LMFDB - Embedded newform 930.2.r.b.119.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(119,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("930.119");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.r (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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			119.1
Character	$\chi$	$=$	930.119
Dual form			930.2.r.b.719.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-1.72090 - 0.196245i) q^{3} +1.00000 q^{4} +(-1.99884 - 1.00231i) q^{5} +(-1.72090 - 0.196245i) q^{6} +(1.33698 + 0.771903i) q^{7} +1.00000 q^{8} +(2.92298 + 0.675436i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-1.72090 - 0.196245i) q^{3} +1.00000 q^{4} +(-1.99884 - 1.00231i) q^{5} +(-1.72090 - 0.196245i) q^{6} +(1.33698 + 0.771903i) q^{7} +1.00000 q^{8} +(2.92298 + 0.675436i) q^{9} +(-1.99884 - 1.00231i) q^{10} +(0.513693 + 0.889742i) q^{11} +(-1.72090 - 0.196245i) q^{12} +(0.187971 + 0.325576i) q^{13} +(1.33698 + 0.771903i) q^{14} +(3.24310 + 2.11714i) q^{15} +1.00000 q^{16} +(-2.40483 - 1.38843i) q^{17} +(2.92298 + 0.675436i) q^{18} +(1.95020 - 3.37784i) q^{19} +(-1.99884 - 1.00231i) q^{20} +(-2.14932 - 1.59074i) q^{21} +(0.513693 + 0.889742i) q^{22} -6.45392i q^{23} +(-1.72090 - 0.196245i) q^{24} +(2.99074 + 4.00693i) q^{25} +(0.187971 + 0.325576i) q^{26} +(-4.89759 - 1.73598i) q^{27} +(1.33698 + 0.771903i) q^{28} +8.51109 q^{29} +(3.24310 + 2.11714i) q^{30} +(2.94274 + 4.72655i) q^{31} +1.00000 q^{32} +(-0.709405 - 1.63197i) q^{33} +(-2.40483 - 1.38843i) q^{34} +(-1.89872 - 2.88298i) q^{35} +(2.92298 + 0.675436i) q^{36} +(4.88703 - 8.46459i) q^{37} +(1.95020 - 3.37784i) q^{38} +(-0.259586 - 0.597171i) q^{39} +(-1.99884 - 1.00231i) q^{40} +(-0.344972 + 0.199170i) q^{41} +(-2.14932 - 1.59074i) q^{42} +(5.22057 - 9.04229i) q^{43} +(0.513693 + 0.889742i) q^{44} +(-5.16557 - 4.27982i) q^{45} -6.45392i q^{46} -1.66589 q^{47} +(-1.72090 - 0.196245i) q^{48} +(-2.30833 - 3.99815i) q^{49} +(2.99074 + 4.00693i) q^{50} +(3.86599 + 2.86128i) q^{51} +(0.187971 + 0.325576i) q^{52} +(7.56819 - 4.36950i) q^{53} +(-4.89759 - 1.73598i) q^{54} +(-0.134992 - 2.29334i) q^{55} +(1.33698 + 0.771903i) q^{56} +(-4.01898 + 5.43020i) q^{57} +8.51109 q^{58} +(0.110206 + 0.0636277i) q^{59} +(3.24310 + 2.11714i) q^{60} -7.82981i q^{61} +(2.94274 + 4.72655i) q^{62} +(3.38658 + 3.15930i) q^{63} +1.00000 q^{64} +(-0.0493963 - 0.839180i) q^{65} +(-0.709405 - 1.63197i) q^{66} +(-11.9166 + 6.88003i) q^{67} +(-2.40483 - 1.38843i) q^{68} +(-1.26655 + 11.1065i) q^{69} +(-1.89872 - 2.88298i) q^{70} +(-1.70786 + 0.986036i) q^{71} +(2.92298 + 0.675436i) q^{72} +(7.80488 + 13.5185i) q^{73} +(4.88703 - 8.46459i) q^{74} +(-4.36042 - 7.48243i) q^{75} +(1.95020 - 3.37784i) q^{76} +1.58609i q^{77} +(-0.259586 - 0.597171i) q^{78} +(5.86946 + 3.38873i) q^{79} +(-1.99884 - 1.00231i) q^{80} +(8.08757 + 3.94857i) q^{81} +(-0.344972 + 0.199170i) q^{82} +(8.44099 - 4.87341i) q^{83} +(-2.14932 - 1.59074i) q^{84} +(3.41523 + 5.18564i) q^{85} +(5.22057 - 9.04229i) q^{86} +(-14.6467 - 1.67026i) q^{87} +(0.513693 + 0.889742i) q^{88} -8.81000 q^{89} +(-5.16557 - 4.27982i) q^{90} +0.580383i q^{91} -6.45392i q^{92} +(-4.13660 - 8.71140i) q^{93} -1.66589 q^{94} +(-7.28379 + 4.79707i) q^{95} +(-1.72090 - 0.196245i) q^{96} -4.07977i q^{97} +(-2.30833 - 3.99815i) q^{98} +(0.900548 + 2.94766i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 64 q^{2} + 64 q^{4} + 2 q^{5} + 64 q^{8} - 4 q^{9}+O(q^{10}) $ 64 * q + 64 * q^2 + 64 * q^4 + 2 * q^5 + 64 * q^8 - 4 * q^9	$ 64 q + 64 q^{2} + 64 q^{4} + 2 q^{5} + 64 q^{8} - 4 q^{9} + 2 q^{10} + 64 q^{16} + 6 q^{17} - 4 q^{18} + 4 q^{19} + 2 q^{20} + 2 q^{25} + 18 q^{31} + 64 q^{32} - 8 q^{33} + 6 q^{34} + 16 q^{35} - 4 q^{36} + 4 q^{38} - 8 q^{39} + 2 q^{40} + 9 q^{45} - 4 q^{47} + 30 q^{49} + 2 q^{50} - 8 q^{51} - 6 q^{53} + 6 q^{57} + 18 q^{62} + 12 q^{63} + 64 q^{64} - 8 q^{66} + 6 q^{68} - 10 q^{69} + 16 q^{70} - 4 q^{72} - 63 q^{75} + 4 q^{76} - 8 q^{78} - 30 q^{79} + 2 q^{80} - 12 q^{81} - 54 q^{83} - 16 q^{87} + 9 q^{90} - 18 q^{93} - 4 q^{94} - 56 q^{95} + 30 q^{98} - 102 q^{99}+O(q^{100}) $ 64 * q + 64 * q^2 + 64 * q^4 + 2 * q^5 + 64 * q^8 - 4 * q^9 + 2 * q^10 + 64 * q^16 + 6 * q^17 - 4 * q^18 + 4 * q^19 + 2 * q^20 + 2 * q^25 + 18 * q^31 + 64 * q^32 - 8 * q^33 + 6 * q^34 + 16 * q^35 - 4 * q^36 + 4 * q^38 - 8 * q^39 + 2 * q^40 + 9 * q^45 - 4 * q^47 + 30 * q^49 + 2 * q^50 - 8 * q^51 - 6 * q^53 + 6 * q^57 + 18 * q^62 + 12 * q^63 + 64 * q^64 - 8 * q^66 + 6 * q^68 - 10 * q^69 + 16 * q^70 - 4 * q^72 - 63 * q^75 + 4 * q^76 - 8 * q^78 - 30 * q^79 + 2 * q^80 - 12 * q^81 - 54 * q^83 - 16 * q^87 + 9 * q^90 - 18 * q^93 - 4 * q^94 - 56 * q^95 + 30 * q^98 - 102 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−1.72090	−	0.196245i	−0.993561	−	0.113302i
$3$	−1.72090	−	0.196245i	−0.993561	−	0.113302i
$4$	1.00000			0.500000
$5$	−1.99884	−	1.00231i	−0.893909	−	0.448248i
$5$	−1.99884	−	1.00231i	−0.893909	−	0.448248i
$6$	−1.72090	−	0.196245i	−0.702553	−	0.0801168i
$7$	1.33698	+	0.771903i	0.505329	+	0.291752i	0.730912	−	0.682472i	$-0.239095\pi$
$7$	1.33698	+	0.771903i	0.505329	+	0.291752i	−0.225582	+	0.974224i	$0.572428\pi$
$8$	1.00000			0.353553
$9$	2.92298	+	0.675436i	0.974325	+	0.225145i
$10$	−1.99884	−	1.00231i	−0.632089	−	0.316959i
$11$	0.513693	+	0.889742i	0.154884	+	0.268267i	0.933017	−	0.359833i	$-0.117166\pi$
$11$	0.513693	+	0.889742i	0.154884	+	0.268267i	−0.778133	+	0.628100i	$0.783833\pi$
$12$	−1.72090	−	0.196245i	−0.496780	−	0.0566512i
$13$	0.187971	+	0.325576i	0.0521338	+	0.0902985i	0.890915	−	0.454171i	$-0.150064\pi$
$13$	0.187971	+	0.325576i	0.0521338	+	0.0902985i	−0.838781	+	0.544469i	$0.816731\pi$
$14$	1.33698	+	0.771903i	0.357322	+	0.206300i
$15$	3.24310	+	2.11714i	0.837366	+	0.546643i
$16$	1.00000			0.250000
$17$	−2.40483	−	1.38843i	−0.583256	−	0.336743i	0.179170	−	0.983818i	$-0.442659\pi$
$17$	−2.40483	−	1.38843i	−0.583256	−	0.336743i	−0.762426	+	0.647075i	$0.775992\pi$
$18$	2.92298	+	0.675436i	0.688952	+	0.159202i
$19$	1.95020	−	3.37784i	0.447406	−	0.774930i	−0.550810	−	0.834630i	$-0.685681\pi$
$19$	1.95020	−	3.37784i	0.447406	−	0.774930i	0.998216	+	0.0597004i	$0.0190145\pi$
$20$	−1.99884	−	1.00231i	−0.446955	−	0.224124i
$21$	−2.14932	−	1.59074i	−0.469019	−	0.347128i
$22$	0.513693	+	0.889742i	0.109520	+	0.189694i
$23$		−	6.45392i		−	1.34574i	−0.739763	−	0.672868i	$-0.765062\pi$
$23$		−	6.45392i		−	1.34574i	0.739763	−	0.672868i	$-0.234938\pi$
$24$	−1.72090	−	0.196245i	−0.351277	−	0.0400584i
$25$	2.99074	+	4.00693i	0.598148	+	0.801386i
$26$	0.187971	+	0.325576i	0.0368642	+	0.0638507i
$27$	−4.89759	−	1.73598i	−0.942542	−	0.334089i
$28$	1.33698	+	0.771903i	0.252665	+	0.145876i
$29$	8.51109			1.58047			0.790235	−	0.612804i	$-0.209959\pi$
$29$	8.51109			1.58047			0.790235	+	0.612804i	$0.209959\pi$
$30$	3.24310	+	2.11714i	0.592107	+	0.386535i
$31$	2.94274	+	4.72655i	0.528532	+	0.848913i
$31$	2.94274	+	4.72655i	0.528532	+	0.848913i
$32$	1.00000			0.176777
$33$	−0.709405	−	1.63197i	−0.123492	−	0.284089i
$34$	−2.40483	−	1.38843i	−0.412425	−	0.238113i
$35$	−1.89872	−	2.88298i	−0.320941	−	0.487313i
$36$	2.92298	+	0.675436i	0.487163	+	0.112573i
$37$	4.88703	−	8.46459i	0.803423	−	1.39157i	−0.113927	−	0.993489i	$-0.536343\pi$
$37$	4.88703	−	8.46459i	0.803423	−	1.39157i	0.917350	−	0.398081i	$-0.130324\pi$
$38$	1.95020	−	3.37784i	0.316364	−	0.547958i
$39$	−0.259586	−	0.597171i	−0.0415671	−	0.0956239i
$40$	−1.99884	−	1.00231i	−0.316045	−	0.158479i
$41$	−0.344972	+	0.199170i	−0.0538755	+	0.0311051i	−0.526696	−	0.850054i	$-0.676569\pi$
$41$	−0.344972	+	0.199170i	−0.0538755	+	0.0311051i	0.472820	+	0.881159i	$0.343236\pi$
$42$	−2.14932	−	1.59074i	−0.331647	−	0.245457i
$43$	5.22057	−	9.04229i	0.796129	−	1.37894i	−0.125991	−	0.992031i	$-0.540211\pi$
$43$	5.22057	−	9.04229i	0.796129	−	1.37894i	0.922120	−	0.386905i	$-0.126456\pi$
$44$	0.513693	+	0.889742i	0.0774421	+	0.134134i
$45$	−5.16557	−	4.27982i	−0.770037	−	0.637999i
$46$		−	6.45392i		−	0.951579i
$47$	−1.66589			−0.242995			−0.121498	−	0.992592i	$-0.538770\pi$
$47$	−1.66589			−0.242995			−0.121498	+	0.992592i	$0.538770\pi$
$48$	−1.72090	−	0.196245i	−0.248390	−	0.0283256i
$49$	−2.30833	−	3.99815i	−0.329761	−	0.571164i
$50$	2.99074	+	4.00693i	0.422955	+	0.566665i
$51$	3.86599	+	2.86128i	0.541347	+	0.400659i
$52$	0.187971	+	0.325576i	0.0260669	+	0.0451492i
$53$	7.56819	−	4.36950i	1.03957	−	0.600196i	0.119859	−	0.992791i	$-0.461756\pi$
$53$	7.56819	−	4.36950i	1.03957	−	0.600196i	0.919712	+	0.392595i	$0.128422\pi$
$54$	−4.89759	−	1.73598i	−0.666478	−	0.236237i
$55$	−0.134992	−	2.29334i	−0.0182023	−	0.309233i
$56$	1.33698	+	0.771903i	0.178661	+	0.103150i
$57$	−4.01898	+	5.43020i	−0.532326	+	0.719248i
$58$	8.51109			1.11756
$59$	0.110206	+	0.0636277i	0.0143476	+	0.00828362i	0.507157	−	0.861854i	$-0.330697\pi$
$59$	0.110206	+	0.0636277i	0.0143476	+	0.00828362i	−0.492809	+	0.870138i	$0.664030\pi$
$60$	3.24310	+	2.11714i	0.418683	+	0.273322i
$61$		−	7.82981i		−	1.00250i	−0.865301	−	0.501252i	$-0.832873\pi$
$61$		−	7.82981i		−	1.00250i	0.865301	−	0.501252i	$-0.167127\pi$
$62$	2.94274	+	4.72655i	0.373729	+	0.600272i
$63$	3.38658	+	3.15930i	0.426668	+	0.398034i
