435i	0.768799	−	0.639490i	$-0.220854\pi$
$859$	−4.96533	−	8.60020i	−0.169415	−	0.293435i	−0.938214	+	0.346055i	$0.887521\pi$
$860$		−	46.7956i		−	1.59572i
$861$	28.6577	+	35.3727i	0.976653	+	1.20550i
$862$		−	6.05643i		−	0.206283i
$863$	−9.65865	+	5.57643i	−0.328784	+	0.189824i	−0.655301	−	0.755368i	$-0.727458\pi$
$863$	−9.65865	+	5.57643i	−0.328784	+	0.189824i	0.326517	+	0.945191i	$0.394125\pi$
$864$	0.912305	+	5.11544i	0.0310373	+	0.174031i
$865$	30.6667	+	17.7055i	1.04270	+	0.602003i
$866$	−9.44782	−	16.3641i	−0.321050	−	0.556075i
$867$	−20.4971	−	6.12188i	−0.696119	−	0.207910i
$868$	−0.703142	−	1.46478i	−0.0238662	−	0.0497180i
$869$			46.1558i			1.56573i
$870$	−2.20769	−	9.28799i	−0.0748476	−	0.314892i
$871$	−1.56820	−	0.905400i	−0.0531364	−	0.0306783i
$872$	3.50069	−	6.06338i	0.118548	−	0.205332i
$873$	34.4553	+	1.96174i	1.16614	+	0.0663947i
$874$	10.5076	+	8.25978i	0.355426	+	0.279391i
$875$	−31.9808	−	2.43694i	−1.08115	−	0.0823836i
$876$	−18.3200	−	5.47164i	−0.618975	−	0.184870i
$877$	24.9150	+	43.1541i	0.841321	+	1.45721i	0.888778	+	0.458337i	$0.151555\pi$
$877$	24.9150	+	43.1541i	0.841321	+	1.45721i	−0.0474572	+	0.998873i	$0.515112\pi$
$878$	15.5839	+	8.99736i	0.525931	+	0.303646i
$879$	19.3509	−	18.2805i	0.652690	−	0.616586i
$880$	6.41577	+	11.1124i	0.216276	+	0.374600i
$881$	−42.6260			−1.43611			−0.718053	−	0.695988i	$-0.754967\pi$
$881$	−42.6260			−1.43611			−0.718053	+	0.695988i	$0.754967\pi$
$882$	6.49852	+	19.9692i	0.218817	+	0.672398i
$883$	24.9254			0.838807			0.419403	−	0.907800i	$-0.362239\pi$
$883$	24.9254			0.838807			0.419403	+	0.907800i	$0.362239\pi$
$884$	−7.27451	−	12.5998i	−0.244668	−	0.423778i
$885$	−49.3620	−	52.2524i	−1.65929	−	1.75645i
$886$	−7.19509	+	12.4623i	−0.241724	+	0.418678i
$887$	1.80015	−	1.03932i	0.0604433	−	0.0348969i	−0.469474	−	0.882946i	$-0.655556\pi$
$887$	1.80015	−	1.03932i	0.0604433	−	0.0348969i	0.529917	+	0.848049i	$0.322223\pi$
$888$	−4.93898	−	1.47513i	−0.165741	−	0.0495020i
$889$	−2.32588	−	0.177233i	−0.0780077	−	0.00594419i
$890$		−	20.7127i		−	0.694292i
$891$	−18.8283	+	25.4289i	−0.630772	+	0.851901i
$892$	1.22637	−	2.12413i	0.0410619	−	0.0711212i
$893$	−3.07170	+	5.32034i	−0.102790	+	0.178038i
$894$	21.6106	−	5.13668i	0.722766	−	0.171796i
$895$		−	43.6103i		−	1.45773i
$896$	−2.38518	+	1.14496i	−0.0796832	+	0.0382504i
$897$	−32.3083	−	45.7988i	−1.07874	−	1.52918i
$898$	−6.06445	−	10.5039i	−0.202373	−	0.350521i
$899$	−0.803163	−	0.463706i	−0.0267870	−	0.0154655i
$900$	22.2942	−	11.2330i	0.743141	−	0.374433i
$901$	10.3466	+	17.9208i	0.344694	+	0.597028i
$902$	−34.9254			−1.16289
