LMFDB - Embedded newform 804.2.j.a.499.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(499,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("804.499");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			499.2
Character	$\chi$	$=$	804.499
Dual form			804.2.j.a.775.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39611 + 0.225574i) q^{2} -1.00000 q^{3} +(1.89823 - 0.629851i) q^{4} +3.70048i q^{5} +(1.39611 - 0.225574i) q^{6} +(0.353219 - 0.611794i) q^{7} +(-2.50806 + 1.30753i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-1.39611 + 0.225574i) q^{2} -1.00000 q^{3} +(1.89823 - 0.629851i) q^{4} +3.70048i q^{5} +(1.39611 - 0.225574i) q^{6} +(0.353219 - 0.611794i) q^{7} +(-2.50806 + 1.30753i) q^{8} +1.00000 q^{9} +(-0.834732 - 5.16627i) q^{10} +(0.976153 - 1.69075i) q^{11} +(-1.89823 + 0.629851i) q^{12} +(4.03748 - 2.33104i) q^{13} +(-0.355127 + 0.933807i) q^{14} -3.70048i q^{15} +(3.20658 - 2.39121i) q^{16} +(2.41991 + 4.19141i) q^{17} +(-1.39611 + 0.225574i) q^{18} +(2.54760 - 1.47086i) q^{19} +(2.33075 + 7.02438i) q^{20} +(-0.353219 + 0.611794i) q^{21} +(-0.981426 + 2.58066i) q^{22} +(3.52628 - 2.03590i) q^{23} +(2.50806 - 1.30753i) q^{24} -8.69357 q^{25} +(-5.11094 + 4.16514i) q^{26} -1.00000 q^{27} +(0.285154 - 1.38380i) q^{28} +(1.55739 - 2.69748i) q^{29} +(0.834732 + 5.16627i) q^{30} +(-1.59346 + 2.75995i) q^{31} +(-3.93733 + 4.06170i) q^{32} +(-0.976153 + 1.69075i) q^{33} +(-4.32392 - 5.30578i) q^{34} +(2.26393 + 1.30708i) q^{35} +(1.89823 - 0.629851i) q^{36} +(0.757833 + 1.31260i) q^{37} +(-3.22494 + 2.62815i) q^{38} +(-4.03748 + 2.33104i) q^{39} +(-4.83850 - 9.28103i) q^{40} +(-4.21634 - 2.43431i) q^{41} +(0.355127 - 0.933807i) q^{42} +1.46178 q^{43} +(0.788047 - 3.82426i) q^{44} +3.70048i q^{45} +(-4.46382 + 3.63777i) q^{46} +(1.31947 + 0.761798i) q^{47} +(-3.20658 + 2.39121i) q^{48} +(3.25047 + 5.62998i) q^{49} +(12.1372 - 1.96104i) q^{50} +(-2.41991 - 4.19141i) q^{51} +(6.19588 - 6.96787i) q^{52} +9.51083i q^{53} +(1.39611 - 0.225574i) q^{54} +(6.25658 + 3.61224i) q^{55} +(-0.0859553 + 1.99626i) q^{56} +(-2.54760 + 1.47086i) q^{57} +(-1.56580 + 4.11727i) q^{58} -6.93788i q^{59} +(-2.33075 - 7.02438i) q^{60} +(-6.25445 + 3.61101i) q^{61} +(1.60207 - 4.21263i) q^{62} +(0.353219 - 0.611794i) q^{63} +(4.58072 - 6.55873i) q^{64} +(8.62598 + 14.9406i) q^{65} +(0.981426 - 2.58066i) q^{66} +(4.19794 + 7.02690i) q^{67} +(7.23351 + 6.43208i) q^{68} +(-3.52628 + 2.03590i) q^{69} +(-3.45553 - 1.31414i) q^{70} +(12.3139 + 7.10944i) q^{71} +(-2.50806 + 1.30753i) q^{72} +(3.11313 + 5.39210i) q^{73} +(-1.35411 - 1.66159i) q^{74} +8.69357 q^{75} +(3.90952 - 4.39664i) q^{76} +(-0.689592 - 1.19441i) q^{77} +(5.11094 - 4.16514i) q^{78} +(3.44615 - 5.96891i) q^{79} +(8.84862 + 11.8659i) q^{80} +1.00000 q^{81} +(6.43558 + 2.44746i) q^{82} +(-14.7865 + 8.53701i) q^{83} +(-0.285154 + 1.38380i) q^{84} +(-15.5102 + 8.95483i) q^{85} +(-2.04080 + 0.329739i) q^{86} +(-1.55739 + 2.69748i) q^{87} +(-0.237545 + 5.51684i) q^{88} +7.16886 q^{89} +(-0.834732 - 5.16627i) q^{90} -3.29348i q^{91} +(5.41138 - 6.08563i) q^{92} +(1.59346 - 2.75995i) q^{93} +(-2.01397 - 0.765914i) q^{94} +(5.44289 + 9.42736i) q^{95} +(3.93733 - 4.06170i) q^{96} +(3.59557 - 2.07590i) q^{97} +(-5.80799 - 7.12684i) q^{98} +(0.976153 - 1.69075i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 68 q^{3} - 2 q^{4} + 4 q^{7} - 6 q^{8} + 68 q^{9}+O(q^{10}) $ 68 * q - 68 * q^3 - 2 * q^4 + 4 * q^7 - 6 * q^8 + 68 * q^9	$ 68 q - 68 q^{3} - 2 q^{4} + 4 q^{7} - 6 q^{8} + 68 q^{9} + 18 q^{10} + 2 q^{12} + 6 q^{13} + 10 q^{14} - 2 q^{16} - 36 q^{20} - 4 q^{21} - 22 q^{22} + 6 q^{24} - 68 q^{25} - q^{26} - 68 q^{27} + q^{28} - 8 q^{29} - 18 q^{30} + 2 q^{31} + 15 q^{32} - 2 q^{36} + 12 q^{37} - 22 q^{38} - 6 q^{39} + 18 q^{40} - 10 q^{42} - 4 q^{43} - 31 q^{44} + 32 q^{46} + 2 q^{48} - 46 q^{49} - 9 q^{50} - 28 q^{52} - 11 q^{56} + 4 q^{58} + 36 q^{60} + 6 q^{61} - 34 q^{62} + 4 q^{63} + 16 q^{64} + 22 q^{66} - 18 q^{67} + 34 q^{68} + 56 q^{70} - 36 q^{71} - 6 q^{72} + 6 q^{73} - 53 q^{74} + 68 q^{75} + 14 q^{76} - 4 q^{77} + q^{78} + 6 q^{79} + 55 q^{80} + 68 q^{81} - 26 q^{82} + 12 q^{83} - q^{84} - 21 q^{86} + 8 q^{87} - 50 q^{88} + 18 q^{90} + 10 q^{92} - 2 q^{93} - 16 q^{94} + 20 q^{95} - 15 q^{96} + 18 q^{97} - 70 q^{98}+O(q^{100}) $ 68 * q - 68 * q^3 - 2 * q^4 + 4 * q^7 - 6 * q^8 + 68 * q^9 + 18 * q^10 + 2 * q^12 + 6 * q^13 + 10 * q^14 - 2 * q^16 - 36 * q^20 - 4 * q^21 - 22 * q^22 + 6 * q^24 - 68 * q^25 - q^26 - 68 * q^27 + q^28 - 8 * q^29 - 18 * q^30 + 2 * q^31 + 15 * q^32 - 2 * q^36 + 12 * q^37 - 22 * q^38 - 6 * q^39 + 18 * q^40 - 10 * q^42 - 4 * q^43 - 31 * q^44 + 32 * q^46 + 2 * q^48 - 46 * q^49 - 9 * q^50 - 28 * q^52 - 11 * q^56 + 4 * q^58 + 36 * q^60 + 6 * q^61 - 34 * q^62 + 4 * q^63 + 16 * q^64 + 22 * q^66 - 18 * q^67 + 34 * q^68 + 56 * q^70 - 36 * q^71 - 6 * q^72 + 6 * q^73 - 53 * q^74 + 68 * q^75 + 14 * q^76 - 4 * q^77 + q^78 + 6 * q^79 + 55 * q^80 + 68 * q^81 - 26 * q^82 + 12 * q^83 - q^84 - 21 * q^86 + 8 * q^87 - 50 * q^88 + 18 * q^90 + 10 * q^92 - 2 * q^93 - 16 * q^94 + 20 * q^95 - 15 * q^96 + 18 * q^97 - 70 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−1.39611	+	0.225574i	−0.987197	+	0.159505i