$64$	1.00000			0.125000
$65$	−0.0493963	−	0.839180i	−0.00612685	−	0.104088i
$66$	−0.709405	−	1.63197i	−0.0873217	−	0.200881i
$67$	−11.9166	+	6.88003i	−1.45584	+	0.840529i	−0.998803	−	0.0489184i	$-0.984423\pi$
$67$	−11.9166	+	6.88003i	−1.45584	+	0.840529i	−0.457037	+	0.889448i	$0.651089\pi$
$68$	−2.40483	−	1.38843i	−0.291628	−	0.168372i
$69$	−1.26655	+	11.1065i	−0.152475	+	1.33707i
$70$	−1.89872	−	2.88298i	−0.226940	−	0.344582i
$71$	−1.70786	+	0.986036i	−0.202686	+	0.117021i	−0.597908	−	0.801565i	$-0.704001\pi$
$71$	−1.70786	+	0.986036i	−0.202686	+	0.117021i	0.395222	+	0.918586i	$0.370668\pi$
$72$	2.92298	+	0.675436i	0.344476	+	0.0796009i
$73$	7.80488	+	13.5185i	0.913492	+	1.58222i	0.809094	+	0.587680i	$0.199958\pi$
$73$	7.80488	+	13.5185i	0.913492	+	1.58222i	0.104399	+	0.994536i	$0.466708\pi$
$74$	4.88703	−	8.46459i	0.568106	−	0.983989i
$75$	−4.36042	−	7.48243i	−0.503497	−	0.863997i
$76$	1.95020	−	3.37784i	0.223703	−	0.387465i
$77$			1.58609i			0.180751i
$78$	−0.259586	−	0.597171i	−0.0293924	−	0.0676163i
$79$	5.86946	+	3.38873i	0.660366	+	0.381262i	0.792416	−	0.609981i	$-0.208823\pi$
$79$	5.86946	+	3.38873i	0.660366	+	0.381262i	−0.132051	+	0.991243i	$0.542156\pi$
$80$	−1.99884	−	1.00231i	−0.223477	−	0.112062i
$81$	8.08757	+	3.94857i	0.898619	+	0.438730i
$82$	−0.344972	+	0.199170i	−0.0380958	+	0.0219946i
$83$	8.44099	−	4.87341i	0.926519	−	0.534926i	0.0408103	−	0.999167i	$-0.487006\pi$
$83$	8.44099	−	4.87341i	0.926519	−	0.534926i	0.885709	+	0.464241i	$0.153673\pi$
$84$	−2.14932	−	1.59074i	−0.234510	−	0.173564i
$85$	3.41523	+	5.18564i	0.370434	+	0.562461i
$86$	5.22057	−	9.04229i	0.562948	−	0.975055i
$87$	−14.6467	−	1.67026i	−1.57029	−	0.179071i
$88$	0.513693	+	0.889742i	0.0547599	+	0.0948468i
$89$	−8.81000			−0.933859			−0.466929	−	0.884295i	$-0.654640\pi$
$89$	−8.81000			−0.933859			−0.466929	+	0.884295i	$0.654640\pi$
$90$	−5.16557	−	4.27982i	−0.544499	−	0.451133i
$91$			0.580383i			0.0608406i
$92$		−	6.45392i		−	0.672868i
$93$	−4.13660	−	8.71140i	−0.428945	−	0.903331i
$94$	−1.66589			−0.171824
$95$	−7.28379	+	4.79707i	−0.747301	+	0.492169i
$96$	−1.72090	−	0.196245i	−0.175638	−	0.0200292i
$97$		−	4.07977i		−	0.414238i	−0.978316	−	0.207119i	$-0.933591\pi$
$97$		−	4.07977i		−	0.414238i	0.978316	−	0.207119i	$-0.0664087\pi$
$98$	−2.30833	−	3.99815i	−0.233177	−	0.403874i
$99$	0.900548	+	2.94766i	0.0905084	+	0.296251i
$100$	2.99074	+	4.00693i	0.299074	+	0.400693i
$101$			9.70684i			0.965867i	0.875657	+	0.482933i	$0.160429\pi$
$101$			9.70684i			0.965867i	−0.875657	+	0.482933i	$0.839571\pi$
$102$	3.86599	+	2.86128i	0.382790	+	0.283309i
$103$	−15.6515	+	9.03639i	−1.54219	+	0.890382i	−0.543486	+	0.839418i	$0.682896\pi$
$103$	−15.6515	+	9.03639i	−1.54219	+	0.890382i	−0.998701	+	0.0509633i	$0.983771\pi$
$104$	0.187971	+	0.325576i	0.0184321	+	0.0319253i
$105$	2.70172	+	5.33393i	0.263661	+	0.520538i
$106$	7.56819	−	4.36950i	0.735087	−	0.424403i
$107$	−6.43590	+	11.1473i	−0.622182	+	1.07765i	0.366896	+	0.930262i	$0.380420\pi$
$107$	−6.43590	+	11.1473i	−0.622182	+	1.07765i	−0.989079	+	0.147390i	$0.952913\pi$
$108$	−4.89759	−	1.73598i	−0.471271	−	0.167044i
$109$	4.00561			0.383668			0.191834	−	0.981427i	$-0.438556\pi$
$109$	4.00561			0.383668			0.191834	+	0.981427i	$0.438556\pi$
$110$	−0.134992	−	2.29334i	−0.0128709	−	0.218661i
$111$	−10.0712	+	13.6076i	−0.955918	+	1.29158i
$112$	1.33698	+	0.771903i	0.126332	+	0.0729380i
$113$	−0.622160	−	1.07761i	−0.0585279	−	0.101373i	0.835277	−	0.549830i	$-0.185307\pi$
$113$	−0.622160	−	1.07761i	−0.0585279	−	0.101373i	−0.893805	+	0.448456i	$0.851974\pi$
$114$	−4.01898	+	5.43020i	−0.376412	+	0.508585i
$115$	−6.46884	+	12.9004i	−0.603223	+	1.20297i
$116$	8.51109			0.790235
$117$	0.329530	+	1.07861i	0.0304650	+	0.0997178i
$118$	0.110206	+	0.0636277i	0.0101453	+	0.00585740i
$119$	−2.14346	−	3.71259i	−0.196491	−	0.340332i
$120$	3.24310	+	2.11714i	0.296053	+	0.193268i
$121$	4.97224	−	8.61217i	0.452022	−	0.782925i
$122$		−	7.82981i		−	0.708878i
$123$	0.632747	−	0.275051i	0.0570529	−	0.0248005i
$124$	2.94274	+	4.72655i	0.264266	+	0.424457i
$125$	−1.96182	−	11.0069i	−0.175471	−	0.984485i
$126$	3.38658	+	3.15930i	0.301700	+	0.281453i
$127$	−6.85953	+	11.8811i	−0.608685	+	1.05427i	0.382773	+	0.923843i	$0.374969\pi$
$127$	−6.85953	+	11.8811i	−0.608685	+	1.05427i	−0.991457	+	0.130430i	$0.958364\pi$
$128$	1.00000			0.0883883
$129$	−10.7586	+	14.5363i	−0.947239	+	1.27985i
$130$	−0.0493963	−	0.839180i	−0.00433234	−	0.0736010i
$131$	3.59435	+	2.07520i	0.314040	+	0.181311i	0.648733	−	0.761016i	$-0.275299\pi$
$131$	3.59435	+	2.07520i	0.314040	+	0.181311i	−0.334693	+	0.942327i	$0.608633\pi$
$132$	−0.709405	−	1.63197i	−0.0617458	−	0.142044i
$133$	5.21473	−	3.01073i	0.452175	−	0.261063i
$134$	−11.9166	+	6.88003i	−1.02943	+	0.594344i
$135$	8.04952	+	8.37886i	0.692792	+	0.721137i
$136$	−2.40483	−	1.38843i	−0.206212	−	0.119057i
$137$	−2.31332	+	1.33559i	−0.197640	+	0.114107i	−0.595554	−	0.803315i	$-0.703067\pi$
$137$	−2.31332	+	1.33559i	−0.197640	+	0.114107i	0.397914	+	0.917423i	$0.369734\pi$
$138$	−1.26655	+	11.1065i	−0.107816	+	0.945451i
$139$			6.83630i			0.579847i	0.957050	+	0.289924i	$0.0936299\pi$
$139$			6.83630i			0.579847i	−0.957050	+	0.289924i	$0.906370\pi$
$140$	−1.89872	−	2.88298i	−0.160471	−	0.243656i
$141$	2.86683	+	0.326924i	0.241431	+	0.0275320i
$142$	−1.70786	+	0.986036i	−0.143321	+	0.0827463i
$143$	−0.193119	+	0.334492i	−0.0161494	+	0.0279716i
$144$	2.92298	+	0.675436i	0.243581	+	0.0562864i
$145$	−17.0123	−	8.53077i	−1.41280	−	0.708442i
$146$	7.80488	+	13.5185i	0.645937	+	1.11880i
$147$	3.18778	+	7.33340i	0.262924	+	0.604848i
$148$	4.88703	−	8.46459i	0.401712	−	0.695785i
$149$	−2.72429	−	1.57287i	−0.223182	−	0.128854i	0.384241	−	0.923233i	$-0.374463\pi$
$149$	−2.72429	−	1.57287i	−0.223182	−	0.128854i	−0.607423	+	0.794379i	$0.707797\pi$
$150$	−4.36042	−	7.48243i	−0.356026	−	0.610938i
$151$		−	1.49881i		−	0.121972i	−0.998139	−	0.0609858i	$-0.980576\pi$
$151$		−	1.49881i		−	0.121972i	0.998139	−	0.0609858i	$-0.0194244\pi$
$152$	1.95020	−	3.37784i	0.158182	−	0.273979i
$153$	−6.09146	−	5.68265i	−0.492465	−	0.459415i
$154$			1.58609i			0.127810i
$155$	−1.14460	−	12.3972i	−0.0919366	−	0.995765i
$156$	−0.259586	−	0.597171i	−0.0207836	−	0.0478119i
$157$		−	15.8265i		−	1.26309i	−0.775339	−	0.631545i	$-0.782421\pi$
$157$		−	15.8265i		−	1.26309i	0.775339	−	0.631545i	$-0.217579\pi$
$158$	5.86946	+	3.38873i	0.466949	+	0.269593i
$159$	−13.8816	+	6.03423i	−1.10088	+	0.478546i
$160$	−1.99884	−	1.00231i	−0.158022	−	0.0792397i
$161$	4.98180	−	8.62874i	0.392621	−	0.680040i
$162$	8.08757	+	3.94857i	0.635420	+	0.310229i
$163$			4.39357i			0.344131i	0.985085	+	0.172066i	$0.0550441\pi$
$163$			4.39357i			0.344131i	−0.985085	+	0.172066i	$0.944956\pi$
$164$	−0.344972	+	0.199170i	−0.0269378	+	0.0155525i
$165$	−0.217750	+	3.97309i	−0.0169518	+	0.309304i
$166$	8.44099	−	4.87341i	0.655148	−	0.378250i
$167$	0.811816	+	0.468702i	0.0628202	+	0.0362693i	0.531081	−	0.847321i	$-0.321786\pi$
$167$	0.811816	+	0.468702i	0.0628202	+	0.0362693i	−0.468261	+	0.883590i	$0.655119\pi$
$168$	−2.14932	−	1.59074i	−0.165823	−	0.122728i
$169$	6.42933	−	11.1359i	0.494564	−	0.856610i
$170$	3.41523	+	5.18564i	0.261936	+	0.397720i
$171$	7.98190	−	8.55611i	0.610391	−	0.654302i
$172$	5.22057	−	9.04229i	0.398065	−	0.689468i
$173$	6.13059	+	10.6185i	0.466100	+	0.807309i	0.999250	−	0.0387117i	$-0.0123254\pi$
$173$	6.13059	+	10.6185i	0.466100	+	0.807309i	−0.533151	+	0.846020i	$0.678992\pi$
$174$	−14.6467	−	1.67026i	−1.11036	−	0.126622i
$175$	0.905586	+	7.66573i	0.0684559	+	0.579475i
$176$	0.513693	+	0.889742i	0.0387211	+	0.0670668i
$177$	−0.177167	−	0.131124i	−0.0133167	−	0.00985590i
$178$	−8.81000			−0.660338
$179$	2.69380	−	4.66581i	0.201344	−	0.348739i	−0.747617	−	0.664130i	$-0.768802\pi$
$179$	2.69380	−	4.66581i	0.201344	−	0.348739i	0.948962	+	0.315391i	$0.102136\pi$
$180$	−5.16557	−	4.27982i	−0.385019	−	0.318999i
$181$	16.1444	−	9.32095i	1.20000	−	0.692821i	0.239445	−	0.970910i	$-0.423034\pi$
$181$	16.1444	−	9.32095i	1.20000	−	0.692821i	0.960555	+	0.278089i	$0.0897010\pi$
$182$			0.580383i			0.0430208i
$183$	−1.53656	+	13.4743i	−0.113586	+	0.996049i
$184$		−	6.45392i		−	0.475789i
$185$	−18.2526	+	12.0210i	−1.34196	+	0.883805i
$186$	−4.13660	−	8.71140i	−0.303310	−	0.638751i
$187$		−	2.85290i		−	0.208625i
$188$	−1.66589			−0.121498
$189$	−5.20795	−	6.10143i	−0.378823	−	0.443813i
$190$	−7.28379	+	4.79707i	−0.528422	+	0.348016i
$191$	−17.8762	+	10.3208i	−1.29348	+	0.746788i	−0.979269	−	0.202566i	$-0.935072\pi$
$191$	−17.8762	+	10.3208i	−1.29348	+	0.746788i	−0.314207	+	0.949355i	$0.601739\pi$
$192$	−1.72090	−	0.196245i	−0.124195	−	0.0141628i
$193$	5.07739	+	2.93143i	0.365479	+	0.211009i	0.671481	−	0.741021i	$-0.265658\pi$
$193$	5.07739	+	2.93143i	0.365479	+	0.211009i	−0.306003	+	0.952031i	$0.598992\pi$
$194$		−	4.07977i		−	0.292910i
$195$	−0.0796794	+	1.45384i	−0.00570596	+	0.104111i
$196$	−2.30833	−	3.99815i	−0.164881	−	0.285582i
$197$	−21.1684	+	12.2216i	−1.50818	+	0.870750i	−0.508228	+	0.861222i	$0.669699\pi$
$197$	−21.1684	+	12.2216i	−1.50818	+	0.870750i	−0.999955	+	0.00952755i	$0.996967\pi$
$198$	0.900548	+	2.94766i	0.0639991	+	0.209481i