$903$	36.9857	+	45.6521i	1.23081	+	1.51921i
$904$			3.52659i			0.117293i
$905$	−47.6811	+	27.5287i	−1.58497	+	0.915085i
$906$	20.5051	+	21.7058i	0.681237	+	0.721127i
$907$	46.1644	+	26.6530i	1.53286	+	0.884999i	0.999228	+	0.0392832i	$0.0125075\pi$
$907$	46.1644	+	26.6530i	1.53286	+	0.884999i	0.533634	+	0.845715i	$0.320826\pi$
$908$	−10.4950	−	18.1778i	−0.348288	−	0.603252i
$909$	22.2017	−	33.8520i	0.736383	−	1.12280i
$910$	53.7888	+	36.7714i	1.78308	+	1.21896i
$911$	36.3305			1.20368			0.601842	−	0.798616i	$-0.294434\pi$
$911$	36.3305			1.20368			0.601842	+	0.798616i	$0.294434\pi$
$912$	4.69618	−	1.11625i	0.155506	−	0.0369626i
$913$	1.45860	−	2.52637i	0.0482727	−	0.0836107i
$914$	5.53186	−	9.58146i	0.182978	−	0.316927i
$915$	20.0398	−	4.76330i	0.662494	−	0.157470i
$916$		−	2.82608i		−	0.0933763i
$917$	16.5918	−	7.96459i	0.547910	−	0.263014i
$918$	8.56884	−	7.21871i	0.282814	−	0.238253i
$919$	−40.1045	+	23.1543i	−1.32293	+	0.763791i	−0.984194	−	0.177092i	$-0.943331\pi$
$919$	−40.1045	+	23.1543i	−1.32293	+	0.763791i	−0.338731	+	0.940883i	$0.609998\pi$
$920$	−6.50895	−	16.2489i	−0.214594	−	0.535710i
$921$	−19.6914	+	18.6022i	−0.648855	+	0.612963i
$922$	−8.99400	−	15.5781i	−0.296202	−	0.513036i
$923$			82.1666i			2.70455i
$924$	−15.0419	−	5.77010i	−0.494843	−	0.189822i
$925$			24.7644i			0.814248i
$926$	22.4842	−	12.9812i	0.738876	−	0.426590i
$927$	−9.38104	−	18.6186i	−0.308114	−	0.611516i
$928$	−0.755075	+	1.30783i	−0.0247866	+	0.0429316i
$929$	−35.0774	+	20.2520i	−1.15085	+	0.664445i	−0.949095	−	0.314990i	$-0.897999\pi$
$929$	−35.0774	+	20.2520i	−1.15085	+	0.664445i	−0.201758	+	0.979435i	$0.564666\pi$
$930$	1.11103	−	3.71992i	0.0364321	−	0.121981i
$931$	18.1774	−	7.08159i	0.595741	−	0.232090i
$932$			7.65582i			0.250775i
$933$	−19.5499	+	4.64687i	−0.640035	+	0.152132i
$934$	−3.25455	−	1.87901i	−0.106492	−	0.0614832i
$935$	13.8340	−	23.9613i	0.452422	−	0.783617i
$936$	−20.2093	−	1.15063i	−0.660563	−	0.0376096i
$937$			8.08144i			0.264009i	0.991249	+	0.132005i	$0.0421414\pi$
$937$			8.08144i			0.264009i	−0.991249	+	0.132005i	$0.957859\pi$
$938$	0.707992	+	0.0539491i	0.0231168	+	0.00176150i
$939$	6.14168	−	20.5634i	0.200426	−	0.671061i
$940$	6.96780	−	4.02286i	0.227265	−	0.131211i
$941$	25.0639	−	43.4120i	0.817060	−	1.41519i	−0.0907792	−	0.995871i	$-0.528936\pi$
$941$	25.0639	−	43.4120i	0.817060	−	1.41519i	0.907839	−	0.419318i	$-0.137731\pi$
$942$	19.5930	−	18.5092i	0.638374	−	0.603062i
$943$	47.1597	+	6.77062i	1.53573	+	0.220482i
$944$			11.3705i			0.370079i
$945$	−20.6051	+	45.7512i	−0.670284	+	1.48829i
$946$	−45.0748			−1.46551