$2$	−1.39611	+	0.225574i	−0.987197	+	0.159505i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	1.89823	−	0.629851i	0.949116	−	0.314925i
$5$			3.70048i			1.65491i	0.561535	+	0.827453i	$0.310211\pi$
$5$			3.70048i			1.65491i	−0.561535	+	0.827453i	$0.689789\pi$
$6$	1.39611	−	0.225574i	0.569959	−	0.0920902i
$7$	0.353219	−	0.611794i	0.133504	−	0.231236i	−0.791521	−	0.611142i	$-0.790710\pi$
$7$	0.353219	−	0.611794i	0.133504	−	0.231236i	0.925025	+	0.379906i	$0.124044\pi$
$8$	−2.50806	+	1.30753i	−0.886733	+	0.462282i
$9$	1.00000			0.333333
$10$	−0.834732	−	5.16627i	−0.263966	−	1.63372i
$11$	0.976153	−	1.69075i	0.294321	−	0.509779i	−0.680506	−	0.732743i	$-0.738240\pi$
$11$	0.976153	−	1.69075i	0.294321	−	0.509779i	0.974827	+	0.222964i	$0.0715731\pi$
$12$	−1.89823	+	0.629851i	−0.547973	+	0.181822i
$13$	4.03748	−	2.33104i	1.11980	−	0.646515i	0.178448	−	0.983949i	$-0.442892\pi$
$13$	4.03748	−	2.33104i	1.11980	−	0.646515i	0.941349	+	0.337435i	$0.109559\pi$
$14$	−0.355127	+	0.933807i	−0.0949118	+	0.249570i
$15$		−	3.70048i		−	0.955460i
$16$	3.20658	−	2.39121i	0.801644	−	0.597802i
$17$	2.41991	+	4.19141i	0.586914	+	1.01657i	0.994634	+	0.103458i	$0.0329907\pi$
$17$	2.41991	+	4.19141i	0.586914	+	1.01657i	−0.407720	+	0.913107i	$0.633676\pi$
$18$	−1.39611	+	0.225574i	−0.329066	+	0.0531683i
$19$	2.54760	−	1.47086i	0.584460	−	0.337438i	−0.178444	−	0.983950i	$-0.557106\pi$
$19$	2.54760	−	1.47086i	0.584460	−	0.337438i	0.762904	+	0.646512i	$0.223773\pi$
$20$	2.33075	+	7.02438i	0.521172	+	1.57070i
$21$	−0.353219	+	0.611794i	−0.0770787	+	0.133504i
$22$	−0.981426	+	2.58066i	−0.209241	+	0.550198i
$23$	3.52628	−	2.03590i	0.735279	−	0.424514i	−0.0850711	−	0.996375i	$-0.527112\pi$
$23$	3.52628	−	2.03590i	0.735279	−	0.424514i	0.820350	+	0.571861i	$0.193778\pi$
$24$	2.50806	−	1.30753i	0.511955	−	0.266899i
$25$	−8.69357			−1.73871
$26$	−5.11094	+	4.16514i	−1.00234	+	0.816851i
$27$	−1.00000			−0.192450
$28$	0.285154	−	1.38380i	0.0538889	−	0.261514i
$29$	1.55739	−	2.69748i	0.289200	−	0.500909i	−0.684419	−	0.729089i	$-0.739944\pi$
$29$	1.55739	−	2.69748i	0.289200	−	0.500909i	0.973619	+	0.228180i	$0.0732775\pi$
$30$	0.834732	+	5.16627i	0.152401	+	0.943228i
$31$	−1.59346	+	2.75995i	−0.286193	+	0.495701i	−0.972898	−	0.231235i	$-0.925723\pi$
$31$	−1.59346	+	2.75995i	−0.286193	+	0.495701i	0.686704	+	0.726937i	$0.259057\pi$
$32$	−3.93733	+	4.06170i	−0.696028	+	0.718014i
$33$	−0.976153	+	1.69075i	−0.169926	+	0.294321i
$34$	−4.32392	−	5.30578i	−0.741547	−	0.909934i
$35$	2.26393	+	1.30708i	0.382674	+	0.220937i
$36$	1.89823	−	0.629851i	0.316372	−	0.104975i
$37$	0.757833	+	1.31260i	0.124587	+	0.215791i	0.921571	−	0.388209i	$-0.126906\pi$
$37$	0.757833	+	1.31260i	0.124587	+	0.215791i	−0.796984	+	0.604000i	$0.793573\pi$
$38$	−3.22494	+	2.62815i	−0.523155	+	0.426342i
$39$	−4.03748	+	2.33104i	−0.646515	+	0.373266i
$40$	−4.83850	−	9.28103i	−0.765034	−	1.46746i
$41$	−4.21634	−	2.43431i	−0.658482	−	0.380175i	0.133216	−	0.991087i	$-0.457470\pi$
$41$	−4.21634	−	2.43431i	−0.658482	−	0.380175i	−0.791698	+	0.610912i	$0.790803\pi$
$42$	0.355127	−	0.933807i	0.0547973	−	0.144089i
$43$	1.46178			0.222919			0.111460	−	0.993769i	$-0.464447\pi$
$43$	1.46178			0.222919			0.111460	+	0.993769i	$0.464447\pi$
$44$	0.788047	−	3.82426i	0.118803	−	0.576529i
$45$			3.70048i			0.551635i
$46$	−4.46382	+	3.63777i	−0.658154	+	0.536359i
$47$	1.31947	+	0.761798i	0.192465	+	0.111120i	0.593136	−	0.805102i	$-0.297890\pi$
$47$	1.31947	+	0.761798i	0.192465	+	0.111120i	−0.400671	+	0.916222i	$0.631223\pi$
$48$	−3.20658	+	2.39121i	−0.462829	+	0.345141i
$49$	3.25047	+	5.62998i	0.464353	+	0.804283i
$50$	12.1372	−	1.96104i	1.71645	−	0.277333i
$51$	−2.41991	−	4.19141i	−0.338855	−	0.586914i
$52$	6.19588	−	6.96787i	0.859213	−	0.966270i
$53$			9.51083i			1.30641i	0.757180	+	0.653207i	$0.226577\pi$
$53$			9.51083i			1.30641i	−0.757180	+	0.653207i	$0.773423\pi$
$54$	1.39611	−	0.225574i	0.189986	−	0.0306967i
$55$	6.25658	+	3.61224i	0.843637	+	0.487074i
$56$	−0.0859553	+	1.99626i	−0.0114863	+	0.266761i
$57$	−2.54760	+	1.47086i	−0.337438	+	0.194820i
$58$	−1.56580	+	4.11727i	−0.205600	+	0.540624i
$59$		−	6.93788i		−	0.903234i	−0.892212	−	0.451617i	$-0.850847\pi$
$59$		−	6.93788i		−	0.903234i	0.892212	−	0.451617i	$-0.149153\pi$
$60$	−2.33075	−	7.02438i	−0.300899	−	0.906843i
$61$	−6.25445	+	3.61101i	−0.800801	+	0.462342i	−0.843751	−	0.536735i	$-0.819658\pi$
$61$	−6.25445	+	3.61101i	−0.800801	+	0.462342i	0.0429505	+	0.999077i	$0.486324\pi$
$62$	1.60207	−	4.21263i	0.203463	−	0.535004i
$63$	0.353219	−	0.611794i	0.0445014	−	0.0770787i