$199$	−1.84228	+	1.06364i	−0.130595	+	0.0753993i	−0.563874	−	0.825861i	$-0.690690\pi$
$199$	−1.84228	+	1.06364i	−0.130595	+	0.0753993i	0.433279	+	0.901260i	$0.357356\pi$
$200$	2.99074	+	4.00693i	0.211477	+	0.283333i
$201$	21.8574	−	9.50125i	1.54170	−	0.670167i
$202$			9.70684i			0.682971i
$203$	11.3791	+	6.56974i	0.798658	+	0.461105i
$204$	3.86599	+	2.86128i	0.270673	+	0.200330i
$205$	0.889174	−	0.0523390i	0.0621026	−	0.00365552i
$206$	−15.6515	+	9.03639i	−1.09049	+	0.629595i
$207$	4.35921	−	18.8647i	0.302986	−	1.31118i
$208$	0.187971	+	0.325576i	0.0130335	+	0.0225746i
$209$	4.00721			0.277185
$210$	2.70172	+	5.33393i	0.186437	+	0.368076i
$211$	11.5557	−	20.0151i	0.795530	−	1.37790i	−0.126972	−	0.991906i	$-0.540526\pi$
$211$	11.5557	−	20.0151i	0.795530	−	1.37790i	0.922502	−	0.385992i	$-0.126141\pi$
$212$	7.56819	−	4.36950i	0.519785	−	0.300098i
$213$	3.13256	−	1.36171i	0.214640	−	0.0933026i
$214$	−6.43590	+	11.1473i	−0.439949	+	0.762015i
$215$	−19.4983	+	12.8415i	−1.32977	+	0.875781i
$216$	−4.89759	−	1.73598i	−0.333239	−	0.118118i
$217$	0.285938	+	8.59079i	0.0194107	+	0.583181i
$218$	4.00561			0.271294
$219$	−10.7785	−	24.7955i	−0.728341	−	1.67553i
$220$	−0.134992	−	2.29334i	−0.00910113	−	0.154617i
$221$		−	1.04394i		−	0.0702229i
$222$	−10.0712	+	13.6076i	−0.675936	+	0.913285i
$223$	−6.82575	+	11.8225i	−0.457086	+	0.791696i	−0.998805	−	0.0488632i	$-0.984440\pi$
$223$	−6.82575	+	11.8225i	−0.457086	+	0.791696i	0.541720	+	0.840559i	$0.317774\pi$
$224$	1.33698	+	0.771903i	0.0893305	+	0.0515750i
$225$	6.03544	+	13.7322i	0.402362	+	0.915480i
$226$	−0.622160	−	1.07761i	−0.0413855	−	0.0716817i
$227$	9.21100	+	15.9539i	0.611356	+	1.05890i	0.991012	+	0.133771i	$0.0427088\pi$
$227$	9.21100	+	15.9539i	0.611356	+	1.05890i	−0.379657	+	0.925127i	$0.623958\pi$
$228$	−4.01898	+	5.43020i	−0.266163	+	0.359624i
$229$	−9.98391	−	5.76421i	−0.659755	−	0.380910i	0.132429	−	0.991193i	$-0.457723\pi$
$229$	−9.98391	−	5.76421i	−0.659755	−	0.380910i	−0.792184	+	0.610283i	$0.791056\pi$
$230$	−6.46884	+	12.9004i	−0.426543	+	0.850625i
$231$	0.311262	−	2.72949i	0.0204795	−	0.179587i
$232$	8.51109			0.558780
$233$	2.92070			0.191342			0.0956708	−	0.995413i	$-0.469500\pi$
$233$	2.92070			0.191342			0.0956708	+	0.995413i	$0.469500\pi$
$234$	0.329530	+	1.07861i	0.0215420	+	0.0705111i
$235$	3.32986	+	1.66975i	0.217216	+	0.108922i
$236$	0.110206	+	0.0636277i	0.00717382	+	0.00414181i
$237$	−9.43571	−	6.98352i	−0.612915	−	0.453628i
$238$	−2.14346	−	3.71259i	−0.138940	−	0.240651i
$239$	7.54702	+	13.0718i	0.488176	+	0.845546i	0.999908	−	0.0135994i	$-0.00432895\pi$
$239$	7.54702	+	13.0718i	0.488176	+	0.845546i	−0.511731	+	0.859146i	$0.670996\pi$
$240$	3.24310	+	2.11714i	0.209341	+	0.136661i
$241$	−14.6295	−	8.44634i	−0.942368	−	0.544076i	−0.0516662	−	0.998664i	$-0.516453\pi$
$241$	−14.6295	−	8.44634i	−0.942368	−	0.544076i	−0.890702	+	0.454588i	$0.849787\pi$
$242$	4.97224	−	8.61217i	0.319628	−	0.553611i
$243$	−13.1430	−	8.38223i	−0.843123	−	0.537720i
$244$		−	7.82981i		−	0.501252i
$245$	0.606598	+	10.3053i	0.0387541	+	0.658383i
$246$	0.632747	−	0.275051i	0.0403425	−	0.0175366i
$247$	1.46632			0.0933000
$248$	2.94274	+	4.72655i	0.186864	+	0.300136i
$249$	−15.4825	+	6.73013i	−0.981162	+	0.426505i
$250$	−1.96182	−	11.0069i	−0.124077	−	0.696136i
$251$	2.64324	−	4.57822i	0.166840	−	0.288975i	−0.770467	−	0.637479i	$-0.779977\pi$
$251$	2.64324	−	4.57822i	0.166840	−	0.288975i	0.937307	+	0.348505i	$0.113310\pi$
$252$	3.38658	+	3.15930i	0.213334	+	0.199017i
$253$	5.74233	−	3.31533i	0.361017	−	0.208433i
$254$	−6.85953	+	11.8811i	−0.430405	+	0.745484i
$255$	−4.85961	−	9.59417i	−0.304320	−	0.600810i
$256$	1.00000			0.0625000
$257$	10.5068	+	18.1983i	0.655395	+	1.13518i	0.981795	+	0.189945i	$0.0608310\pi$
$257$	10.5068	+	18.1983i	0.655395	+	1.13518i	−0.326400	+	0.945232i	$0.605836\pi$
$258$	−10.7586	+	14.5363i	−0.669799	+	0.904993i
$259$	13.0677	−	7.54464i	0.811987	−	0.468801i
$260$	−0.0493963	−	0.839180i	−0.00306343	−	0.0520438i
$261$	24.8777	+	5.74870i	1.53989	+	0.355836i
$262$	3.59435	+	2.07520i	0.222060	+	0.128206i
$263$		−	4.36646i		−	0.269248i	−0.990897	−	0.134624i	$-0.957017\pi$
$263$		−	4.36646i		−	0.269248i	0.990897	−	0.134624i	$-0.0429826\pi$
$264$	−0.709405	−	1.63197i	−0.0436609	−	0.100441i
$265$	−19.5072	+	1.14824i	−1.19832	+	0.0705361i
$266$	5.21473	−	3.01073i	0.319736	−	0.184600i
$267$	15.1611	+	1.72892i	0.927845	+	0.105808i
$268$	−11.9166	+	6.88003i	−0.727920	+	0.420265i
$269$	−10.8340	−	18.7651i	−0.660561	−	1.14413i	−0.980468	−	0.196677i	$-0.936985\pi$
$269$	−10.8340	−	18.7651i	−0.660561	−	1.14413i	0.319907	−	0.947449i	$-0.396348\pi$
$270$	8.04952	+	8.37886i	0.489878	+	0.509921i
$271$			1.13263i			0.0688022i	0.999408	+	0.0344011i	$0.0109524\pi$
$271$			1.13263i			0.0688022i	−0.999408	+	0.0344011i	$0.989048\pi$
$272$	−2.40483	−	1.38843i	−0.145814	−	0.0841858i
$273$	0.113897	−	0.998779i	0.00689338	−	0.0604488i
$274$	−2.31332	+	1.33559i	−0.139752	+	0.0806861i
$275$	−2.02881	+	4.71932i	−0.122342	+	0.284586i
$276$	−1.26655	+	11.1065i	−0.0762375	+	0.668535i
$277$	7.95261			0.477826			0.238913	−	0.971041i	$-0.423209\pi$
$277$	7.95261			0.477826			0.238913	+	0.971041i	$0.423209\pi$
$278$			6.83630i			0.410014i
$279$	5.40908	+	15.8032i	0.323833	+	0.946114i
$280$	−1.89872	−	2.88298i	−0.113470	−	0.172291i
$281$		−	5.04955i		−	0.301231i	−0.988592	−	0.150615i	$-0.951874\pi$
$281$		−	5.04955i		−	0.301231i	0.988592	−	0.150615i	$-0.0481255\pi$
$282$	2.86683	+	0.326924i	0.170717	+	0.0194680i
$283$		−	1.60911i		−	0.0956514i	−0.998856	−	0.0478257i	$-0.984771\pi$
$283$		−	1.60911i		−	0.0956514i	0.998856	−	0.0478257i	$-0.0152292\pi$
$284$	−1.70786	+	0.986036i	−0.101343	+	0.0585105i
$285$	13.4761	−	6.82585i	0.798253	−	0.404328i
$286$	−0.193119	+	0.334492i	−0.0114194	+	0.0197789i
$287$	−0.614958			−0.0362999
$288$	2.92298	+	0.675436i	0.172238	+	0.0398005i
$289$	−4.64454	−	8.04457i	−0.273208	−	0.473210i
$290$	−17.0123	−	8.53077i	−0.998998	−	0.500944i
$291$	−0.800636	+	7.02086i	−0.0469341	+	0.411570i
$292$	7.80488	+	13.5185i	0.456746	+	0.791108i
$293$	−3.77291	+	6.53488i	−0.220416	+	0.381772i	−0.954934	−	0.296817i	$-0.904075\pi$
$293$	−3.77291	+	6.53488i	−0.220416	+	0.381772i	0.734518	+	0.678589i	$0.237408\pi$
$294$	3.18778	+	7.33340i	0.185915	+	0.427692i
$295$	−0.156510	−	0.237643i	−0.00911238	−	0.0138361i
$296$	4.88703	−	8.46459i	0.284053	−	0.491994i
$297$	−0.971285	−	5.24935i	−0.0563597	−	0.304598i
$298$	−2.72429	−	1.57287i	−0.157814	−	0.0911139i
$299$	2.10124	−	1.21315i	0.121518	−	0.0701584i
$300$	−4.36042	−	7.48243i	−0.251749	−	0.431998i
$301$	13.9595	−	8.05955i	0.804615	−	0.464545i
$302$		−	1.49881i		−	0.0862469i
$303$	1.90492	−	16.7045i	0.109435	−	0.959647i
$304$	1.95020	−	3.37784i	0.111852	−	0.193733i
$305$	−7.84792	+	15.6506i	−0.449370	+	0.896148i
$306$	−6.09146	−	5.68265i	−0.348225	−	0.324855i
$307$	−8.97518	−	5.18182i	−0.512241	−	0.295742i	0.221514	−	0.975157i	$-0.428900\pi$
$307$	−8.97518	−	5.18182i	−0.512241	−	0.295742i	−0.733754	+	0.679415i	$0.762234\pi$
$308$			1.58609i			0.0903756i
$309$	28.7079	−	12.4792i	1.63314	−	0.709915i
$310$	−1.14460	−	12.3972i	−0.0650090	−	0.704112i
$311$			3.99276i			0.226409i	0.993572	+	0.113204i	$0.0361115\pi$
$311$			3.99276i			0.226409i	−0.993572	+	0.113204i	$0.963889\pi$
$312$	−0.259586	−	0.597171i	−0.0146962	−	0.0338081i
$313$	13.6821	−	23.6981i	0.773359	−	1.33950i	−0.162354	−	0.986733i	$-0.551909\pi$
$313$	13.6821	−	23.6981i	0.773359	−	1.33950i	0.935712	−	0.352764i	$-0.114758\pi$
$314$		−	15.8265i		−	0.893140i
$315$	−3.60263	−	9.70934i	−0.202985	−	0.547059i
$316$	5.86946	+	3.38873i	0.330183	+	0.190631i
$317$	0.977241	−	1.69263i	0.0548873	−	0.0950676i	−0.837276	−	0.546780i	$-0.815853\pi$
$317$	0.977241	−	1.69263i	0.0548873	−	0.0950676i	0.892164	+	0.451712i	$0.149187\pi$
$318$	−13.8816	+	6.03423i	−0.778440	+	0.338383i
$319$	4.37209	+	7.57268i	0.244790	+	0.423988i
$320$	−1.99884	−	1.00231i	−0.111739	−	0.0560310i
$321$	13.2631	−	17.9204i	0.740276	−	1.00022i
$322$	4.98180	−	8.62874i	0.277625	−	0.480861i
$323$	−9.37978	+	5.41542i	−0.521905	+	0.301322i
$324$	8.08757	+	3.94857i	0.449310	+	0.219365i
$325$	−0.742385	+	1.72690i	−0.0411801	+	0.0957912i
$326$			4.39357i			0.243338i
$327$	−6.89325	−	0.786083i	−0.381197	−	0.0434705i
$328$	−0.344972	+	0.199170i	−0.0190479	+	0.0109973i
$329$	−2.22726	−	1.28591i	−0.122793	−	0.0708944i
$330$	−0.217750	+	3.97309i	−0.0119867	+	0.218711i
$331$	−26.9889	+	15.5820i	−1.48344	+	0.856466i	−0.999823	−	0.0188129i	$-0.994011\pi$
$331$	−26.9889	+	15.5820i	−1.48344	+	0.856466i	−0.483619	+	0.875279i	$0.660678\pi$
$332$	8.44099	−	4.87341i	0.463260	−	0.267463i
$333$	20.0020	−	21.4409i	1.09610	−	1.17495i
$334$	0.811816	+	0.468702i	0.0444206	+	0.0256462i
$335$	30.7153	−	1.80798i	1.67815	−	0.0987804i
$336$	−2.14932	−	1.59074i	−0.117255	−	0.0867821i
$337$	30.0010			1.63426			0.817128	−	0.576456i	$-0.195565\pi$
$337$	30.0010			1.63426			0.817128	+	0.576456i	$0.195565\pi$
$338$	6.42933	−	11.1359i	0.349710	−	0.605715i
$339$	0.859197	+	1.97656i	0.0466652	+	0.107352i
$340$	3.41523	+	5.18564i	0.185217	+	0.281231i
$341$	−2.69374	+	5.04628i	−0.145874	+	0.273271i
$342$	7.98190	−	8.55611i	0.431612	−	0.462662i
$343$		−	17.9339i		−	0.968338i