$947$	−21.7748	+	12.5717i	−0.707587	+	0.408525i	−0.810167	−	0.586199i	$-0.800624\pi$
$947$	−21.7748	+	12.5717i	−0.707587	+	0.408525i	0.102580	+	0.994725i	$0.467290\pi$
$948$	−15.6156	−	16.5300i	−0.507173	−	0.536870i
$949$	37.2411	−	64.5035i	1.20890	−	2.09387i
$950$	−11.5954	−	20.0838i	−0.376204	−	0.651604i
$951$	10.6618	−	35.6977i	0.345734	−	1.15758i
$952$	4.70959	+	3.21960i	0.152639	+	0.104348i
$953$	−23.9112			−0.774558			−0.387279	−	0.921963i	$-0.626585\pi$
$953$	−23.9112			−0.774558			−0.387279	+	0.921963i	$0.626585\pi$
$954$	28.7439	+	1.63655i	0.930617	+	0.0529853i
$955$	21.9356	−	37.9936i	0.709819	−	1.22944i
$956$	2.88449	+	1.66536i	0.0932912	+	0.0538617i
$957$	−8.94645	+	2.12651i	−0.289198	+	0.0687402i
$958$		−	17.1012i		−	0.552516i
$959$	5.94951	−	8.70288i	0.192120	−	0.281031i
$960$	−6.05733	−	1.80914i	−0.195499	−	0.0583899i
$961$	15.3114	+	26.5202i	0.493917	+	0.855489i
$962$	10.0400	−	17.3898i	0.323703	−	0.560670i
$963$	−11.7638	+	5.92723i	−0.379084	+	0.191002i
$964$	−22.1440	+	12.7849i	−0.713211	+	0.411773i
$965$	−19.6891			−0.633814
$966$	19.1925	+	10.7074i	0.617509	+	0.344504i
$967$	8.59156			0.276286			0.138143	−	0.990412i	$-0.455887\pi$
$967$	8.59156			0.276286			0.138143	+	0.990412i	$0.455887\pi$
$968$	1.17753	−	0.679850i	0.0378474	−	0.0218512i
$969$	−7.14752	−	7.56605i	−0.229612	−	0.243057i
$970$	−20.9934	+	36.3617i	−0.674058	+	1.16750i
$971$	−4.21358	−	7.29813i	−0.135220	−	0.234208i	0.790461	−	0.612512i	$-0.209841\pi$
$971$	−4.21358	−	7.29813i	−0.135220	−	0.234208i	−0.925682	+	0.378304i	$0.876507\pi$
$972$	−1.86015	−	15.4771i	−0.0596644	−	0.496427i
$973$	−59.4902	−	4.53316i	−1.90717	−	0.145326i
$974$		−	23.0995i		−	0.740155i
$975$	22.4891	+	94.6143i	0.720229	+	3.03008i
$976$	−2.82177	−	1.62915i	−0.0903227	−	0.0521478i
$977$	−22.8869	+	39.6413i	−0.732217	+	1.26824i	0.223716	+	0.974654i	$0.428181\pi$
$977$	−22.8869	+	39.6413i	−0.732217	+	1.26824i	−0.955933	+	0.293583i	$0.905152\pi$
$978$	−30.6528	+	7.28596i	−0.980170	+	0.232979i
$979$	−19.9511			−0.637639
$980$	−25.2540	−	3.87119i	−0.806708	−	0.123661i
$981$	−11.5191	+	17.5638i	−0.367776	+	0.560767i
$982$	−5.68279	−	9.84288i	−0.181345	−	0.314099i
$983$	17.2369	−	29.8553i	0.549773	−	0.952235i	−0.448516	−	0.893775i	$-0.648047\pi$
$983$	17.2369	−	29.8553i	0.549773	−	0.952235i	0.998290	−	0.0584606i	$-0.0186192\pi$
$984$	12.5080	−	11.8161i	0.398741	−	0.376684i
$985$	57.4181	−	33.1504i	1.82949	−	1.05626i
$986$	3.25627			0.103701
$987$	−3.61801	+	9.43170i	−0.115162	+	0.300214i
$988$			18.8041i			0.598237i
$989$	60.8644	+	8.73818i	1.93538	+	0.277858i
$990$	−17.3212	−	34.3775i	−0.550503	−	1.09259i