$64$	4.58072	−	6.55873i	0.572590	−	0.819842i
$65$	8.62598	+	14.9406i	1.06992	+	1.85316i
$66$	0.981426	−	2.58066i	0.120805	−	0.317657i
$67$	4.19794	+	7.02690i	0.512860	+	0.858473i
$67$	4.19794	+	7.02690i	0.512860	+	0.858473i
$68$	7.23351	+	6.43208i	0.877192	+	0.780004i
$69$	−3.52628	+	2.03590i	−0.424514	+	0.245093i
$70$	−3.45553	−	1.31414i	−0.413015	−	0.157070i
$71$	12.3139	+	7.10944i	1.46139	+	0.843736i	0.999076	−	0.0429790i	$-0.0136848\pi$
$71$	12.3139	+	7.10944i	1.46139	+	0.843736i	0.462317	+	0.886715i	$0.347018\pi$
$72$	−2.50806	+	1.30753i	−0.295578	+	0.154094i
$73$	3.11313	+	5.39210i	0.364365	+	0.631098i	0.988674	−	0.150079i	$-0.0479529\pi$
$73$	3.11313	+	5.39210i	0.364365	+	0.631098i	−0.624309	+	0.781177i	$0.714620\pi$
$74$	−1.35411	−	1.66159i	−0.157412	−	0.193156i
$75$	8.69357			1.00385
$76$	3.90952	−	4.39664i	0.448453	−	0.504330i
$77$	−0.689592	−	1.19441i	−0.0785863	−	0.136115i
$78$	5.11094	−	4.16514i	0.578700	−	0.471609i
$79$	3.44615	−	5.96891i	0.387722	−	0.671555i	−0.604420	−	0.796666i	$-0.706595\pi$
$79$	3.44615	−	5.96891i	0.387722	−	0.671555i	0.992143	+	0.125111i	$0.0399286\pi$
$80$	8.84862	+	11.8659i	0.989306	+	1.32665i
$81$	1.00000			0.111111
$82$	6.43558	+	2.44746i	0.710691	+	0.270276i
$83$	−14.7865	+	8.53701i	−1.62303	+	0.937058i	−0.636930	+	0.770922i	$0.719796\pi$
$83$	−14.7865	+	8.53701i	−1.62303	+	0.937058i	−0.986103	+	0.166137i	$0.946871\pi$
$84$	−0.285154	+	1.38380i	−0.0311128	+	0.150985i
$85$	−15.5102	+	8.95483i	−1.68232	+	0.971288i
$86$	−2.04080	+	0.329739i	−0.220065	+	0.0355567i
$87$	−1.55739	+	2.69748i	−0.166970	+	0.289200i
$88$	−0.237545	+	5.51684i	−0.0253224	+	0.588097i
$89$	7.16886			0.759898			0.379949	−	0.925007i	$-0.375942\pi$
$89$	7.16886			0.759898			0.379949	+	0.925007i	$0.375942\pi$
$90$	−0.834732	−	5.16627i	−0.0879885	−	0.544573i
$91$		−	3.29348i		−	0.345250i
$92$	5.41138	−	6.08563i	0.564175	−	0.634471i
$93$	1.59346	−	2.75995i	0.165234	−	0.286193i
$94$	−2.01397	−	0.765914i	−0.207725	−	0.0789980i
$95$	5.44289	+	9.42736i	0.558429	+	0.967227i
$96$	3.93733	−	4.06170i	0.401852	−	0.414546i
$97$	3.59557	−	2.07590i	0.365074	−	0.210776i	−0.306230	−	0.951958i	$-0.599068\pi$
$97$	3.59557	−	2.07590i	0.365074	−	0.210776i	0.671304	+	0.741182i	$0.265734\pi$
$98$	−5.80799	−	7.12684i	−0.586695	−	0.719920i
$99$	0.976153	−	1.69075i	0.0981070	−	0.169926i
$100$	−16.5024	+	5.47565i	−1.65024	+	0.547565i
$101$	−9.68743	−	5.59304i	−0.963936	−	0.556528i	−0.0665535	−	0.997783i	$-0.521200\pi$
$101$	−9.68743	−	5.59304i	−0.963936	−	0.556528i	−0.897382	+	0.441254i	$0.854534\pi$
$102$	4.32392	+	5.30578i	0.428132	+	0.525351i
$103$	−6.99504	−	4.03859i	−0.689242	−	0.397934i	0.114086	−	0.993471i	$-0.463606\pi$
$103$	−6.99504	−	4.03859i	−0.689242	−	0.397934i	−0.803328	+	0.595537i	$0.796939\pi$
$104$	−7.07834	+	11.1255i	−0.694088	+	1.09095i
$105$	−2.26393	−	1.30708i	−0.220937	−	0.127558i
$106$	−2.14540	−	13.2781i	−0.208379	−	1.28969i
$107$			17.2446i			1.66710i	0.552445	+	0.833549i	$0.313695\pi$
$107$			17.2446i			1.66710i	−0.552445	+	0.833549i	$0.686305\pi$
$108$	−1.89823	+	0.629851i	−0.182658	+	0.0606074i
$109$		−	12.1460i		−	1.16338i	−0.813411	−	0.581690i	$-0.802392\pi$
$109$		−	12.1460i		−	1.16338i	0.813411	−	0.581690i	$-0.197608\pi$
$110$	−9.54968	−	3.63175i	−0.910526	−	0.346274i
$111$	−0.757833	−	1.31260i	−0.0719303	−	0.124587i
$112$	−0.330301	−	2.80638i	−0.0312105	−	0.265178i
$113$	9.72490	+	5.61467i	0.914842	+	0.528184i	0.881986	−	0.471276i	$-0.156206\pi$
$113$	9.72490	+	5.61467i	0.914842	+	0.528184i	0.0328559	+	0.999460i	$0.489540\pi$
$114$	3.22494	−	2.62815i	0.302043	−	0.246149i
$115$	7.53380	+	13.0489i	0.702530	+	1.21682i
$116$	1.25728	−	6.10136i	0.116735	−	0.566497i
$117$	4.03748	−	2.33104i	0.373266	−	0.215505i
$118$	1.56500	+	9.68602i	0.144070	+	0.891670i
$119$	3.41903			0.313422
$120$	4.83850	+	9.28103i	0.441692	+	0.847238i
$121$	3.59425	+	6.22543i	0.326750	+	0.565948i
$122$	7.91734	−	6.45220i	0.716802	−	0.584155i
$123$	4.21634	+	2.43431i	0.380175	+	0.219494i
$124$	−1.28640	+	6.24267i	−0.115522	+	0.560608i
$125$		−	13.6680i		−	1.22250i
$126$	−0.355127	+	0.933807i	−0.0316373	+	0.0831901i
$127$	3.62933	+	2.09539i	0.322051	+	0.185936i	0.652306	−	0.757956i	$-0.273802\pi$
$127$	3.62933	+	2.09539i	0.322051	+	0.185936i	−0.330256	+	0.943892i	$0.607135\pi$
$128$	−4.91570	+	10.1900i	−0.434491	+	0.900676i
$129$	−1.46178			−0.128702
$130$	−15.4130	−	18.9129i	−1.35181	−	1.65877i
$131$		−	18.4641i		−	1.61322i	−0.591087	−	0.806608i	$-0.701301\pi$
$131$		−	18.4641i		−	1.61322i	0.591087	−	0.806608i	$-0.298699\pi$
$132$	−0.788047	+	3.82426i	−0.0685907	+	0.332859i
$133$		−	2.07814i		−	0.180198i
$134$	−7.44586	−	8.86336i	−0.643224	−	0.765678i
$135$		−	3.70048i		−	0.318487i
$136$	−11.5497	−	7.34819i	−0.990376	−	0.630102i
$137$		−	1.92486i		−	0.164452i	−0.996614	−	0.0822261i	$-0.973797\pi$
$137$		−	1.92486i		−	0.164452i	0.996614	−	0.0822261i	$-0.0262030\pi$
$138$	4.46382	−	3.63777i	0.379985	−	0.309667i