$344$	5.22057	−	9.04229i	0.281474	−	0.487527i
$345$	13.6639	−	20.9307i	0.735637	−	1.12687i
$346$	6.13059	+	10.6185i	0.329582	+	0.570853i
$347$	−24.1184	−	13.9247i	−1.29474	−	0.747519i	−0.315250	−	0.949009i	$-0.602088\pi$
$347$	−24.1184	−	13.9247i	−1.29474	−	0.747519i	−0.979491	+	0.201489i	$0.935422\pi$
$348$	−14.6467	−	1.67026i	−0.785146	−	0.0895354i
$349$	−0.179771			−0.00962290			−0.00481145	−	0.999988i	$-0.501532\pi$
$349$	−0.179771			−0.00962290			−0.00481145	+	0.999988i	$0.501532\pi$
$350$	0.905586	+	7.66573i	0.0484056	+	0.409750i
$351$	−0.355414	−	1.92085i	−0.0189706	−	0.102527i
$352$	0.513693	+	0.889742i	0.0273799	+	0.0474234i
$353$	22.5131	+	12.9979i	1.19825	+	0.691810i	0.960165	−	0.279434i	$-0.0901469\pi$
$353$	22.5131	+	12.9979i	1.19825	+	0.691810i	0.238085	+	0.971244i	$0.423480\pi$
$354$	−0.177167	−	0.131124i	−0.00941633	−	0.00696917i
$355$	4.40207	−	0.259117i	0.233637	−	0.0137525i
$356$	−8.81000			−0.466929
$357$	2.96010	+	6.80963i	0.156665	+	0.360404i
$358$	2.69380	−	4.66581i	0.142372	−	0.246595i
$359$	−22.0678	+	12.7409i	−1.16469	+	0.672437i	−0.952425	−	0.304774i	$-0.901419\pi$
$359$	−22.0678	+	12.7409i	−1.16469	+	0.672437i	−0.212270	+	0.977211i	$0.568086\pi$
$360$	−5.16557	−	4.27982i	−0.272249	−	0.225567i
$361$	1.89346	+	3.27956i	0.0996556	+	0.172609i
$362$	16.1444	−	9.32095i	0.848529	−	0.489898i
$363$	−10.2468	+	13.8449i	−0.537818	+	0.726668i
$364$			0.580383i			0.0304203i
$365$	−2.05102	−	34.8442i	−0.107355	−	1.82383i
$366$	−1.53656	+	13.4743i	−0.0803175	+	0.704313i
$367$	2.49692	+	4.32480i	0.130338	+	0.225753i	0.923807	−	0.382859i	$-0.125060\pi$
$367$	2.49692	+	4.32480i	0.130338	+	0.225753i	−0.793469	+	0.608611i	$0.791727\pi$
$368$		−	6.45392i		−	0.336434i
$369$	−1.14287	+	0.349161i	−0.0594954	+	0.0181766i
$370$	−18.2526	+	12.0210i	−0.948906	+	0.624945i
$371$	13.4913			0.700434
$372$	−4.13660	−	8.71140i	−0.214473	−	0.451665i
$373$			19.2108i			0.994695i	0.867551	+	0.497348i	$0.165693\pi$
$373$			19.2108i			0.994695i	−0.867551	+	0.497348i	$0.834307\pi$
$374$		−	2.85290i		−	0.147520i
$375$	1.21605	+	19.3267i	0.0627966	+	0.998026i
$376$	−1.66589			−0.0859119
$377$	1.59984	+	2.77100i	0.0823959	+	0.142714i
$378$	−5.20795	−	6.10143i	−0.267868	−	0.313823i
$379$	1.48922	−	2.57941i	0.0764962	−	0.132495i	−0.825240	−	0.564783i	$-0.808960\pi$
$379$	1.48922	−	2.57941i	0.0764962	−	0.132495i	0.901736	+	0.432287i	$0.142293\pi$
$380$	−7.28379	+	4.79707i	−0.373651	+	0.246084i
$381$	14.1361	−	19.0999i	0.724217	−	0.978519i
$382$	−17.8762	+	10.3208i	−0.914625	+	0.528059i
$383$	1.46961	−	0.848480i	0.0750936	−	0.0433553i	−0.461983	−	0.886889i	$-0.652862\pi$
$383$	1.46961	−	0.848480i	0.0750936	−	0.0433553i	0.537077	+	0.843533i	$0.319529\pi$
$384$	−1.72090	−	0.196245i	−0.0878192	−	0.0100146i
$385$	1.58975	−	3.17033i	0.0810213	−	0.161575i
$386$	5.07739	+	2.93143i	0.258432	+	0.149206i
$387$	21.3671	−	22.9042i	1.08615	−	1.16429i
$388$		−	4.07977i		−	0.207119i
$389$	−9.98486	+	17.2943i	−0.506253	+	0.876855i	0.493721	+	0.869620i	$0.335636\pi$
$389$	−9.98486	+	17.2943i	−0.506253	+	0.876855i	−0.999974	+	0.00723493i	$0.997697\pi$
$390$	−0.0796794	+	1.45384i	−0.00403472	+	0.0736179i
$391$	−8.96081	+	15.5206i	−0.453167	+	0.784909i
$392$	−2.30833	−	3.99815i	−0.116588	−	0.201937i
$393$	−5.77825	−	4.27658i	−0.291474	−	0.215725i
$394$	−21.1684	+	12.2216i	−1.06645	+	0.615713i
$395$	−8.33555	−	12.6566i	−0.419407	−	0.636821i
$396$	0.900548	+	2.94766i	0.0452542	+	0.148126i
$397$	9.34804	+	5.39709i	0.469164	+	0.270872i	0.715890	−	0.698213i	$-0.246021\pi$
$397$	9.34804	+	5.39709i	0.469164	+	0.270872i	−0.246725	+	0.969085i	$0.579355\pi$
$398$	−1.84228	+	1.06364i	−0.0923449	+	0.0533154i
$399$	−9.56487	+	4.15779i	−0.478842	+	0.208150i
$400$	2.99074	+	4.00693i	0.149537	+	0.200346i
$401$	0.264115			0.0131893			0.00659463	−	0.999978i	$-0.497901\pi$
$401$	0.264115			0.0131893			0.00659463	+	0.999978i	$0.497901\pi$
$402$	21.8574	−	9.50125i	1.09015	−	0.473880i
$403$	−0.985698	+	1.84654i	−0.0491011	+	0.0919828i
$404$			9.70684i			0.482933i
$405$	−12.2081	−	15.9988i	−0.606624	−	0.794989i
$406$	11.3791	+	6.56974i	0.564736	+	0.326051i
$407$	10.0417			0.497751
$408$	3.86599	+	2.86128i	0.191395	+	0.141654i
$409$	13.7705	+	7.95043i	0.680910	+	0.393123i	0.800198	−	0.599736i	$-0.204728\pi$
$409$	13.7705	+	7.95043i	0.680910	+	0.393123i	−0.119288	+	0.992860i	$0.538061\pi$
$410$	0.889174	−	0.0523390i	0.0439132	−	0.00258484i
$411$	4.24308	−	1.84444i	0.209296	−	0.0909796i
$412$	−15.6515	+	9.03639i	−0.771093	+	0.445191i
$413$	0.0982288	+	0.170137i	0.00483353	+	0.00837191i
$414$	4.35921	−	18.8647i	0.214244	−	0.927147i
$415$	−21.7569	+	1.28067i	−1.06800	+	0.0628654i
$416$	0.187971	+	0.325576i	0.00921605	+	0.0159627i
$417$	1.34159	−	11.7646i	0.0656980	−	0.576113i
$418$	4.00721			0.195999
$419$		−	11.4212i		−	0.557960i	−0.960297	−	0.278980i	$-0.910004\pi$
$419$		−	11.4212i		−	0.557960i	0.960297	−	0.278980i	$-0.0899964\pi$
$420$	2.70172	+	5.33393i	0.131831	+	0.260269i
$421$	−6.90636	−	11.9622i	−0.336595	−	0.583000i	0.647195	−	0.762325i	$-0.275942\pi$
$421$	−6.90636	−	11.9622i	−0.336595	−	0.583000i	−0.983790	+	0.179324i	$0.942609\pi$
$422$	11.5557	−	20.0151i	0.562525	−	0.974322i
$423$	−4.86936	−	1.12520i	−0.236757	−	0.0547093i
$424$	7.56819	−	4.36950i	0.367544	−	0.212201i
$425$	−1.62888	−	13.7884i	−0.0790125	−	0.668836i
$426$	3.13256	−	1.36171i	0.151773	−	0.0659749i
$427$	6.04386	−	10.4683i	0.292483	−	0.506595i
$428$	−6.43590	+	11.1473i	−0.311091	+	0.538826i
$429$	0.397980	−	0.537728i	0.0192147	−	0.0259617i
$430$	−19.4983	+	12.8415i	−0.940291	+	0.619271i
$431$	−17.8930	−	10.3305i	−0.861876	−	0.497605i	0.00276373	−	0.999996i	$-0.499120\pi$
$431$	−17.8930	−	10.3305i	−0.861876	−	0.497605i	−0.864640	+	0.502392i	$0.832454\pi$
$432$	−4.89759	−	1.73598i	−0.235635	−	0.0835222i
$433$	−24.4899			−1.17691			−0.588454	−	0.808531i	$-0.700263\pi$
$433$	−24.4899			−1.17691			−0.588454	+	0.808531i	$0.700263\pi$
$434$	0.285938	+	8.59079i	0.0137255	+	0.412371i
$435$	27.6023	+	18.0192i	1.32343	+	0.863953i
$436$	4.00561			0.191834
$437$	−21.8003	−	12.5864i	−1.04285	−	0.602090i
$438$	−10.7785	−	24.7955i	−0.515015	−	1.18478i
$439$	19.4289	+	33.6519i	0.927291	+	1.60612i	0.787834	+	0.615887i	$0.211202\pi$
$439$	19.4289	+	33.6519i	0.927291	+	1.60612i	0.139457	+	0.990228i	$0.455464\pi$
$440$	−0.134992	−	2.29334i	−0.00643547	−	0.109330i
$441$	−4.04670	−	13.2456i	−0.192700	−	0.630743i
$442$		−	1.04394i		−	0.0496551i
$443$	−0.814290	−	1.41039i	−0.0386881	−	0.0670097i	0.846033	−	0.533131i	$-0.178985\pi$
$443$	−0.814290	−	1.41039i	−0.0386881	−	0.0670097i	−0.884721	+	0.466121i	$0.845651\pi$
$444$	−10.0712	+	13.6076i	−0.477959	+	0.645790i
$445$	17.6098	+	8.83038i	0.834785	+	0.418600i
$446$	−6.82575	+	11.8225i	−0.323209	+	0.559814i
$447$	4.37955	+	3.24138i	0.207146	+	0.153312i
$448$	1.33698	+	0.771903i	0.0631662	+	0.0364690i
$449$	19.0406			0.898582			0.449291	−	0.893385i	$-0.351677\pi$
$449$	19.0406			0.898582			0.449291	+	0.893385i	$0.351677\pi$
$450$	6.03544	+	13.7322i	0.284513	+	0.647342i
$451$	−0.354419	−	0.204624i	−0.0166889	−	0.00963537i
$452$	−0.622160	−	1.07761i	−0.0292639	−	0.0506866i
$453$	−0.294135	+	2.57930i	−0.0138197	+	0.121186i
$454$	9.21100	+	15.9539i	0.432294	+	0.748755i
$455$	0.581725	−	1.16009i	0.0272717	−	0.0543860i
$456$	−4.01898	+	5.43020i	−0.188206	+	0.254292i
$457$	−22.5473			−1.05472			−0.527359	−	0.849643i	$-0.676818\pi$
$457$	−22.5473			−1.05472			−0.527359	+	0.849643i	$0.676818\pi$
$458$	−9.98391	−	5.76421i	−0.466517	−	0.269344i
$459$	9.36758	+	10.9747i	0.437241	+	0.512254i
$460$	−6.46884	+	12.9004i	−0.301611	+	0.601483i
$461$	11.7772			0.548521			0.274260	−	0.961655i	$-0.411567\pi$
$461$	11.7772			0.548521			0.274260	+	0.961655i	$0.411567\pi$
$462$	0.311262	−	2.72949i	0.0144812	−	0.126987i
$463$	3.90256			0.181367			0.0906837	−	0.995880i	$-0.471095\pi$
$463$	3.90256			0.181367			0.0906837	+	0.995880i	$0.471095\pi$
$464$	8.51109			0.395117
$465$	−0.463146	+	21.5589i	−0.0214779	+	0.999769i
$466$	2.92070			0.135299
$467$	−25.0156			−1.15758			−0.578791	−	0.815476i	$-0.696475\pi$
$467$	−25.0156			−1.15758			−0.578791	+	0.815476i	$0.696475\pi$
$468$	0.329530	+	1.07861i	0.0152325	+	0.0498589i
$469$	−21.2429			−0.980905
$470$	3.32986	+	1.66975i	0.153595	+	0.0770196i
$471$	−3.10587	+	27.2358i	−0.143111	+	1.25496i
$472$	0.110206	+	0.0636277i	0.00507266	+	0.00292870i
$473$	10.7271			0.493231
$474$	−9.43571	−	6.98352i	−0.433397	−	0.320763i
$475$	19.3673	−	2.28794i	0.888633	−	0.104978i
$476$	−2.14346	−	3.71259i	−0.0982455	−	0.170166i
$477$	25.0729	−	7.66010i	1.14801	−	0.350732i
$478$	7.54702	+	13.0718i	0.345193	+	0.597891i
$479$	1.68801	+	0.974574i	0.0771272	+	0.0445294i	0.538068	−	0.842902i	$-0.319154\pi$
$479$	1.68801	+	0.974574i	0.0771272	+	0.0445294i	−0.460940	+	0.887431i	$0.652488\pi$
$480$	3.24310	+	2.11714i	0.148027	+	0.0966338i
$481$	3.67449			0.167542
$482$	−14.6295	−	8.44634i	−0.666355	−	0.384720i
$483$	−10.2665	+	13.8715i	−0.467143	+	0.631176i
$484$	4.97224	−	8.61217i	0.226011	−	0.391462i
$485$	−4.08920	+	8.15482i	−0.185681	+	0.370291i
$486$	−13.1430	−	8.38223i	−0.596178	−	0.380226i
$487$	−4.75311	−	8.23263i	−0.215384	−	0.373056i	0.738007	−	0.674793i	$-0.235767\pi$