$991$	−3.59324	+	6.22367i	−0.114143	+	0.197702i	−0.917437	−	0.397881i	$-0.869746\pi$
$991$	−3.59324	+	6.22367i	−0.114143	+	0.197702i	0.803294	+	0.595583i	$0.203079\pi$
$992$	−0.531843	+	0.307060i	−0.0168860	+	0.00974916i
$993$	6.79085	+	2.02823i	0.215501	+	0.0643638i
$994$	−13.9429	−	29.0457i	−0.442241	−	0.921274i
$995$		−	13.4748i		−	0.427181i
$996$	0.332357	+	1.39826i	0.0105311	+	0.0443057i
$997$	−8.54609	+	14.8023i	−0.270657	+	0.468792i	−0.969030	−	0.246942i	$-0.920574\pi$
$997$	−8.54609	+	14.8023i	−0.270657	+	0.468792i	0.698373	+	0.715734i	$0.253908\pi$
$998$	−12.1118	−	6.99273i	−0.383391	−	0.221351i
$999$	14.5414	+	5.26047i	0.460070	+	0.166434i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.j.a.137.9	✓	128
3.2	odd	2	inner	966.2.j.a.137.46	yes	128
7.2	even	3	inner	966.2.j.a.275.45	yes	128
21.2	odd	6	inner	966.2.j.a.275.10	yes	128
23.22	odd	2	inner	966.2.j.a.137.10	yes	128
69.68	even	2	inner	966.2.j.a.137.45	yes	128
161.114	odd	6	inner	966.2.j.a.275.46	yes	128
483.275	even	6	inner	966.2.j.a.275.9	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.j.a.137.9	✓	128	1.1	even	1	trivial
966.2.j.a.137.10	yes	128	23.22	odd	2	inner
966.2.j.a.137.45	yes	128	69.68	even	2	inner
966.2.j.a.137.46	yes	128	3.2	odd	2	inner
966.2.j.a.275.9	yes	128	483.275	even	6	inner
966.2.j.a.275.10	yes	128	21.2	odd	6	inner
966.2.j.a.275.45	yes	128	7.2	even	3	inner
966.2.j.a.275.46	yes	128	161.114	odd	6	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.25907 + 1.18943i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.82493 - 3.16086i) q^{5} +(0.495676 - 1.65961i) q^{6} +(-2.63810 - 0.201024i) q^{7} +1.00000i q^{8} +(0.170531 - 2.99515i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.25907 + 1.18943i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.82493 - 3.16086i) q^{5} +(0.495676 - 1.65961i) q^{6} +(-2.63810 - 0.201024i) q^{7} +1.00000i q^{8} +(0.170531 - 2.99515i) q^{9} +(3.16086 + 1.82493i) q^{10} +(1.75782 - 3.04463i) q^{11} +(0.400537 + 1.68510i) q^{12} -6.74736 q^{13} +(2.38518 - 1.14496i) q^{14} +(6.05733 + 1.80914i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.07813 + 1.86737i) q^{17} +(1.34989 + 2.67914i) q^{18} +(2.41351 - 1.39344i) q^{19} -3.64985 q^{20} +(3.56067 - 2.88473i) q^{21} +3.51564i q^{22} +(0.681540 - 4.74716i) q^{23} +(-1.18943 - 1.25907i) q^{24} +(-4.16070 + 7.20655i) q^{25} +(5.84338 - 3.37368i) q^{26} +(3.34780 + 3.97395i) q^{27} +(-1.49314 + 2.18415i) q^{28} +1.51015i q^{29} +(-6.15037 + 1.46190i) q^{30} +(-0.307060 + 0.531843i) q^{31} +(0.866025 + 0.500000i) q^{32} +(1.40814 + 5.92421i) q^{33} -2.15625i q^{34} +(4.17893 + 