$139$	−22.4280			−1.90232			−0.951158	−	0.308705i	$-0.900104\pi$
$139$	−22.4280			−1.90232			−0.951158	+	0.308705i	$0.900104\pi$
$140$	5.12073	+	1.05521i	0.432781	+	0.0891811i
$141$	−1.31947	−	0.761798i	−0.111120	−	0.0641550i
$142$	−18.7953	−	7.14785i	−1.57726	−	0.599834i
$143$		−	9.10181i		−	0.761132i
$144$	3.20658	−	2.39121i	0.267215	−	0.199267i
$145$	9.98196	+	5.76309i	0.828957	+	0.478598i
$146$	−5.56259	−	6.82572i	−0.460363	−	0.564900i
$147$	−3.25047	−	5.62998i	−0.268094	−	0.464353i
$148$	2.26529	+	2.01431i	0.186206	+	0.165575i
$149$	8.06155			0.660428			0.330214	−	0.943906i	$-0.392879\pi$
$149$	8.06155			0.660428			0.330214	+	0.943906i	$0.392879\pi$
$150$	−12.1372	+	1.96104i	−0.990995	+	0.160118i
$151$	−0.397241	+	0.229347i	−0.0323270	+	0.0186640i	−0.516076	−	0.856543i	$-0.672608\pi$
$151$	−0.397241	+	0.229347i	−0.0323270	+	0.0186640i	0.483749	+	0.875207i	$0.339275\pi$
$152$	−4.46635	+	7.02008i	−0.362268	+	0.569403i
$153$	2.41991	+	4.19141i	0.195638	+	0.338855i
$154$	1.23217	+	1.51197i	0.0992912	+	0.121838i
$155$	−10.2131	−	5.89656i	−0.820339	−	0.473623i
$156$	−6.19588	+	6.96787i	−0.496067	+	0.557876i
$157$	1.58029	+	2.73714i	0.126121	+	0.218447i	0.922170	−	0.386784i	$-0.126414\pi$
$157$	1.58029	+	2.73714i	0.126121	+	0.218447i	−0.796050	+	0.605231i	$0.793081\pi$
$158$	−3.46477	+	9.11061i	−0.275642	+	0.724801i
$159$		−	9.51083i		−	0.754258i
$160$	−15.0303	−	14.5700i	−1.18825	−	1.15186i
$161$		−	2.87647i		−	0.226698i
$162$	−1.39611	+	0.225574i	−0.109689	+	0.0177228i
$163$	13.9617	+	8.06078i	1.09356	+	0.631369i	0.934523	−	0.355903i	$-0.115827\pi$
$163$	13.9617	+	8.06078i	1.09356	+	0.631369i	0.159041	+	0.987272i	$0.449160\pi$
$164$	−9.53685	−	1.96521i	−0.744703	−	0.153457i
$165$	−6.25658	−	3.61224i	−0.487074	−	0.281212i
$166$	18.7179	−	15.2540i	1.45279	−	1.18394i
$167$	−15.5367	−	8.97012i	−1.20227	−	0.694129i	−0.241208	−	0.970473i	$-0.577544\pi$
$167$	−15.5367	−	8.97012i	−1.20227	−	0.694129i	−0.961059	+	0.276344i	$0.910877\pi$
$168$	0.0859553	−	1.99626i	0.00663160	−	0.154015i
$169$	4.36752	−	7.56476i	0.335963	−	0.581905i
$170$	19.6340	−	16.0006i	1.50586	−	1.22719i
$171$	2.54760	−	1.47086i	0.194820	−	0.112479i
$172$	2.77480	−	0.920703i	0.211576	−	0.0702029i
$173$	−2.39642	−	4.15072i	−0.182196	−	0.315573i	0.760432	−	0.649418i	$-0.224987\pi$
$173$	−2.39642	−	4.15072i	−0.182196	−	0.315573i	−0.942628	+	0.333845i	$0.891654\pi$
$174$	1.56580	−	4.11727i	0.118703	−	0.312130i
$175$	−3.07074	+	5.31867i	−0.232126	+	0.402054i
$176$	−0.912817	−	7.75569i	−0.0688062	−	0.584607i
$177$			6.93788i			0.521483i
$178$	−10.0085	+	1.61711i	−0.750169	+	0.121207i
$179$	−4.43228			−0.331284			−0.165642	−	0.986186i	$-0.552970\pi$
$179$	−4.43228			−0.331284			−0.165642	+	0.986186i	$0.552970\pi$
$180$	2.33075	+	7.02438i	0.173724	+	0.523566i
$181$	8.33135	−	14.4303i	0.619264	−	1.07260i	−0.370356	−	0.928890i	$-0.620764\pi$
$181$	8.33135	−	14.4303i	0.619264	−	1.07260i	0.989620	−	0.143707i	$-0.0459023\pi$
$182$	0.742922	+	4.59805i	0.0550691	+	0.340830i
$183$	6.25445	−	3.61101i	0.462342	−	0.266934i
$184$	−6.18211	+	9.71686i	−0.455751	+	0.716337i
$185$	−4.85727	+	2.80435i	−0.357114	+	0.206180i
$186$	−1.60207	+	4.21263i	−0.117469	+	0.308885i
$187$	9.44880			0.690965
$188$	2.98449	+	0.614999i	0.217666	+	0.0448534i
$189$	−0.353219	+	0.611794i	−0.0256929	+	0.0445014i
$190$	−9.72543	−	11.9338i	−0.705557	−	0.865772i
$191$	−4.91644	−	8.51552i	−0.355741	−	0.616161i	0.631504	−	0.775373i	$-0.282438\pi$
$191$	−4.91644	−	8.51552i	−0.355741	−	0.616161i	−0.987244	+	0.159212i	$0.949105\pi$
$192$	−4.58072	+	6.55873i	−0.330585	+	0.473336i
$193$	15.2168			1.09533			0.547664	−	0.836698i	$-0.315517\pi$
$193$	15.2168			1.09533			0.547664	+	0.836698i	$0.315517\pi$
$194$	−4.55153	+	3.70925i	−0.326781	+	0.266308i
$195$	−8.62598	−	14.9406i	−0.617719	−	1.06992i
$196$	9.71620	+	8.63971i	0.694015	+	0.617122i
$197$	−13.9200	−	8.03674i	−0.991762	−	0.572594i	−0.0859613	−	0.996298i	$-0.527396\pi$
$197$	−13.9200	−	8.03674i	−0.991762	−	0.572594i	−0.905800	+	0.423705i	$0.860729\pi$
$198$	−0.981426	+	2.58066i	−0.0697469	+	0.183399i
$199$	−12.6422	+	7.29900i	−0.896185	+	0.517413i	−0.875960	−	0.482383i	$-0.839771\pi$
$199$	−12.6422	+	7.29900i	−0.896185	+	0.517413i	−0.0202243	+	0.999795i	$0.506438\pi$
$200$	21.8040	−	11.3671i	1.54177	−	0.803776i
$201$	−4.19794	−	7.02690i	−0.296100	−	0.495639i
$202$	14.7863	+	5.62326i	1.04036	+	0.395651i
$203$	−1.10020	−	1.90560i	−0.0772188	−	0.133747i
$204$	−7.23351	−	6.43208i	−0.506447	−	0.450336i
$205$	9.00811	−	15.6025i	0.629154	−	1.08973i
$206$	10.6768	+	4.06041i	0.743890	+	0.282902i
$207$	3.52628	−	2.03590i	0.245093	−	0.141505i
$208$	7.37249	−	17.1291i	0.511190	−	1.18769i
$209$		−	5.74313i		−	0.397261i
$210$	3.45553	+	1.31414i	0.238455	+	0.0906844i
$211$	−7.89775	+	4.55977i	−0.543703	+	0.313907i	−0.746579	−	0.665297i	$-0.768305\pi$
$211$	−7.89775	+	4.55977i	−0.543703	+	0.313907i	0.202875	+	0.979205i	$0.434971\pi$