$487$	−4.75311	−	8.23263i	−0.215384	−	0.373056i	−0.953391	+	0.301737i	$0.902434\pi$
$488$		−	7.82981i		−	0.354439i
$489$	0.862219	−	7.56089i	0.0389909	−	0.341915i
$490$	0.606598	+	10.3053i	0.0274033	+	0.465547i
$491$	5.73978	+	9.94159i	0.259033	+	0.448658i	0.965983	−	0.258605i	$-0.0832629\pi$
$491$	5.73978	+	9.94159i	0.259033	+	0.448658i	−0.706950	+	0.707263i	$0.749930\pi$
$492$	0.632747	−	0.275051i	0.0285264	−	0.0124003i
$493$	−20.4677	−	11.8170i	−0.921819	−	0.532212i
$494$	1.46632			0.0659731
$495$	1.15443	−	6.79454i	0.0518875	−	0.305392i
$496$	2.94274	+	4.72655i	0.132133	+	0.212228i
$497$	−3.04450			−0.136564
$498$	−15.4825	+	6.73013i	−0.693786	+	0.301584i
$499$	7.03371	+	4.06092i	0.314872	+	0.181792i	0.649105	−	0.760699i	$-0.275144\pi$
$499$	7.03371	+	4.06092i	0.314872	+	0.181792i	−0.334232	+	0.942491i	$0.608477\pi$
$500$	−1.96182	−	11.0069i	−0.0877354	−	0.492242i
$501$	−1.30507	−	0.965904i	−0.0583063	−	0.0431534i
$502$	2.64324	−	4.57822i	0.117973	−	0.204336i
$503$	3.55593	−	6.15905i	0.158551	−	0.274618i	−0.775795	−	0.630985i	$-0.782651\pi$
$503$	3.55593	−	6.15905i	0.158551	−	0.274618i	0.934346	+	0.356366i	$0.115984\pi$
$504$	3.38658	+	3.15930i	0.150850	+	0.140726i
$505$	9.72929	−	19.4024i	0.432948	−	0.863397i
$506$	5.74233	−	3.31533i	0.255278	−	0.147385i
$507$	−13.2496	+	17.9021i	−0.588435	+	0.795059i
$508$	−6.85953	+	11.8811i	−0.304342	+	0.527137i
$509$	−18.8282	−	32.6115i	−0.834547	−	1.44548i	−0.894398	−	0.447271i	$-0.852396\pi$
$509$	−18.8282	−	32.6115i	−0.834547	−	1.44548i	0.0598509	−	0.998207i	$-0.480937\pi$
$510$	−4.85961	−	9.59417i	−0.215187	−	0.424837i
$511$			24.0985i			1.06605i
$512$	1.00000			0.0441942
$513$	−15.4151	+	13.1578i	−0.680594	+	0.580930i
$514$	10.5068	+	18.1983i	0.463434	+	0.802691i
$515$	40.3421	−	2.37464i	1.77769	−	0.104639i
$516$	−10.7586	+	14.5363i	−0.473620	+	0.639927i
$517$	−0.855758	−	1.48222i	−0.0376362	−	0.0651878i
$518$	13.0677	−	7.54464i	0.574161	−	0.331492i
$519$	−8.46628	−	19.4764i	−0.371629	−	0.854920i
$520$	−0.0493963	−	0.839180i	−0.00216617	−	0.0368005i
$521$	13.2213	+	7.63331i	0.579235	+	0.334421i	0.760829	−	0.648952i	$-0.224792\pi$
$521$	13.2213	+	7.63331i	0.579235	+	0.334421i	−0.181594	+	0.983374i	$0.558126\pi$
$522$	24.8777	+	5.74870i	1.08887	+	0.251614i
$523$	−19.1867			−0.838976			−0.419488	−	0.907761i	$-0.637790\pi$
$523$	−19.1867			−0.838976			−0.419488	+	0.907761i	$0.637790\pi$
$524$	3.59435	+	2.07520i	0.157020	+	0.0906554i
$525$	−0.0540567	−	13.3696i	−0.00235923	−	0.583499i
$526$		−	4.36646i		−	0.190387i
$527$	−0.514319	−	15.4523i	−0.0224041	−	0.673114i
$528$	−0.709405	−	1.63197i	−0.0308729	−	0.0710222i
$529$	−18.6531			−0.811005
$530$	−19.5072	+	1.14824i	−0.847339	+	0.0498765i
$531$	0.279154	+	0.260420i	0.0121143	+	0.0113012i
$532$	5.21473	−	3.01073i	0.226087	−	0.130532i
$533$	−0.129690	−	0.0748763i	−0.00561748	−	0.00324325i
$534$	15.1611	+	1.72892i	0.656086	+	0.0748178i
$535$	24.0374	−	15.8309i	1.03923	−	0.684431i
$536$	−11.9166	+	6.88003i	−0.514717	+	0.297172i
$537$	−5.55140	+	7.50073i	−0.239561	+	0.323680i
$538$	−10.8340	−	18.7651i	−0.467087	−	0.809019i
$539$	2.37155	−	4.10764i	0.102150	−	0.176929i
$540$	8.04952	+	8.37886i	0.346396	+	0.360569i
$541$	−17.1144	+	29.6430i	−0.735805	+	1.27445i	0.218564	+	0.975823i	$0.429863\pi$
$541$	−17.1144	+	29.6430i	−0.735805	+	1.27445i	−0.954369	+	0.298630i	$0.903470\pi$
$542$			1.13263i			0.0486505i
$543$	−29.6120	+	12.8721i	−1.27077	+	0.552397i
$544$	−2.40483	−	1.38843i	−0.103106	−	0.0595284i
$545$	−8.00659	−	4.01487i	−0.342964	−	0.171978i
$546$	0.113897	−	0.998779i	0.00487436	−	0.0427438i
$547$	1.75842	−	1.01522i	0.0751845	−	0.0434078i	−0.461936	−	0.886913i	$-0.652845\pi$
$547$	1.75842	−	1.01522i	0.0751845	−	0.0434078i	0.537121	+	0.843505i	$0.319512\pi$
$548$	−2.31332	+	1.33559i	−0.0988199	+	0.0570537i
$549$	5.28854	−	22.8863i	0.225709	−	0.976766i
$550$	−2.02881	+	4.71932i	−0.0865088	+	0.201232i
$551$	16.5983	−	28.7491i	0.707112	−	1.22475i
$552$	−1.26655	+	11.1065i	−0.0539080	+	0.472726i
$553$	5.23155	+	9.06131i	0.222468	+	0.385326i
$554$	7.95261			0.337874
$555$	33.7699	−	17.1050i	1.43345	−	0.726067i
$556$			6.83630i			0.289924i
$557$			33.1315i			1.40383i	0.712262	+	0.701914i	$0.247671\pi$
$557$			33.1315i			1.40383i	−0.712262	+	0.701914i	$0.752329\pi$
$558$	5.40908	+	15.8032i	0.228985	+	0.669004i
$559$	3.92527			0.166021
$560$	−1.89872	−	2.88298i	−0.0802354	−	0.121828i
$561$	−0.559869	+	4.90955i	−0.0236377	+	0.207281i
$562$		−	5.04955i		−	0.213002i
$563$	−12.4807	−	21.6173i	−0.526000	−	0.911059i	−0.999541	−	0.0302875i	$-0.990358\pi$
$563$	−12.4807	−	21.6173i	−0.526000	−	0.911059i	0.473541	−	0.880772i	$-0.342976\pi$
$564$	2.86683	+	0.326924i	0.120715	+	0.0137660i
$565$	0.163495	+	2.77758i	0.00687829	+	0.116853i
$566$		−	1.60911i		−	0.0676357i
$567$	7.76497	+	11.5220i	0.326098	+	0.483877i
$568$	−1.70786	+	0.986036i	−0.0716604	+	0.0413731i
$569$	21.8683	+	37.8769i	0.916765	+	1.58788i	0.804297	+	0.594228i	$0.202542\pi$
$569$	21.8683	+	37.8769i	0.916765	+	1.58788i	0.112468	+	0.993655i	$0.464124\pi$
$570$	13.4761	−	6.82585i	0.564450	−	0.285903i
$571$	15.2061	−	8.77926i	0.636356	−	0.367400i	−0.146853	−	0.989158i	$-0.546915\pi$
$571$	15.2061	−	8.77926i	0.636356	−	0.367400i	0.783210	+	0.621758i	$0.213581\pi$
$572$	−0.193119	+	0.334492i	−0.00807471	+	0.0139858i
$573$	32.7885	−	14.2530i	1.36976	−	0.595426i
$574$	−0.614958			−0.0256679
$575$	25.8604	−	19.3020i	1.07845	−	0.804949i
$576$	2.92298	+	0.675436i	0.121791	+	0.0281432i
$577$	6.87881	+	3.97148i	0.286369	+	0.165335i	0.636303	−	0.771439i	$-0.280463\pi$
$577$	6.87881	+	3.97148i	0.286369	+	0.165335i	−0.349934	+	0.936774i	$0.613796\pi$
$578$	−4.64454	−	8.04457i	−0.193187	−	0.334610i
$579$	−8.16239	−	6.04111i	−0.339217	−	0.251060i
$580$	−17.0123	−	8.53077i	−0.706398	−	0.354221i
$581$	15.0472			0.624263
$582$	−0.800636	+	7.02086i	−0.0331874	+	0.291024i
$583$	7.77545	+	4.48916i	0.322026	+	0.185922i
$584$	7.80488	+	13.5185i	0.322968	+	0.559398i
$585$	0.422429	−	2.48627i	0.0174653	−	0.102795i
$586$	−3.77291	+	6.53488i	−0.155858	+	0.269953i
$587$		−	24.5924i		−	1.01504i	−0.861641	−	0.507518i	$-0.830563\pi$
$587$		−	24.5924i		−	1.01504i	0.861641	−	0.507518i	$-0.169437\pi$
$588$	3.18778	+	7.33340i	0.131462	+	0.302424i
$589$	21.7045	−	0.722417i	0.894317	−	0.0297667i
$590$	−0.156510	−	0.237643i	−0.00644343	−	0.00978360i
$591$	38.8270	−	16.8779i	1.59713	−	0.694262i
$592$	4.88703	−	8.46459i	0.200856	−	0.347893i
$593$	1.81903			0.0746988			0.0373494	−	0.999302i	$-0.488109\pi$
$593$	1.81903			0.0746988			0.0373494	+	0.999302i	$0.488109\pi$
$594$	−0.971285	−	5.24935i	−0.0398523	−	0.215384i
$595$	0.563273	+	9.56930i	0.0230920	+	0.392303i
$596$	−2.72429	−	1.57287i	−0.111591	−	0.0644272i
$597$	3.37910	−	1.46887i	0.138297	−	0.0601170i
$598$	2.10124	−	1.21315i	0.0859261	−	0.0496095i
$599$	1.06433	−	0.614489i	0.0434872	−	0.0251073i	−0.478099	−	0.878306i	$-0.658674\pi$
$599$	1.06433	−	0.614489i	0.0434872	−	0.0251073i	0.521586	+	0.853199i	$0.325341\pi$
$600$	−4.36042	−	7.48243i	−0.178013	−	0.305469i
$601$	−25.0413	−	14.4576i	−1.02145	−	0.589737i	−0.106930	−	0.994267i	$-0.534102\pi$
$601$	−25.0413	−	14.4576i	−1.02145	−	0.589737i	−0.914525	+	0.404530i	$0.867435\pi$
$602$	13.9595	−	8.05955i	0.568949	−	0.328483i
$603$	−39.4788	+	12.0613i	−1.60770	+	0.491173i
$604$		−	1.49881i		−	0.0609858i
$605$	−18.5708	+	12.2306i	−0.755011	+	0.497246i
$606$	1.90492	−	16.7045i	0.0773822	−	0.678573i
$607$	−28.2808	+	16.3279i	−1.14788	+	0.662729i	−0.948370	−	0.317166i	$-0.897269\pi$
$607$	−28.2808	+	16.3279i	−1.14788	+	0.662729i	−0.199511	+	0.979896i	$0.563935\pi$
$608$	1.95020	−	3.37784i	0.0790910	−	0.136990i
$609$	−18.2930	−	13.5389i	−0.741270	−	0.548626i
$610$	−7.84792	+	15.6506i	−0.317753	+	0.633673i
$611$	−0.313140	−	0.542374i	−0.0126683	−	0.0219421i
$612$	−6.09146	−	5.68265i	−0.246233	−	0.229707i
$613$	8.26593	−	14.3170i	0.333858	−	0.578258i	−0.649407	−	0.760441i	$-0.724983\pi$
$613$	8.26593	−	14.3170i	0.333858	−	0.578258i	0.983265	+	0.182183i	$0.0583162\pi$
$614$	−8.97518	−	5.18182i	−0.362209	−	0.209121i
$615$	−1.54045	−	0.0844262i	−0.0621169	−	0.00340439i
$616$			1.58609i			0.0639052i
$617$	−15.8749	+	27.4961i	−0.639098	+	1.10695i	0.346533	+	0.938038i	$0.387359\pi$
$617$	−15.8749	+	27.4961i	−0.639098	+	1.10695i	−0.985631	+	0.168913i	$0.945974\pi$
$618$	28.7079	−	12.4792i	1.15480	−	0.501986i
$619$		−	26.0610i		−	1.04748i	−0.851879	−	0.523739i	$-0.824537\pi$
$619$		−	26.0610i		−	1.04748i	0.851879	−	0.523739i	$-0.175463\pi$
$620$	−1.14460	−	12.3972i	−0.0459683	−	0.497882i
$621$	−11.2039	+	31.6087i	−0.449595	+	1.26841i
$622$			3.99276i			0.160095i
$623$	−11.7788	−	6.80047i	−0.471906	−	0.272455i
$624$	−0.259586	−	0.597171i	−0.0103918	−	0.0239060i
$625$	−7.11095	+	23.9674i	−0.284438	+	0.958694i
$626$	13.6821	−	23.6981i	0.546847	−	0.947167i
$627$	−6.89600	−	0.786397i	−0.275400	−	0.0314057i
$628$		−	15.8265i		−	0.631545i
$629$	−23.5050	+	13.5706i	−0.937204	+	0.541095i
$630$	−3.60263	−	9.70934i	−0.143532	−	0.386829i
$631$	−34.4127	+	19.8682i	−1.36995	+	0.790940i	−0.990921	−	0.134445i	$-0.957075\pi$
$631$	−34.4127	+	19.8682i	−1.36995	+	0.790940i	−0.379028	+	0.925385i	$0.623742\pi$
$632$	5.86946	+	3.38873i	0.233474	+	0.134797i