8.70554i) q^{35} +(-2.50861 - 1.64526i) q^{36} +(2.57728 - 1.48799i) q^{37} +(-1.39344 + 2.41351i) q^{38} +(8.49541 - 8.02548i) q^{39} +(3.16086 - 1.82493i) q^{40} +9.93430i q^{41} +(-1.64127 + 4.27858i) q^{42} +12.8212i q^{43} +(-1.75782 - 3.04463i) q^{44} +(-9.77846 + 4.92690i) q^{45} +(1.78335 + 4.45193i) q^{46} +(-1.90907 + 1.10220i) q^{47} +(1.65961 + 0.495676i) q^{48} +(6.91918 + 1.06064i) q^{49} -8.32141i q^{50} +(-0.863659 - 3.63351i) q^{51} +(-3.37368 + 5.84338i) q^{52} +(4.79840 - 8.31108i) q^{53} +(-4.88625 - 1.76764i) q^{54} -12.8315 q^{55} +(0.201024 - 2.63810i) q^{56} +(-1.38139 + 4.62513i) q^{57} +(-0.755075 - 1.30783i) q^{58} +(-9.84716 - 5.68526i) q^{59} +(4.59543 - 4.34123i) q^{60} +(2.82177 - 1.62915i) q^{61} -0.614119i q^{62} +(-1.05197 + 7.86723i) q^{63} -1.00000 q^{64} +(12.3134 + 21.3275i) q^{65} +(-4.18159 - 4.42644i) q^{66} +(0.232417 + 0.134186i) q^{67} +(1.07813 + 1.86737i) q^{68} +(4.78828 + 6.78766i) q^{69} +(-7.97183 - 5.44975i) q^{70} -12.1776i q^{71} +(2.99515 + 0.170531i) q^{72} +(-5.51937 + 9.55983i) q^{73} +(-1.48799 + 2.57728i) q^{74} +(-3.33303 - 14.0224i) q^{75} -2.78688i q^{76} +(-5.24935 + 7.67869i) q^{77} +(-3.34450 + 11.1980i) q^{78} +(-11.3698 + 6.56436i) q^{79} +(-1.82493 + 3.16086i) q^{80} +(-8.94184 - 1.02153i) q^{81} +(-4.96715 - 8.60336i) q^{82} +0.829779 q^{83} +(-0.717912 - 4.52599i) q^{84} +7.87001 q^{85} +(-6.41062 - 11.1035i) q^{86} +(-1.79621 - 1.90139i) q^{87} +(3.04463 + 1.75782i) q^{88} +(-2.83747 - 4.91465i) q^{89} +(6.00495 - 9.15605i) q^{90} +(17.8002 + 1.35638i) q^{91} +(-3.77039 - 2.96381i) q^{92} +(-0.245977 - 1.03485i) q^{93} +(1.10220 - 1.90907i) q^{94} +(-8.80894 - 5.08585i) q^{95} +(-1.68510 + 0.400537i) q^{96} +11.5037i q^{97} +(-6.52251 + 2.54105i) q^{98} +(-8.81936 - 5.78413i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 64 q^{4} + 8 q^{6} - 4 q^{9}+O(q^{10}) \) 128 * q + 64 * q^4 + 8 * q^6 - 4 * q^9	\( 128 q + 64 q^{4} + 8 q^{6} - 4 q^{9} - 64 q^{16} + 4 q^{24} - 72 q^{25} + 24 q^{27} - 8 q^{36} + 4 q^{39} + 12 q^{46} + 72 q^{49} + 4 q^{54} - 96 q^{55} - 128 q^{64} - 56 q^{69} + 32 q^{70} - 40 q^{73} - 40 q^{75} - 16 q^{78} + 36 q^{81} - 32 q^{82} - 64 q^{85} - 24 q^{87} + 32 q^{93} - 8 q^{94} - 4 q^{96}+O(q^{100}) \) 128 * q + 64 * q^4 + 8 * q^6 - 4 * q^9 - 64 * q^16 + 4 * q^24 - 72 * q^25 + 24 * q^27 - 8 * q^36 + 4 * q^39 + 12 * q^46 + 72 * q^49 + 4 * q^54 - 96 * q^55 - 128 * q^64 - 56 * q^69 + 32 * q^70 - 40 * q^73 - 40 * q^75 - 16 * q^78 + 36 * q^81 - 32 * q^82 - 64 * q^85 - 24 * q^87 + 32 * q^93 - 8 * q^94 - 4 * q^96

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