$212$	5.99041	+	18.0538i	0.411423	+	1.23994i
$213$	−12.3139	−	7.10944i	−0.843736	−	0.487131i
$214$	−3.88993	−	24.0753i	−0.265910	−	1.64576i
$215$			5.40929i			0.368910i
$216$	2.50806	−	1.30753i	0.170652	−	0.0889662i
$217$	1.12568	+	1.94973i	0.0764161	+	0.132357i
$218$	2.73983	+	16.9572i	0.185565	+	1.14849i
$219$	−3.11313	−	5.39210i	−0.210366	−	0.364365i
$220$	14.1516	+	2.91615i	0.954101	+	0.196607i
$221$	19.5407	+	11.2818i	1.31445	+	0.758897i
$222$	1.35411	+	1.66159i	0.0908816	+	0.111519i
$223$		−	4.78143i		−	0.320188i	−0.987102	−	0.160094i	$-0.948820\pi$
$223$		−	4.78143i		−	0.320188i	0.987102	−	0.160094i	$-0.0511798\pi$
$224$	1.09418	+	3.84350i	0.0731082	+	0.256805i
$225$	−8.69357			−0.579571
$226$	−14.8435	−	5.64501i	−0.987377	−	0.375500i
$227$	−11.5826	−	6.68725i	−0.768767	−	0.443848i	0.0636673	−	0.997971i	$-0.479720\pi$
$227$	−11.5826	−	6.68725i	−0.768767	−	0.443848i	−0.832435	+	0.554123i	$0.813054\pi$
$228$	−3.90952	+	4.39664i	−0.258914	+	0.291175i
$229$	11.1964	−	6.46424i	0.739878	−	0.427169i	−0.0821470	−	0.996620i	$-0.526178\pi$
$229$	11.1964	−	6.46424i	0.739878	−	0.427169i	0.822025	+	0.569451i	$0.192844\pi$
$230$	−13.4615	−	16.5183i	−0.887624	−	1.08918i
$231$	0.689592	+	1.19441i	0.0453718	+	0.0785863i
$232$	−0.378988	+	8.80176i	−0.0248818	+	0.577864i
$233$	13.7454	+	7.93593i	0.900493	+	0.519900i	0.877360	−	0.479832i	$-0.159303\pi$
$233$	13.7454	+	7.93593i	0.900493	+	0.519900i	0.0231331	+	0.999732i	$0.492636\pi$
$234$	−5.11094	+	4.16514i	−0.334113	+	0.272284i
$235$	−2.81902	+	4.88269i	−0.183893	+	0.318511i
$236$	−4.36983	−	13.1697i	−0.284452	−	0.857275i
$237$	−3.44615	+	5.96891i	−0.223852	+	0.387722i
$238$	−4.77334	+	0.771245i	−0.309410	+	0.0499924i
$239$	−14.5156	+	25.1417i	−0.938934	+	1.62628i	−0.171469	+	0.985190i	$0.554851\pi$
$239$	−14.5156	+	25.1417i	−0.938934	+	1.62628i	−0.767465	+	0.641091i	$0.778482\pi$
$240$	−8.84862	−	11.8659i	−0.571176	−	0.765939i
$241$	27.2729			1.75680			0.878402	−	0.477923i	$-0.158610\pi$
$241$	27.2729			1.75680			0.878402	+	0.477923i	$0.158610\pi$
$242$	−6.42226	−	7.88060i	−0.412838	−	0.506584i
$243$	−1.00000			−0.0641500
$244$	−9.59801	+	10.7939i	−0.614450	+	0.691009i
$245$	−20.8337	+	12.0283i	−1.33101	+	0.768461i
$246$	−6.43558	−	2.44746i	−0.410318	−	0.156044i
$247$	6.85727	−	11.8771i	0.436318	−	0.755725i
$248$	0.387765	−	9.00561i	0.0246231	−	0.571857i
$249$	14.7865	−	8.53701i	0.937058	−	0.541011i
$250$	3.08314	+	19.0820i	0.194995	+	1.20685i
$251$	−8.32086	−	14.4122i	−0.525208	−	0.909687i	−0.999569	−	0.0293565i	$-0.990654\pi$
$251$	−8.32086	−	14.4122i	−0.525208	−	0.909687i	0.474361	−	0.880330i	$-0.342679\pi$
$252$	0.285154	−	1.38380i	0.0179630	−	0.0871713i
$253$		−	7.94938i		−	0.499773i
$254$	−5.53960	−	2.10671i	−0.347585	−	0.132187i
$255$	15.5102	−	8.95483i	0.971288	−	0.560773i
$256$	4.56426	−	15.3352i	0.285266	−	0.958448i
$257$	12.7014	−	21.9995i	0.792294	−	1.37229i	−0.132249	−	0.991216i	$-0.542220\pi$
$257$	12.7014	−	21.9995i	0.792294	−	1.37229i	0.924543	−	0.381077i	$-0.124447\pi$
$258$	2.04080	−	0.329739i	0.127055	−	0.0205287i
$259$	1.07072			0.0665316
$260$	25.7845	+	22.9277i	1.59909	+	1.42192i
$261$	1.55739	−	2.69748i	0.0963999	−	0.166970i
$262$	4.16502	+	25.7779i	0.257316	+	1.59256i
$263$		−	16.2207i		−	1.00021i	−0.865964	−	0.500107i	$-0.833294\pi$
$263$		−	16.2207i		−	1.00021i	0.865964	−	0.500107i	$-0.166706\pi$
$264$	0.237545	−	5.51684i	0.0146199	−	0.339538i
$265$	−35.1947			−2.16199
$266$	0.468775	+	2.90131i	0.0287424	+	0.177891i
$267$	−7.16886			−0.438727
$268$	12.3946	+	10.6946i	0.757118	+	0.653278i
$269$	7.59119			0.462843			0.231422	−	0.972854i	$-0.425662\pi$
$269$	7.59119			0.462843			0.231422	+	0.972854i	$0.425662\pi$
$270$	0.834732	+	5.16627i	0.0508002	+	0.314409i
$271$	8.48021			0.515136			0.257568	−	0.966260i	$-0.417079\pi$
$271$	8.48021			0.515136			0.257568	+	0.966260i	$0.417079\pi$
$272$	17.7821	+	7.65355i	1.07820	+	0.464065i
$273$			3.29348i			0.199330i
$274$	0.434199	+	2.68732i	0.0262309	+	0.162347i
$275$	−8.48625	+	14.6986i	−0.511740	+	0.886360i
$276$	−5.41138	+	6.08563i	−0.325727	+	0.366312i
$277$	−18.8350			−1.13169			−0.565844	−	0.824513i	$-0.691449\pi$
$277$	−18.8350			−1.13169			−0.565844	+	0.824513i	$0.691449\pi$
$278$	31.3119	−	5.05916i	1.87796	−	0.303429i
$279$	−1.59346	+	2.75995i	−0.0953978	+	0.165234i
$280$	−7.38712	−	0.318076i	−0.441465	−	0.0190087i
$281$	−17.6702	+	10.2019i	−1.05411	+	0.608593i	−0.923798	−	0.382880i	$-0.874932\pi$
$281$	−17.6702	+	10.2019i	−1.05411	+	0.608593i	−0.130316	+	0.991473i	$0.541599\pi$
$282$	2.01397	+	0.765914i	0.119930	+	0.0456095i
$283$			24.5780i			1.46101i	0.682908	+	0.730504i	$0.260715\pi$
$283$			24.5780i			1.46101i	−0.682908	+	0.730504i	$0.739285\pi$
$284$	27.8526	+	5.73945i	1.65275	+	0.340574i
$285$	−5.44289	−	9.42736i	−0.322409	−	0.558429i
$286$	2.05313	+	12.7071i	0.121404	+	0.751387i
$287$	−2.97859	+	1.71969i	−0.175820	+	0.101510i