$633$	−23.8141	+	32.1762i	−0.946527	+	1.27889i
$634$	0.977241	−	1.69263i	0.0388112	−	0.0672230i
$635$	25.6196	−	16.8730i	1.01668	−	0.669583i
$636$	−13.8816	+	6.03423i	−0.550440	+	0.239273i
$637$	0.867799	−	1.50307i	0.0343835	−	0.0595539i
$638$	4.37209	+	7.57268i	0.173093	+	0.299805i
$639$	−5.65805	+	1.72861i	−0.223829	+	0.0683826i
$640$	−1.99884	−	1.00231i	−0.0790112	−	0.0396199i
$641$	−14.5109	−	25.1336i	−0.573145	−	0.992717i	−0.996240	−	0.0866315i	$-0.972390\pi$
$641$	−14.5109	−	25.1336i	−0.573145	−	0.992717i	0.423095	−	0.906085i	$-0.360944\pi$
$642$	13.2631	−	17.9204i	0.523454	−	0.707260i
$643$	35.8903			1.41538			0.707689	−	0.706524i	$-0.249738\pi$
$643$	35.8903			1.41538			0.707689	+	0.706524i	$0.249738\pi$
$644$	4.98180	−	8.62874i	0.196311	−	0.340020i
$645$	36.0746	−	18.2724i	1.42044	−	0.719475i
$646$	−9.37978	+	5.41542i	−0.369043	+	0.213067i
$647$		−	18.5646i		−	0.729848i	−0.931037	−	0.364924i	$-0.881095\pi$
$647$		−	18.5646i		−	0.729848i	0.931037	−	0.364924i	$-0.118905\pi$
$648$	8.08757	+	3.94857i	0.317710	+	0.155114i
$649$			0.130740i			0.00513201i
$650$	−0.742385	+	1.72690i	−0.0291188	+	0.0677346i
$651$	1.19383	−	14.8400i	0.0467900	−	0.581625i
$652$			4.39357i			0.172066i
$653$	49.0326			1.91879			0.959397	−	0.282059i	$-0.0910175\pi$
$653$	49.0326			1.91879			0.959397	+	0.282059i	$0.0910175\pi$
$654$	−6.89325	−	0.786083i	−0.269547	−	0.0307383i
$655$	−5.10454	−	7.75065i	−0.199451	−	0.302843i
$656$	−0.344972	+	0.199170i	−0.0134689	+	0.00777626i
$657$	13.6826	+	44.7858i	0.533810	+	1.74726i
$658$	−2.22726	−	1.28591i	−0.0868276	−	0.0501299i
$659$			12.2807i			0.478387i	0.970972	+	0.239193i	$0.0768830\pi$
$659$			12.2807i			0.478387i	−0.970972	+	0.239193i	$0.923117\pi$
$660$	−0.217750	+	3.97309i	−0.00847590	+	0.154652i
$661$	−11.4381	−	19.8114i	−0.444891	−	0.770575i	0.553153	−	0.833080i	$-0.313424\pi$
$661$	−11.4381	−	19.8114i	−0.444891	−	0.770575i	−0.998045	+	0.0625050i	$0.980091\pi$
$662$	−26.9889	+	15.5820i	−1.04895	+	0.605613i
$663$	−0.204868	+	1.79651i	−0.00795642	+	0.0697707i
$664$	8.44099	−	4.87341i	0.327574	−	0.189125i
$665$	−13.4411	+	0.791178i	−0.521224	+	0.0306806i
$666$	20.0020	−	21.4409i	0.775061	−	0.830819i
$667$		−	54.9299i		−	2.12689i
$668$	0.811816	+	0.468702i	0.0314101	+	0.0181346i
$669$	14.0665	−	19.0059i	0.543844	−	0.734809i
$670$	30.7153	−	1.80798i	1.18663	−	0.0698483i
$671$	6.96652	−	4.02212i	0.268939	−	0.155272i
$672$	−2.14932	−	1.59074i	−0.0829117	−	0.0613642i
$673$	4.34577	+	7.52710i	0.167517	+	0.290148i	0.937546	−	0.347860i	$-0.113092\pi$
$673$	4.34577	+	7.52710i	0.167517	+	0.290148i	−0.770029	+	0.638009i	$0.779758\pi$
$674$	30.0010			1.15559
$675$	−7.69148	−	24.8161i	−0.296045	−	0.955174i
$676$	6.42933	−	11.1359i	0.247282	−	0.428305i
$677$	10.1999	−	5.88889i	0.392012	−	0.226328i	−0.291019	−	0.956717i	$-0.593994\pi$
$677$	10.1999	−	5.88889i	0.392012	−	0.226328i	0.683032	+	0.730389i	$0.260661\pi$
$678$	0.859197	+	1.97656i	0.0329973	+	0.0759092i
$679$	3.14919	−	5.45455i	0.120855	−	0.209327i
$680$	3.41523	+	5.18564i	0.130968	+	0.198860i
$681$	−12.7203	−	29.2627i	−0.487443	−	1.12135i
$682$	−2.69374	+	5.04628i	−0.103149	+	0.193232i
$683$	23.6362			0.904413			0.452206	−	0.891913i	$-0.350637\pi$
$683$	23.6362			0.904413			0.452206	+	0.891913i	$0.350637\pi$
$684$	7.98190	−	8.55611i	0.305195	−	0.327151i
$685$	5.96263	−	0.350976i	0.227821	−	0.0134101i
$686$		−	17.9339i		−	0.684719i
$687$	16.0501	+	11.8789i	0.612349	+	0.453209i
$688$	5.22057	−	9.04229i	0.199032	−	0.344734i
$689$	2.84520	+	1.64268i	0.108394	+	0.0625811i
$690$	13.6639	−	20.9307i	0.520174	−	0.796819i
$691$	−12.8593	−	22.2729i	−0.489189	−	0.847300i	0.510734	−	0.859739i	$-0.329374\pi$
$691$	−12.8593	−	22.2729i	−0.489189	−	0.847300i	−0.999923	+	0.0124388i	$0.996041\pi$
$692$	6.13059	+	10.6185i	0.233050	+	0.403654i
$693$	−1.07130	+	4.63609i	−0.0406953	+	0.176110i
$694$	−24.1184	−	13.9247i	−0.915520	−	0.528576i
$695$	6.85211	−	13.6647i	0.259915	−	0.518331i
$696$	−14.6467	−	1.67026i	−0.555182	−	0.0633111i
$697$	1.10613			0.0418977
$698$	−0.179771			−0.00680442
$699$	−5.02623	−	0.573174i	−0.190109	−	0.0216795i
$700$	0.905586	+	7.66573i	0.0342279	+	0.289737i
$701$	19.4763	+	11.2446i	0.735608	+	0.424704i	0.820470	−	0.571689i	$-0.193712\pi$
$701$	19.4763	+	11.2446i	0.735608	+	0.424704i	−0.0848620	+	0.996393i	$0.527045\pi$
$702$	−0.355414	−	1.92085i	−0.0134142	−	0.0724978i
$703$	−19.0614	−	33.0153i	−0.718913	−	1.24519i
$704$	0.513693	+	0.889742i	0.0193605	+	0.0335334i
$705$	−5.40266	−	3.52693i	−0.203476	−	0.132832i
$706$	22.5131	+	12.9979i	0.847291	+	0.489184i
$707$	−7.49274	+	12.9778i	−0.281794	+	0.488081i
$708$	−0.177167	−	0.131124i	−0.00665835	−	0.00492795i
$709$			20.9882i			0.788229i	0.919061	+	0.394114i	$0.128949\pi$
$709$			20.9882i			0.788229i	−0.919061	+	0.394114i	$0.871051\pi$
$710$	4.40207	−	0.259117i	0.165207	−	0.00972448i
$711$	14.8674	+	13.8696i	0.557571	+	0.520152i
$712$	−8.81000			−0.330169
$713$	30.5048	−	18.9922i	1.14241	−	0.711265i
$714$	2.96010	+	6.80963i	0.110779	+	0.254844i
$715$	0.721280	−	0.475031i	0.0269743	−	0.0177652i
$716$	2.69380	−	4.66581i	0.100672	−	0.174369i
$717$	−10.4224	−	23.9763i	−0.389230	−	0.895413i
$718$	−22.0678	+	12.7409i	−0.823563	+	0.475485i
$719$	21.9814	−	38.0730i	0.819769	−	1.41988i	−0.0860825	−	0.996288i	$-0.527435\pi$
$719$	21.9814	−	38.0730i	0.819769	−	1.41988i	0.905852	−	0.423594i	$-0.139232\pi$
$720$	−5.16557	−	4.27982i	−0.192509	−	0.159500i
$721$	−27.9009			−1.03908
$722$	1.89346	+	3.27956i	0.0704671	+	0.122053i
$723$	23.5183	+	17.4062i	0.874655	+	0.647345i
$724$	16.1444	−	9.32095i	0.600000	−	0.346410i
$725$	25.4545	+	34.1033i	0.945355	+	1.26657i
$726$	−10.2468	+	13.8449i	−0.380295	+	0.513832i
$727$	−2.89588	−	1.67194i	−0.107402	−	0.0620088i	0.445337	−	0.895363i	$-0.353084\pi$
$727$	−2.89588	−	1.67194i	−0.107402	−	0.0620088i	−0.552739	+	0.833354i	$0.686417\pi$
$728$			0.580383i			0.0215104i
$729$	20.9728	+	17.0042i	0.776769	+	0.629785i
$730$	−2.05102	−	34.8442i	−0.0759115	−	1.28964i
$731$	−25.1091	+	14.4968i	−0.928695	+	0.536182i
$732$	−1.53656	+	13.4743i	−0.0567931	+	0.498025i
$733$	−13.6734	+	7.89434i	−0.505038	+	0.291584i	−0.730792	−	0.682600i	$-0.760849\pi$
$733$	−13.6734	+	7.89434i	−0.505038	+	0.291584i	0.225753	+	0.974184i	$0.427516\pi$
$734$	2.49692	+	4.32480i	0.0921631	+	0.159631i
$735$	0.978481	−	17.8535i	0.0360918	−	0.658535i
$736$		−	6.45392i		−	0.237895i
$737$	−12.2429	−	7.06845i	−0.450973	−	0.260370i
$738$	−1.14287	+	0.349161i	−0.0420696	+	0.0128528i
$739$	−17.8484	+	10.3048i	−0.656564	+	0.379067i	−0.790966	−	0.611860i	$-0.790422\pi$
$739$	−17.8484	+	10.3048i	−0.656564	+	0.379067i	0.134403	+	0.990927i	$0.457088\pi$
$740$	−18.2526	+	12.0210i	−0.670978	+	0.441903i
$741$	−2.52339	−	0.287759i	−0.0926992	−	0.0105711i
$742$	13.4913			0.495282
$743$			20.7432i			0.760995i	0.924782	+	0.380498i	$0.124247\pi$
$743$			20.7432i			0.760995i	−0.924782	+	0.380498i	$0.875753\pi$
$744$	−4.13660	−	8.71140i	−0.151655	−	0.319376i
$745$	3.86892	+	5.87451i	0.141746	+	0.215225i
$746$			19.2108i			0.703356i
$747$	27.9645	−	8.54350i	1.02317	−	0.312590i
$748$		−	2.85290i		−	0.104312i
$749$	−17.2093	+	9.93579i	−0.628814	+	0.363046i
$750$	1.21605	+	19.3267i	0.0444039	+	0.705711i
$751$	−22.7853	+	39.4653i	−0.831448	+	1.44011i	0.0654411	+	0.997856i	$0.479155\pi$
$751$	−22.7853	+	39.4653i	−0.831448	+	1.44011i	−0.896890	+	0.442255i	$0.854179\pi$
$752$	−1.66589			−0.0607489
$753$	−5.44719	+	7.35992i	−0.198507	+	0.268211i
$754$	1.59984	+	2.77100i	0.0582627	+	0.100914i
$755$	−1.50228	+	2.99589i	−0.0546735	+	0.109032i
$756$	−5.20795	−	6.10143i	−0.189411	−	0.221907i
$757$	2.15437	+	3.73148i	0.0783019	+	0.135623i	0.902517	−	0.430653i	$-0.141717\pi$
$757$	2.15437	+	3.73148i	0.0783019	+	0.135623i	−0.824216	+	0.566276i	$0.808384\pi$
$758$	1.48922	−	2.57941i	0.0540910	−	0.0936883i
$759$	−10.5326	+	4.57844i	−0.382308	+	0.166187i
$760$	−7.28379	+	4.79707i	−0.264211	+	0.174008i
$761$	−12.8583	+	22.2712i	−0.466112	+	0.807330i	−0.999251	−	0.0386975i	$-0.987679\pi$
$761$	−12.8583	+	22.2712i	−0.466112	+	0.807330i	0.533139	+	0.846028i	$0.321012\pi$
$762$	14.1361	−	19.0999i	0.512099	−	0.691917i
$763$	5.35541	+	3.09194i	0.193879	+	0.111936i
$764$	−17.8762	+	10.3208i	−0.646738	+	0.373394i
$765$	6.48007	+	17.4643i	0.234288	+	0.631422i
$766$	1.46961	−	0.848480i	0.0530992	−	0.0306568i
$767$			0.0478407i			0.00172743i
$768$	−1.72090	−	0.196245i	−0.0620975	−	0.00708140i
$769$	15.8767	−	27.4993i	0.572529	−	0.991650i	−0.423776	−	0.905767i	$-0.639296\pi$
$769$	15.8767	−	27.4993i	0.572529	−	0.991650i	0.996305	−	0.0858830i	$-0.0273711\pi$
$770$	1.58975	−	3.17033i	0.0572907	−	0.114251i
$771$	−14.5098	−	33.3793i	−0.522556	−	1.20212i
$772$	5.07739	+	2.93143i	0.182739	+	0.105505i
$773$		−	16.2971i		−	0.586166i	−0.956087	−	0.293083i	$-0.905319\pi$
$773$		−	16.2971i		−	0.586166i	0.956087	−	0.293083i	$-0.0946813\pi$
$774$	21.3671	−	22.9042i	0.768024	−	0.823275i
$775$	−10.1380	+	25.9272i	−0.364166	+	0.931334i
$776$		−	4.07977i		−	0.146455i
$777$	−23.9688	+	10.4191i	−0.859874	+	0.373782i
$778$	−9.98486	+	17.2943i	−0.357975	+	0.620030i
$779$			1.55368i			0.0556664i
$780$	−0.0796794	+	1.45384i	−0.00285298	+	0.0520557i
$781$	−1.75464	−	1.01304i	−0.0627858	−	0.0362494i