$288$	−3.93733	+	4.06170i	−0.232009	+	0.239338i
$289$	−3.21192	+	5.56320i	−0.188936	+	0.327247i
$290$	−15.2359	−	5.79422i	−0.894682	−	0.340248i
$291$	−3.59557	+	2.07590i	−0.210776	+	0.121691i
$292$	9.30567	+	8.27466i	0.544573	+	0.484238i
$293$	−25.4264			−1.48542			−0.742712	−	0.669611i	$-0.766461\pi$
$293$	−25.4264			−1.48542			−0.742712	+	0.669611i	$0.766461\pi$
$294$	5.80799	+	7.12684i	0.338729	+	0.415646i
$295$	25.6735			1.49477
$296$	−3.61696	−	2.30120i	−0.210232	−	0.133755i
$297$	−0.976153	+	1.69075i	−0.0566421	+	0.0981070i
$298$	−11.2548	+	1.81847i	−0.651972	+	0.105341i
$299$	9.49152	−	16.4398i	0.548909	−	0.950738i
$300$	16.5024	−	5.47565i	0.952767	−	0.316137i
$301$	0.516328	−	0.894307i	0.0297607	−	0.0515470i
$302$	0.502857	−	0.409801i	0.0289362	−	0.0235814i
$303$	9.68743	+	5.59304i	0.556528	+	0.321312i
$304$	4.65195	−	10.8083i	0.266808	−	0.619897i
$305$	−13.3625	−	23.1445i	−0.765133	−	1.32525i
$306$	−4.32392	−	5.30578i	−0.247182	−	0.303311i
$307$	7.87815	−	4.54845i	0.449630	−	0.259594i	−0.258044	−	0.966133i	$-0.583078\pi$
$307$	7.87815	−	4.54845i	0.449630	−	0.259594i	0.707674	+	0.706539i	$0.249745\pi$
$308$	−2.06130	−	1.83292i	−0.117454	−	0.104441i
$309$	6.99504	+	4.03859i	0.397934	+	0.229747i
$310$	15.5888	+	5.92841i	0.885382	+	0.336711i
$311$	−2.52656			−0.143268			−0.0716340	−	0.997431i	$-0.522821\pi$
$311$	−2.52656			−0.143268			−0.0716340	+	0.997431i	$0.522821\pi$
$312$	7.07834	−	11.1255i	0.400732	−	0.629859i
$313$		−	18.3699i		−	1.03833i	−0.854674	−	0.519165i	$-0.826243\pi$
$313$		−	18.3699i		−	1.03833i	0.854674	−	0.519165i	$-0.173757\pi$
$314$	−2.82368	−	3.46487i	−0.159349	−	0.195534i
$315$	2.26393	+	1.30708i	0.127558	+	0.0736457i
$316$	2.78208	−	13.5009i	0.156504	−	0.759488i
$317$	6.99505	+	12.1158i	0.392881	+	0.680490i	0.992828	−	0.119550i	$-0.0381450\pi$
$317$	6.99505	+	12.1158i	0.392881	+	0.680490i	−0.599947	+	0.800040i	$0.704812\pi$
$318$	2.14540	+	13.2781i	0.120308	+	0.744602i
$319$	−3.04050	−	5.26630i	−0.170235	−	0.294856i
$320$	24.2705	+	16.9509i	1.35676	+	0.947583i
$321$		−	17.2446i		−	0.962500i
$322$	0.648857	+	4.01586i	0.0361594	+	0.223795i
$323$	12.3299	+	7.11869i	0.686056	+	0.396095i
$324$	1.89823	−	0.629851i	0.105457	−	0.0349917i
$325$	−35.1001	+	20.2651i	−1.94701	+	1.12410i
$326$	−21.3103	−	8.10433i	−1.18027	−	0.448857i
$327$			12.1460i			0.671678i
$328$	13.7578	+	0.592385i	0.759646	+	0.0327090i
$329$	0.932127	−	0.538164i	0.0513898	−	0.0296699i
$330$	9.54968	+	3.63175i	0.525693	+	0.199921i
$331$	−3.88024	+	6.72078i	−0.213277	+	0.369407i	−0.952738	−	0.303792i	$-0.901747\pi$
$331$	−3.88024	+	6.72078i	−0.213277	+	0.369407i	0.739461	+	0.673200i	$0.235081\pi$
$332$	−22.6912	+	25.5185i	−1.24534	+	1.40051i
$333$	0.757833	+	1.31260i	0.0415290	+	0.0719303i
$334$	23.7143	+	9.01858i	1.29759	+	0.493475i
$335$	−26.0029	+	15.5344i	−1.42069	+	0.848734i
$336$	0.330301	+	2.80638i	0.0180194	+	0.153101i
$337$	16.0259	−	9.25255i	0.872985	−	0.504018i	0.00464615	−	0.999989i	$-0.498521\pi$
$337$	16.0259	−	9.25255i	0.872985	−	0.504018i	0.868339	+	0.495971i	$0.165188\pi$
$338$	−4.39111	+	11.5464i	−0.238845	+	0.628043i
$339$	−9.72490	−	5.61467i	−0.528184	−	0.304947i
$340$	−23.8018	+	26.7675i	−1.29083	+	1.45167i
$341$	3.11092	+	5.38826i	0.168466	+	0.291791i
$342$	−3.22494	+	2.62815i	−0.174385	+	0.142114i
$343$	9.53759			0.514981
$344$	−3.66623	+	1.91132i	−0.197670	+	0.103052i
$345$	−7.53380	−	13.0489i	−0.405606	−	0.702530i
$346$	4.28195	+	5.25428i	0.230199	+	0.282472i
$347$	15.5246	−	26.8895i	0.833406	−	1.44350i	−0.0619154	−	0.998081i	$-0.519721\pi$
$347$	15.5246	−	26.8895i	0.833406	−	1.44350i	0.895322	−	0.445420i	$-0.146946\pi$
$348$	−1.25728	+	6.10136i	−0.0673972	+	0.327067i
$349$	−7.80914			−0.418014			−0.209007	−	0.977914i	$-0.567023\pi$
$349$	−7.80914			−0.418014			−0.209007	+	0.977914i	$0.567023\pi$
$350$	3.08732	−	8.11811i	0.165024	−	0.433931i
$351$	−4.03748	+	2.33104i	−0.215505	+	0.124422i
$352$	3.02387	+	10.6219i	0.161173	+	0.566148i
$353$	−16.6335	+	9.60337i	−0.885313	+	0.511136i	−0.872406	−	0.488781i	$-0.837442\pi$
$353$	−16.6335	+	9.60337i	−0.885313	+	0.511136i	−0.0129064	+	0.999917i	$0.504108\pi$
$354$	−1.56500	−	9.68602i	−0.0831790	−	0.514806i
$355$	−26.3084	+	45.5674i	−1.39630	+	2.41847i
$356$	13.6082	−	4.51531i	0.721232	−	0.239311i
$357$	−3.41903			−0.180954
$358$	6.18794	−	0.999807i	0.327043	−	0.0528414i
$359$		−	21.7199i		−	1.14633i	−0.819440	−	0.573165i	$-0.805715\pi$
$359$		−	21.7199i		−	1.14633i	0.819440	−	0.573165i	$-0.194285\pi$
$360$	−4.83850	−	9.28103i	−0.255011	−	0.489153i
$361$	−5.17314	+	8.96015i	−0.272271	+	0.471587i
$362$	−8.37635	+	22.0256i	−0.440251	+	1.15764i
$363$	−3.59425	−	6.22543i	−0.188649	−	0.326750i
$364$	−2.07440	−	6.25178i	−0.108728	−	0.327683i
$365$	−19.9534	+	11.5201i	−1.04441	+	0.602989i
$366$	−7.91734	+	6.45220i	−0.413846	+	0.337262i
$367$	−14.4383	+	25.0079i	−0.753674	+	1.30540i	0.192357	+	0.981325i	$0.438387\pi$