$782$	−8.96081	+	15.5206i	−0.320438	+	0.555014i
$783$	−41.6838	−	14.7751i	−1.48966	−	0.528017i
$784$	−2.30833	−	3.99815i	−0.0824404	−	0.142791i
$785$	−15.8631	+	31.6346i	−0.566177	+	1.12909i
$786$	−5.77825	−	4.27658i	−0.206104	−	0.152540i
$787$	−9.03496	+	15.6490i	−0.322061	+	0.557827i	−0.980913	−	0.194446i	$-0.937709\pi$
$787$	−9.03496	+	15.6490i	−0.322061	+	0.557827i	0.658852	+	0.752273i	$0.271042\pi$
$788$	−21.1684	+	12.2216i	−0.754092	+	0.435375i
$789$	−0.856898	+	7.51423i	−0.0305064	+	0.267514i
$790$	−8.33555	−	12.6566i	−0.296566	−	0.450301i
$791$		−	1.92099i		−	0.0683025i
$792$	0.900548	+	2.94766i	0.0319996	+	0.104741i
$793$	2.54920	−	1.47178i	0.0905246	−	0.0522644i
$794$	9.34804	+	5.39709i	0.331749	+	0.191536i
$795$	33.7952	+	1.85219i	1.19859	+	0.0656904i
$796$	−1.84228	+	1.06364i	−0.0652977	+	0.0376997i
$797$	−29.1757	+	16.8446i	−1.03346	+	0.596667i	−0.917973	−	0.396643i	$-0.870175\pi$
$797$	−29.1757	+	16.8446i	−1.03346	+	0.596667i	−0.115484	+	0.993309i	$0.536842\pi$
$798$	−9.56487	+	4.15779i	−0.338593	+	0.147184i
$799$	4.00619	+	2.31297i	0.141729	+	0.0818271i
$800$	2.99074	+	4.00693i	0.105739	+	0.141666i
$801$	−25.7514	−	5.95060i	−0.909882	−	0.210254i
$802$	0.264115			0.00932621
$803$	−8.01863	+	13.8887i	−0.282971	+	0.490120i
$804$	21.8574	−	9.50125i	0.770849	−	0.335083i
$805$	−18.6065	+	12.2542i	−0.655794	+	0.431902i
$806$	−0.985698	+	1.84654i	−0.0347197	+	0.0650416i
$807$	14.9617	+	34.4189i	0.526676	+	1.21160i
$808$			9.70684i			0.341485i
$809$	23.1348	−	40.0707i	0.813376	−	1.40881i	−0.0971116	−	0.995274i	$-0.530960\pi$
$809$	23.1348	−	40.0707i	0.813376	−	1.40881i	0.910488	−	0.413536i	$-0.135706\pi$
$810$	−12.2081	−	15.9988i	−0.428948	−	0.562142i
$811$	22.0092	+	38.1210i	0.772847	+	1.33861i	0.935996	+	0.352009i	$0.114502\pi$
$811$	22.0092	+	38.1210i	0.772847	+	1.33861i	−0.163149	+	0.986601i	$0.552165\pi$
$812$	11.3791	+	6.56974i	0.399329	+	0.230553i
$813$	0.222273	−	1.94914i	0.00779545	−	0.0683592i
$814$	10.0417			0.351963
$815$	4.40373	−	8.78206i	0.154256	−	0.307622i
$816$	3.86599	+	2.86128i	0.135337	+	0.100165i
$817$	−20.3623	−	35.2685i	−0.712386	−	1.23389i
$818$	13.7705	+	7.95043i	0.481476	+	0.277980i
$819$	−0.392011	+	1.69644i	−0.0136980	+	0.0592785i
$820$	0.889174	−	0.0523390i	0.0310513	−	0.00182776i
$821$	−13.4791			−0.470423			−0.235212	−	0.971944i	$-0.575578\pi$
$821$	−13.4791			−0.470423			−0.235212	+	0.971944i	$0.575578\pi$
$822$	4.24308	−	1.84444i	0.147994	−	0.0643323i
$823$	5.80325	−	10.0515i	0.202289	−	0.350374i	−0.746977	−	0.664850i	$-0.768495\pi$
$823$	5.80325	−	10.0515i	0.202289	−	0.350374i	0.949265	+	0.314476i	$0.101829\pi$
$824$	−15.6515	+	9.03639i	−0.545245	+	0.314797i
$825$	4.41752	−	7.72332i	0.153798	−	0.268891i
$826$	0.0982288	+	0.170137i	0.00341782	+	0.00591984i
$827$	−26.3362	+	15.2052i	−0.915799	+	0.528737i	−0.882292	−	0.470702i	$-0.844001\pi$
$827$	−26.3362	+	15.2052i	−0.915799	+	0.528737i	−0.0335064	+	0.999439i	$0.510667\pi$
$828$	4.35921	−	18.8647i	0.151493	−	0.655592i
$829$			37.8099i			1.31319i	0.754242	+	0.656596i	$0.228004\pi$
$829$			37.8099i			1.31319i	−0.754242	+	0.656596i	$0.771996\pi$
$830$	−21.7569	+	1.28067i	−0.755193	+	0.0444526i
$831$	−13.6856	−	1.56066i	−0.474749	−	0.0541388i
$832$	0.187971	+	0.325576i	0.00651673	+	0.0112873i
$833$			12.8198i			0.444180i
$834$	1.34159	−	11.7646i	0.0464555	−	0.407374i
$835$	−1.15291	−	1.75055i	−0.0398980	−	0.0605805i
$836$	4.00721			0.138592
$837$	−6.20717	−	28.2572i	−0.214551	−	0.976713i
$838$		−	11.4212i		−	0.394537i
$839$			7.40864i			0.255774i	0.991789	+	0.127887i	$0.0408196\pi$
$839$			7.40864i			0.255774i	−0.991789	+	0.127887i	$0.959180\pi$
$840$	2.70172	+	5.33393i	0.0932183	+	0.184038i
$841$	43.4386			1.49788
$842$	−6.90636	−	11.9622i	−0.238009	−	0.412244i
$843$	−0.990951	+	8.68975i	−0.0341301	+	0.299291i
$844$	11.5557	−	20.0151i	0.397765	−	0.688949i
$845$	−24.0129	+	15.8148i	−0.826069	+	0.544045i
$846$	−4.86936	−	1.12520i	−0.167412	−	0.0386853i
$847$	13.2955	−	7.67618i	0.456840	−	0.263757i
$848$	7.56819	−	4.36950i	0.259893	−	0.150049i
$849$	−0.315780	+	2.76911i	−0.0108375	+	0.0950354i
$850$	−1.62888	−	13.7884i	−0.0558703	−	0.472938i
$851$	−54.6298	−	31.5405i	−1.87269	−	1.08120i
$852$	3.13256	−	1.36171i	0.107320	−	0.0466513i
$853$			47.1423i			1.61412i	0.590469	+	0.807060i	$0.298943\pi$
$853$			47.1423i			1.61412i	−0.590469	+	0.807060i	$0.701057\pi$
$854$	6.04386	−	10.4683i	0.206817	−	0.358217i
$855$	−24.5305	+	9.10197i	−0.838924	+	0.311281i
$856$	−6.43590	+	11.1473i	−0.219975	+	0.381007i
$857$	19.7492	+	34.2067i	0.674621	+	1.16848i	0.976579	+	0.215157i	$0.0690264\pi$
$857$	19.7492	+	34.2067i	0.674621	+	1.16848i	−0.301958	+	0.953321i	$0.597640\pi$
$858$	0.397980	−	0.537728i	0.0135868	−	0.0183577i
$859$	11.7626	−	6.79114i	0.401335	−	0.231711i	−0.285725	−	0.958312i	$-0.592234\pi$
$859$	11.7626	−	6.79114i	0.401335	−	0.231711i	0.687060	+	0.726601i	$0.258901\pi$
$860$	−19.4983	+	12.8415i	−0.664886	+	0.437890i
$861$	1.05828	+	0.120683i	0.0360661	+	0.00411286i
$862$	−17.8930	−	10.3305i	−0.609439	−	0.351860i
$863$	29.8077	−	17.2095i	1.01466	−	0.585817i	0.102111	−	0.994773i	$-0.467440\pi$
$863$	29.8077	−	17.2095i	1.01466	−	0.585817i	0.912554	+	0.408956i	$0.134107\pi$
$864$	−4.89759	−	1.73598i	−0.166619	−	0.0590591i
$865$	−1.61103	−	27.3694i	−0.0547768	−	0.930589i
$866$	−24.4899			−0.832199
$867$	6.41406	+	14.7554i	0.217833	+	0.501118i
$868$	0.285938	+	8.59079i	0.00970537	+	0.291591i
$869$			6.96307i			0.236206i
$870$	27.6023	+	18.0192i	0.935807	+	0.610907i
$871$	−4.47994	−	2.58650i	−0.151797	−	0.0876401i
$872$	4.00561			0.135647
$873$	2.75562	−	11.9251i	0.0932638	−	0.403602i
$874$	−21.8003	−	12.5864i	−0.737407	−	0.425742i
$875$	5.87333	−	16.2303i	0.198555	−	0.548683i
$876$	−10.7785	−	24.7955i	−0.364171	−	0.837764i
$877$	−36.0214	+	20.7969i	−1.21636	+	0.702263i	−0.964136	−	0.265407i	$-0.914494\pi$
$877$	−36.0214	+	20.7969i	−1.21636	+	0.702263i	−0.252219	+	0.967670i	$0.581160\pi$
$878$	19.4289	+	33.6519i	0.655694	+	1.13570i
$879$	7.77524	−	10.5054i	0.262252	−	0.354340i
$880$	−0.134992	−	2.29334i	−0.00455056	−	0.0773083i
$881$	26.1192	+	45.2398i	0.879978	+	1.52417i	0.851364	+	0.524576i	$0.175776\pi$
$881$	26.1192	+	45.2398i	0.879978	+	1.52417i	0.0286139	+	0.999591i	$0.490891\pi$
$882$	−4.04670	−	13.2456i	−0.136259	−	0.446003i
$883$	−31.3676			−1.05560			−0.527802	−	0.849368i	$-0.676984\pi$
$883$	−31.3676			−1.05560			−0.527802	+	0.849368i	$0.676984\pi$
$884$		−	1.04394i		−	0.0351114i
$885$	0.222702	+	0.439673i	0.00748604	+	0.0147795i
$886$	−0.814290	−	1.41039i	−0.0273566	−	0.0473830i
$887$	13.8411	−	23.9734i	0.464737	−	0.804949i	−0.534452	−	0.845199i	$-0.679482\pi$
$887$	13.8411	−	23.9734i	0.464737	−	0.804949i	0.999190	+	0.0402498i	$0.0128154\pi$
$888$	−10.0712	+	13.6076i	−0.337968	+	0.456642i
$889$	−18.3421	+	10.5898i	−0.615173	+	0.355170i
$890$	17.6098	+	8.83038i	0.590282	+	0.295995i
$891$	0.641321	+	9.22421i	0.0214851	+	0.309023i
$892$	−6.82575	+	11.8225i	−0.228543	+	0.395848i
$893$	−3.24882	+	5.62712i	−0.108718	+	0.188305i
$894$	4.37955	+	3.24138i	0.146474	+	0.108408i
$895$	−10.0611	+	6.62618i	−0.336305	+	0.221489i
$896$	1.33698	+	0.771903i	0.0446652	+	0.0257875i
$897$	−3.85409	+	1.67535i	−0.128684	+	0.0559383i
$898$	19.0406			0.635394
$899$	25.0460	+	40.2281i	0.835329	+	1.34168i
$900$	6.03544	+	13.7322i	0.201181	+	0.457740i
$901$	−24.2669			−0.808448
$902$	−0.354419	−	0.204624i	−0.0118009	−	0.00681323i
$903$	−25.6046	+	11.1302i	−0.852067	+	0.370388i
$904$	−0.622160	−	1.07761i	−0.0206927	−	0.0358409i
$905$	−41.6125	+	2.44942i	−1.38325	+	0.0814214i
$906$	−0.294135	+	2.57930i	−0.00977198	+	0.0856915i
$907$			49.8120i			1.65398i	0.562216	+	0.826990i	$0.309949\pi$
$907$			49.8120i			1.65398i	−0.562216	+	0.826990i	$0.690051\pi$
$908$	9.21100	+	15.9539i	0.305678	+	0.529449i
$909$	−6.55635	+	28.3729i	−0.217460	+	0.941068i
$910$	0.581725	−	1.16009i	0.0192840	−	0.0384567i
$911$	−19.7349	+	34.1818i	−0.653846	+	1.13249i	0.328336	+	0.944561i	$0.393512\pi$
$911$	−19.7349	+	34.1818i	−0.653846	+	1.13249i	−0.982182	+	0.187933i	$0.939821\pi$
$912$	−4.01898	+	5.43020i	−0.133082	+	0.179812i
$913$	8.67216	+	5.00687i	0.287007	+	0.165703i
$914$	−22.5473			−0.745798
$915$	16.5768	−	25.3929i	0.548012	−	0.839463i
$916$	−9.98391	−	5.76421i	−0.329878	−	0.190455i
$917$	3.20370	+	5.54898i	0.105796	+	0.183243i
$918$	9.36758	+	10.9747i	0.309176	+	0.362218i
$919$	−0.683021	−	1.18303i	−0.0225308	−	0.0390244i	0.854540	−	0.519385i	$-0.173839\pi$
$919$	−0.683021	−	1.18303i	−0.0225308	−	0.0390244i	−0.877071	+	0.480361i	$0.840506\pi$
$920$	−6.46884	+	12.9004i	−0.213272	+	0.425313i
$921$	14.4285	+	10.6787i	0.475434	+	0.351876i
$922$	11.7772			0.387863
$923$	−0.642059	−	0.370693i	−0.0211336	−	0.0122015i
$924$	0.311262	−	2.72949i	0.0102398	−	0.0897936i
$925$	48.5329	−	5.73340i	1.59575	−	0.188513i
$926$	3.90256			0.128246
$927$	−51.8524	+	15.8416i	−1.70306	+	0.520305i
$928$	8.51109			0.279390
$929$	−48.5537			−1.59299			−0.796497	−	0.604642i	$-0.793316\pi$
$929$	−48.5537			−1.59299			−0.796497	+	0.604642i	$0.793316\pi$
$930$	−0.463146	+	21.5589i	−0.0151871	+	0.706944i
$931$	−18.0068			−0.590149
$932$	2.92070			0.0956708
$933$	0.783561	−	6.87113i	0.0256526	−	0.224951i