$367$	−14.4383	+	25.0079i	−0.753674	+	1.30540i	−0.946031	+	0.324077i	$0.894946\pi$
$368$	6.43902	−	14.9603i	0.335657	−	0.779860i
$369$	−4.21634	−	2.43431i	−0.219494	−	0.126725i
$370$	6.14868	−	5.01084i	0.319655	−	0.260501i
$371$	5.81867	+	3.35941i	0.302090	+	0.174412i
$372$	1.28640	−	6.24267i	0.0666966	−	0.323667i
$373$	18.8728	+	10.8962i	0.977196	+	0.564184i	0.901422	−	0.432941i	$-0.142524\pi$
$373$	18.8728	+	10.8962i	0.977196	+	0.564184i	0.0757737	+	0.997125i	$0.475857\pi$
$374$	−13.1915	+	2.13140i	−0.682119	+	0.110212i
$375$			13.6680i			0.705812i
$376$	−4.30539	−	0.185382i	−0.222034	−	0.00956037i
$377$		−	14.5214i		−	0.747888i
$378$	0.355127	−	0.933807i	0.0182658	−	0.0480298i
$379$	−2.13555	−	3.69888i	−0.109696	−	0.189999i	0.805951	−	0.591982i	$-0.201654\pi$
$379$	−2.13555	−	3.69888i	−0.109696	−	0.189999i	−0.915647	+	0.401983i	$0.868321\pi$
$380$	16.2697	+	14.4671i	0.834618	+	0.742148i
$381$	−3.62933	−	2.09539i	−0.185936	−	0.107350i
$382$	8.78475	+	10.7796i	0.449467	+	0.551530i
$383$	17.6185	+	30.5161i	0.900261	+	1.55930i	0.827155	+	0.561974i	$0.189958\pi$
$383$	17.6185	+	30.5161i	0.900261	+	1.55930i	0.0731065	+	0.997324i	$0.476709\pi$
$384$	4.91570	−	10.1900i	0.250853	−	0.520006i
$385$	4.41989	−	2.55182i	0.225258	−	0.130053i
$386$	−21.2443	+	3.43251i	−1.08131	+	0.174710i
$387$	1.46178			0.0743064
$388$	5.51771	−	6.20522i	0.280120	−	0.315022i
$389$	−10.7493	−	18.6182i	−0.545009	−	0.943983i	−0.998606	−	0.0527762i	$-0.983193\pi$
$389$	−10.7493	−	18.6182i	−0.545009	−	0.943983i	0.453598	−	0.891207i	$-0.350140\pi$
$390$	15.4130	+	18.9129i	0.780468	+	0.957694i
$391$	17.0665	+	9.85337i	0.863092	+	0.498306i
$392$	−15.5138	−	9.87024i	−0.783563	−	0.498522i
$393$			18.4641i			0.931390i
$394$	21.2467	+	8.08015i	1.07040	+	0.407072i
$395$	22.0879	+	12.7524i	1.11136	+	0.641644i
$396$	0.788047	−	3.82426i	0.0396009	−	0.192176i
$397$	−25.4251			−1.27605			−0.638025	−	0.770015i	$-0.720248\pi$
$397$	−25.4251			−1.27605			−0.638025	+	0.770015i	$0.720248\pi$
$398$	16.0035	−	13.0420i	0.802181	−	0.653734i
$399$			2.07814i			0.104037i
$400$	−27.8766	+	20.7881i	−1.39383	+	1.03941i
$401$			21.1205i			1.05471i	0.849646	+	0.527353i	$0.176815\pi$
$401$			21.1205i			1.05471i	−0.849646	+	0.527353i	$0.823185\pi$
$402$	7.44586	+	8.86336i	0.371366	+	0.442064i
$403$			14.8577i			0.740113i
$404$	−21.9118	−	4.51526i	−1.09015	−	0.224642i
$405$			3.70048i			0.183878i
$406$	1.96585	+	2.41225i	0.0975635	+	0.119718i
$407$	2.95904			0.146674
$408$	11.5497	+	7.34819i	0.571794	+	0.363789i
$409$	33.7110	+	19.4631i	1.66690	+	0.962386i	0.969294	+	0.245906i	$0.0790854\pi$
$409$	33.7110	+	19.4631i	1.66690	+	0.962386i	0.697608	+	0.716480i	$0.254248\pi$
$410$	−9.05677	+	23.8148i	−0.447282	+	1.17613i
$411$			1.92486i			0.0949465i
$412$	−15.8219	−	3.26035i	−0.779490	−	0.160626i
$413$	−4.24455	−	2.45059i	−0.208861	−	0.120586i
$414$	−4.46382	+	3.63777i	−0.219385	+	0.178786i
$415$	−31.5910	−	54.7173i	−1.55074	−	2.68597i
$416$	−6.42891	+	25.5771i	−0.315203	+	1.25402i
$417$	22.4280			1.09830
$418$	1.29550	+	8.01803i	0.0633650	+	0.392175i
$419$	10.0954	−	5.82856i	0.493191	−	0.284744i	−0.232706	−	0.972547i	$-0.574758\pi$
$419$	10.0954	−	5.82856i	0.493191	−	0.284744i	0.725897	+	0.687803i	$0.241425\pi$
$420$	−5.12073	−	1.05521i	−0.249866	−	0.0514888i
$421$	−10.0349	−	17.3809i	−0.489069	−	0.847092i	0.510852	−	0.859669i	$-0.329330\pi$
$421$	−10.0349	−	17.3809i	−0.489069	−	0.847092i	−0.999921	+	0.0125765i	$0.995997\pi$
$422$	9.99754	−	8.14745i	0.486673	−	0.396612i
$423$	1.31947	+	0.761798i	0.0641550	+	0.0370399i
$424$	−12.4357	−	23.8537i	−0.603932	−	1.15844i
$425$	−21.0376	−	36.4383i	−1.02048	−	1.76752i
$426$	18.7953	+	7.14785i	0.910633	+	0.346314i
$427$			5.10191i			0.246899i
$428$	10.8615	+	32.7343i	0.525012	+	1.58227i
$429$			9.10181i			0.439440i
$430$	−1.22019	−	7.55195i	−0.0588430	−	0.364187i
$431$	−6.31703	−	3.64714i	−0.304280	−	0.175676i	0.340084	−	0.940395i	$-0.389545\pi$
$431$	−6.31703	−	3.64714i	−0.304280	−	0.175676i	−0.644364	+	0.764719i	$0.722878\pi$
$432$	−3.20658	+	2.39121i	−0.154276	+	0.115047i
$433$	1.48746	+	0.858786i	0.0714828	+	0.0412706i	0.535315	−	0.844652i	$-0.320193\pi$
$433$	1.48746	+	0.858786i	0.0714828	+	0.0412706i	−0.463833	+	0.885923i	$0.653526\pi$
$434$	−2.01138	−	2.46811i	−0.0965493	−	0.118473i
$435$	−9.98196	−	5.76309i	−0.478598	−	0.276319i
$436$	−7.65020	−	23.0560i	−0.366378	−	1.10418i
$437$	5.98904	−	10.3733i	0.286494	−	0.496223i
$438$	5.56259	+	6.82572i	0.265791	+	0.326145i
$439$	26.8671	−	15.5118i	1.28230	−	0.740336i	0.305031	−	0.952343i	$-0.401333\pi$
$439$	26.8671	−	15.5118i	1.28230	−	0.740336i	0.977268	+	0.212007i	$0.0679999\pi$
$440$	−20.4150	−	0.879032i	−0.973246	−	0.0419062i
$441$	3.25047	+	5.62998i	0.154784	+	0.268094i
$442$	−29.8258	−	11.3428i	−1.41867	−	0.539520i
$443$	20.1146	−	34.8395i	0.955673	−	1.65527i	0.222853	−	0.974852i	$-0.428463\pi$