$934$	−25.0156			−0.818534
$935$	−2.85950	+	5.70250i	−0.0935156	+	0.186492i
$936$	0.329530	+	1.07861i	0.0107710	+	0.0352556i
$937$	−39.1556	−	22.6065i	−1.27916	−	0.738523i	−0.302465	−	0.953161i	$-0.597810\pi$
$937$	−39.1556	−	22.6065i	−1.27916	−	0.738523i	−0.976694	+	0.214638i	$0.931143\pi$
$938$	−21.2429			−0.693604
$939$	−28.1962	+	38.0970i	−0.920147	+	1.24325i
$940$	3.32986	+	1.66975i	0.108608	+	0.0544611i
$941$	−12.8532	−	22.2625i	−0.419004	−	0.725736i	0.576836	−	0.816860i	$-0.304287\pi$
$941$	−12.8532	−	22.2625i	−0.419004	−	0.725736i	−0.995840	+	0.0911243i	$0.970954\pi$
$942$	−3.10587	+	27.2358i	−0.101195	+	0.887389i
$943$	1.28542	+	2.22642i	0.0418592	+	0.0725022i
$944$	0.110206	+	0.0636277i	0.00358691	+	0.00207090i
$945$	4.29434	+	17.4158i	0.139695	+	0.566535i
$946$	10.7271			0.348767
$947$	50.6127	+	29.2212i	1.64469	+	0.949563i	0.979134	+	0.203216i	$0.0651394\pi$
$947$	50.6127	+	29.2212i	1.64469	+	0.949563i	0.665557	+	0.746347i	$0.268194\pi$
$948$	−9.43571	−	6.98352i	−0.306458	−	0.226814i
$949$	−2.93419	+	5.08216i	−0.0952477	+	0.164974i
$950$	19.3673	−	2.28794i	0.628358	−	0.0742307i
$951$	−2.01390	+	2.72107i	−0.0653053	+	0.0882366i
$952$	−2.14346	−	3.71259i	−0.0694701	−	0.120326i
$953$		−	39.0732i		−	1.26571i	−0.774272	−	0.632853i	$-0.781884\pi$
$953$		−	39.0732i		−	1.26571i	0.774272	−	0.632853i	$-0.218116\pi$
$954$	25.0729	−	7.66010i	0.811766	−	0.248005i
$955$	46.0764	−	2.71217i	1.49100	−	0.0877638i
$956$	7.54702	+	13.0718i	0.244088	+	0.422773i
$957$	−6.03781	−	13.8898i	−0.195175	−	0.448993i
$958$	1.68801	+	0.974574i	0.0545372	+	0.0314871i
$959$	−4.12380			−0.133164
$960$	3.24310	+	2.11714i	0.104671	+	0.0683304i
$961$	−13.6805	+	27.8180i	−0.441307	+	0.897356i
$962$	3.67449			0.118470
$963$	−26.3413	+	28.2363i	−0.848836	+	0.909901i
$964$	−14.6295	−	8.44634i	−0.471184	−	0.272038i
$965$	−7.21069	−	10.9486i	−0.232120	−	0.352448i
$966$	−10.2665	+	13.8715i	−0.330320	+	0.446309i
$967$	−21.6505	+	37.4997i	−0.696232	+	1.20591i	0.273532	+	0.961863i	$0.411808\pi$
$967$	−21.6505	+	37.4997i	−0.696232	+	1.20591i	−0.969764	+	0.244046i	$0.921525\pi$
$968$	4.97224	−	8.61217i	0.159814	−	0.276806i
$969$	17.2044	−	7.47864i	0.552685	−	0.240249i
$970$	−4.08920	+	8.15482i	−0.131296	+	0.261835i
$971$	27.1343	−	15.6660i	0.870782	−	0.502746i	0.00317422	−	0.999995i	$-0.498990\pi$
$971$	27.1343	−	15.6660i	0.870782	−	0.502746i	0.867608	+	0.497249i	$0.165656\pi$
$972$	−13.1430	−	8.38223i	−0.421562	−	0.268860i
$973$	−5.27696	+	9.13997i	−0.169172	+	0.293014i
$974$	−4.75311	−	8.23263i	−0.152299	−	0.263790i
$975$	1.61647	−	2.82613i	0.0517683	−	0.0905085i
$976$		−	7.82981i		−	0.250626i
$977$	−56.0864			−1.79436			−0.897181	−	0.441664i	$-0.854389\pi$
$977$	−56.0864			−1.79436			−0.897181	+	0.441664i	$0.854389\pi$
$978$	0.862219	−	7.56089i	0.0275707	−	0.241771i
$979$	−4.52564	−	7.83863i	−0.144640	−	0.250524i
$980$	0.606598	+	10.3053i	0.0193771	+	0.329192i
$981$	11.7083	+	2.70554i	0.373817	+	0.0863811i
$982$	5.73978	+	9.94159i	0.183164	+	0.317249i
$983$	23.4649	−	13.5475i	0.748413	−	0.432097i	−0.0767069	−	0.997054i	$-0.524441\pi$
$983$	23.4649	−	13.5475i	0.748413	−	0.432097i	0.825120	+	0.564957i	$0.191107\pi$
$984$	0.632747	−	0.275051i	0.0201712	−	0.00876831i
$985$	54.5620	−	3.21166i	1.73849	−	0.102332i
$986$	−20.4677	−	11.8170i	−0.651824	−	0.376331i
$987$	3.58053	+	2.65001i	0.113970	+	0.0843506i
$988$	1.46632			0.0466500
$989$	−58.3582	−	33.6931i	−1.85568	−	1.07138i
$990$	1.15443	−	6.79454i	0.0366900	−	0.215945i
$991$			57.5784i			1.82904i	0.404544	+	0.914518i	$0.367430\pi$
$991$			57.5784i			1.82904i	−0.404544	+	0.914518i	$0.632570\pi$
$992$	2.94274	+	4.72655i	0.0934322	+	0.150068i
$993$	49.5030	−	21.5186i	1.57093	−	0.682873i
$994$	−3.04450			−0.0965656
$995$	4.74852	−	0.279510i	0.150538	−	0.00886105i
$996$	−15.4825	+	6.73013i	−0.490581	+	0.213252i
$997$	−39.1381	+	22.5964i	−1.23952	+	0.715635i	−0.968995	−	0.247079i	$-0.920529\pi$
$997$	−39.1381	+	22.5964i	−1.23952	+	0.715635i	−0.270521	+	0.962714i	$0.587196\pi$
$998$	7.03371	+	4.06092i	0.222648	+	0.128546i
$999$	−38.6290	+	32.9723i	−1.22217	+	1.04320i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.r.b.119.1	yes	64
3.2	odd	2		930.2.r.a.119.22	✓	64
5.4	even	2		930.2.r.a.119.32	yes	64
15.14	odd	2	inner	930.2.r.b.119.11	yes	64
31.6	odd	6	inner	930.2.r.b.719.11	yes	64
93.68	even	6		930.2.r.a.719.32	yes	64
155.99	odd	6		930.2.r.a.719.22	yes	64
465.254	even	6	inner	930.2.r.b.719.1	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.r.a.119.22	✓	64	3.2	odd	2
930.2.r.a.119.32	yes	64	5.4	even	2
930.2.r.a.719.22	yes	64	155.99	odd	6
930.2.r.a.719.32	yes	64	93.68	even	6
930.2.r.b.119.1	yes	64	1.1	even	1	trivial
930.2.r.b.119.11	yes	64	15.14	odd	2	inner
930.2.r.b.719.1	yes	64	465.254	even	6	inner
930.2.r.b.719.11	yes	64	31.6	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-1.72090 - 0.196245i) q^{3} +1.00000 q^{4} +(-1.99884 - 1.00231i) q^{5} +(-1.72090 - 0.196245i) q^{6} +(1.33698 + 0.771903i) q^{7} +1.00000 q^{8} +(2.92298 + 0.675436i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-1.72090 - 0.196245i) q^{3} +1.00000 q^{4} +(-1.99884 - 1.00231i) q^{5} +(-1.72090 - 0.196245i) q^{6} +(1.33698 + 0.771903i) q^{7} +1.00000 q^{8} +(2.92298 + 0.675436i) q^{9} +(-1.99884 - 1.00231i) q^{10} +(0.513693 + 0.889742i) q^{11} +(-1.72090 - 0.196245i) q^{12} +(0.187971 + 0.325576i) q^{13} +(1.33698 + 0.771903i) q^{14} +(3.24310 + 2.11714i) q^{15} +1.00000 q^{16} +(-2.40483 - 1.38843i) q^{17} +(2.92298 + 0.675436i) q^{18} +(1.95020 - 3.37784i) q^{19} +(-1.99884 - 1.00231i) q^{20} +(-2.14932 - 1.59074i) q^{21} +(0.513693 + 0.889742i) q^{22} -6.45392i q^{23} +(-1.72090 - 0.196245i) q^{24} +(2.99074 + 4.00693i) q^{25} +(0.187971 + 0.325576i) q^{26} +(-4.89759 - 1.73598i) q^{27} +(1.33698 + 0.771903i) q^{28} +8.51109 q^{29} +(3.24310 + 2.11714i) q^{30} +(2.94274 + 4.72655i) q^{31} +1.00000 q^{32} +(-0.709405 - 1.63197i) q^{33} +(-2.40483 - 1.38843i) q^{34} +(-1.89872 - 2.88298i) q^{35} +(2.92298 + 0.675436i) q^{36} +(4.88703 - 8.46459i) q^{37} +(1.95020 - 3.37784i) q^{38} +(-0.259586 - 0.597171i) q^{39} +(-1.99884 - 1.00231i) q^{40} +(-0.344972 + 0.199170i) q^{41} +(-2.14932 - 1.59074i) q^{42} +(5.22057 - 9.04229i) q^{43} +(0.513693 + 0.889742i) q^{44} +(-5.16557 - 4.27982i) q^{45} -6.45392i q^{46} -1.66589 q^{47} +(-1.72090 - 0.196245i) q^{48} +(-2.30833 - 3.99815i) q^{49} +(2.99074 + 4.00693i) q^{50} +(3.86599 + 2.86128i) q^{51} +(0.187971 + 0.325576i) q^{52} +(7.56819 - 4.36950i) q^{53} +(-4.89759 - 1.73598i) q^{54} +(-0.134992 - 2.29334i) q^{55} +(1.33698 + 0.771903i) q^{56} +(-4.01898 + 5.43020i) q^{57} +8.51109 q^{58} +(0.110206 + 0.0636277i) q^{59} +(3.24310 + 2.11714i) q^{60} -7.82981i q^{61} +(2.94274 + 4.72655i) q^{62} +(3.38658 + 3.15930i) q^{63} +1.00000 q^{64} +(-0.0493963 - 0.839180i) q^{65} +(-0.709405 - 1.63197i) q^{66} +(-11.9166 + 6.88003i) q^{67} +(-2.40483 - 1.38843i) q^{68} +(-1.26655 + 11.1065i) q^{69} +(-1.89872 - 2.88298i) q^{70} +(-1.70786 + 0.986036i) q^{71} +(2.92298 + 0.675436i) q^{72} +(7.80488 + 13.5185i) q^{73} +(4.88703 - 8.46459i) q^{74} +(-4.36042 - 7.48243i) q^{75} +(1.95020 - 3.37784i) q^{76} +1.58609i q^{77} +(-0.259586 - 0.597171i) q^{78} +(5.86946 + 3.38873i) q^{79} +(-1.99884 - 1.00231i) q^{80} +(8.08757 + 3.94857i) q^{81} +(-0.344972 + 0.199170i) q^{82} +(8.44099 - 4.87341i) q^{83} +(-2.14932 - 1.59074i) q^{84} +(3.41523 + 5.18564i) q^{85} +(5.22057 - 9.04229i) q^{86} +(-14.6467 - 1.67026i) q^{87} +(0.513693 + 0.889742i) q^{88} -8.81000 q^{89} +(-5.16557 - 4.27982i) q^{90} +0.580383i q^{91} -6.45392i q^{92} +(-4.13660 - 8.71140i) q^{93} -1.66589 q^{94} +(-7.28379 + 4.79707i) q^{95} +(-1.72090 - 0.196245i) q^{96} -4.07977i q^{97} +(-2.30833 - 3.99815i) q^{98} +(0.900548 + 2.94766i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 64 q^{2} + 64 q^{4} + 2 q^{5} + 64 q^{8} - 4 q^{9}+O(q^{10}) \) 64 * q + 64 * q^2 + 64 * q^4 + 2 * q^5 + 64 * q^8 - 4 * q^9	\( 64 q + 64 q^{2} + 64 q^{4} + 2 q^{5} + 64 q^{8} - 4 q^{9} + 2 q^{10} + 64 q^{16} + 6 q^{17} - 4 q^{18} + 4 q^{19} + 2 q^{20} + 2 q^{25} + 18 q^{31} + 64 q^{32} - 8 q^{33} + 6 q^{34} + 16 q^{35} - 4 q^{36} + 4 q^{38} - 8 q^{39} + 2 q^{40} + 9 q^{45} - 4 q^{47} + 30 q^{49} + 2 q^{50} - 8 q^{51} - 6 q^{53} + 6 q^{57} + 18 q^{62} + 12 q^{63} + 64 q^{64} - 8 q^{66} + 6 q^{68} - 10 q^{69} + 16 q^{70} - 4 q^{72} - 63 q^{75} + 4 q^{76} - 8 q^{78} - 30 q^{79} + 2 q^{80} - 12 q^{81} - 54 q^{83} - 16 q^{87} + 9 q^{90} - 18 q^{93} - 4 q^{94} - 56 q^{95} + 30 q^{98} - 102 q^{99}+O(q^{100}) \) 64 * q + 64 * q^2 + 64 * q^4 + 2 * q^5 + 64 * q^8 - 4 * q^9 + 2 * q^10 + 64 * q^16 + 6 * q^17 - 4 * q^18 + 4 * q^19 + 2 * q^20 + 2 * q^25 + 18 * q^31 + 64 * q^32 - 8 * q^33 + 6 * q^34 + 16 * q^35 - 4 * q^36 + 4 * q^38 - 8 * q^39 + 2 * q^40 + 9 * q^45 - 4 * q^47 + 30 * q^49 + 2 * q^50 - 8 * q^51 - 6 * q^53 + 6 * q^57 + 18 * q^62 + 12 * q^63 + 64 * q^64 - 8 * q^66 + 6 * q^68 - 10 * q^69 + 16 * q^70 - 4 * q^72 - 63 * q^75 + 4 * q^76 - 8 * q^78 - 30 * q^79 + 2 * q^80 - 12 * q^81 - 54 * q^83 - 16 * q^87 + 9 * q^90 - 18 * q^93 - 4 * q^94 - 56 * q^95 + 30 * q^98 - 102 * q^99

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