$443$	20.1146	−	34.8395i	0.955673	−	1.65527i	0.732820	−	0.680422i	$-0.238204\pi$
$444$	−2.26529	−	2.01431i	−0.107506	−	0.0955948i
$445$			26.5282i			1.25756i
$446$	1.07857	+	6.67539i	0.0510716	+	0.316089i
$447$	−8.06155			−0.381298
$448$	−2.39459	−	5.11913i	−0.113134	−	0.241856i
$449$	13.3053	−	23.0455i	0.627917	−	1.08758i	−0.360052	−	0.932932i	$-0.617241\pi$
$449$	13.3053	−	23.0455i	0.627917	−	1.08758i	0.987969	−	0.154652i	$-0.0494257\pi$
$450$	12.1372	−	1.96104i	0.572151	−	0.0924444i
$451$	−8.23159	+	4.75251i	−0.387610	+	0.223787i
$452$	21.9965	+	4.53272i	1.03463	+	0.213201i
$453$	0.397241	−	0.229347i	0.0186640	−	0.0107757i
$454$	17.6791	+	6.72337i	0.829721	+	0.315543i
$455$	12.1874			0.571356
$456$	4.46635	−	7.02008i	0.209156	−	0.328745i
$457$	11.7989	−	20.4364i	0.551932	−	0.955973i	−0.446204	−	0.894931i	$-0.647224\pi$
$457$	11.7989	−	20.4364i	0.551932	−	0.955973i	0.998135	−	0.0610420i	$-0.0194424\pi$
$458$	−14.1732	+	11.5504i	−0.662270	+	0.539714i
$459$	−2.41991	−	4.19141i	−0.112952	−	0.195638i
$460$	22.5198	+	20.0247i	1.04999	+	0.933657i
$461$	40.3276			1.87825			0.939123	−	0.343581i	$-0.111640\pi$
$461$	40.3276			1.87825			0.939123	+	0.343581i	$0.111640\pi$
$462$	−1.23217	−	1.51197i	−0.0573258	−	0.0703431i
$463$	6.98568	+	12.0996i	0.324652	+	0.562314i	0.981442	−	0.191760i	$-0.0614194\pi$
$463$	6.98568	+	12.0996i	0.324652	+	0.562314i	−0.656790	+	0.754074i	$0.728086\pi$
$464$	−1.45634	−	12.3737i	−0.0676089	−	0.574435i
$465$	10.2131	+	5.89656i	0.473623	+	0.273446i
$466$	−20.9802	−	7.97880i	−0.971891	−	0.369611i
$467$	16.8631	−	9.73592i	0.780331	−	0.450525i	−0.0562163	−	0.998419i	$-0.517904\pi$
$467$	16.8631	−	9.73592i	0.780331	−	0.450525i	0.836548	+	0.547894i	$0.184570\pi$
$468$	6.19588	−	6.96787i	0.286404	−	0.322090i
$469$	5.78180	−	0.0862341i	0.266979	−	0.00398192i
$470$	2.83425	−	7.45266i	0.130734	−	0.343765i
$471$	−1.58029	−	2.73714i	−0.0728158	−	0.126121i
$472$	9.07149	+	17.4006i	0.417549	+	0.800928i
$473$	1.42692	−	2.47150i	0.0656098	−	0.113640i
$474$	3.46477	−	9.11061i	0.159142	−	0.418464i
$475$	−22.1478	+	12.7870i	−1.01621	+	0.586709i
$476$	6.49012	−	2.15348i	0.297474	−	0.0987046i
$477$			9.51083i			0.435471i
$478$	14.5940	−	38.3748i	0.667513	−	1.75522i
$479$	23.7653	−	13.7209i	1.08586	−	0.626924i	0.153392	−	0.988165i	$-0.450980\pi$
$479$	23.7653	−	13.7209i	1.08586	−	0.626924i	0.932473	+	0.361241i	$0.117647\pi$
$480$	15.0303	+	14.5700i	0.686034	+	0.665027i
$481$	6.11947	+	3.53308i	0.279024	+	0.161095i
$482$	−38.0759	+	6.15206i	−1.73431	+	0.280219i
$483$			2.87647i			0.130884i
$484$	10.7438	+	9.55347i	0.488355	+	0.434248i
$485$	7.68184	+	13.3053i	0.348814	+	0.604164i
$486$	1.39611	−	0.225574i	0.0633287	−	0.0102322i
$487$	−8.39027	−	14.5324i	−0.380199	−	0.658525i	0.610891	−	0.791715i	$-0.290811\pi$
$487$	−8.39027	−	14.5324i	−0.380199	−	0.658525i	−0.991091	+	0.133190i	$0.957478\pi$
$488$	10.9650	−	17.2345i	0.496364	−	0.780170i
$489$	−13.9617	−	8.06078i	−0.631369	−	0.364521i
$490$	26.3727	−	21.4924i	1.19140	−	0.970925i
$491$		−	4.37498i		−	0.197440i	−0.995115	−	0.0987200i	$-0.968525\pi$
$491$		−	4.37498i		−	0.197440i	0.995115	−	0.0987200i	$-0.0314748\pi$
$492$	9.53685	+	1.96521i	0.429954	+	0.0885987i
$493$	15.0750			0.678942
$494$	−6.89432	+	18.1286i	−0.310190	+	0.815644i
$495$	6.25658	+	3.61224i	0.281212	+	0.162358i
$496$	1.49007	+	12.6603i	0.0669061	+	0.568463i
$497$	8.69902	−	5.02238i	0.390205	−	0.225285i
$498$	−18.7179	+	15.2540i	−0.838768	+	0.683550i
$499$	5.81192	+	10.0665i	0.260177	+	0.450640i	0.966289	−	0.257461i	$-0.0828857\pi$
$499$	5.81192	+	10.0665i	0.260177	+	0.450640i	−0.706112	+	0.708100i	$0.749552\pi$
$500$	−8.60879	−	25.9450i	−0.384997	−	1.16030i
$501$	15.5367	+	8.97012i	0.694129	+	0.400756i
$502$	14.8678	+	18.2439i	0.663583	+	0.814267i
$503$	−10.0543	+	17.4146i	−0.448300	+	0.776479i	−0.998276	−	0.0587022i	$-0.981304\pi$
$503$	−10.0543	+	17.4146i	−0.448300	+	0.776479i	0.549975	+	0.835181i	$0.314637\pi$
$504$	−0.0859553	+	1.99626i	−0.00382876	+	0.0889205i
$505$	20.6970	−	35.8482i	0.921002	−	1.59522i
$506$	1.79317	+	11.0982i	0.0797163	+	0.493375i
$507$	−4.36752	+	7.56476i	−0.193968	+	0.335963i
$508$	8.20909	+	1.69161i	0.364219	+	0.0750530i
$509$	−15.7821			−0.699531			−0.349765	−	0.936837i	$-0.613739\pi$
$509$	−15.7821			−0.699531			−0.349765	+	0.936837i	$0.613739\pi$
$510$	−19.6340	+	16.0006i	−0.869406	+	0.708519i
$511$	4.39847			0.194577
$512$	−2.91298	+	22.4391i	−0.128737	+	0.991679i
$513$	−2.54760	+	1.47086i	−0.112479	+	0.0649400i
$514$	−12.7701	+	33.5788i	−0.563263	+	1.48110i
$515$	14.9447	−	25.8850i	0.658543	−	1.14063i
$516$	−2.77480	+	0.920703i	−0.122154	+	0.0405317i
$517$	2.57602	−	1.48726i	0.113293	−	0.0654098i
$518$	−1.49485	+	0.241527i	−0.0656798	+	0.0106121i
$519$	2.39642	+	4.15072i	0.105191	+	0.182196i
$520$	−41.1698	−	26.1933i	−1.80542	−	1.14865i
$521$		−	11.9864i		−	0.525133i	−0.964914	−	0.262567i	$-0.915431\pi$
$521$		−	11.9864i		−	0.525133i	0.964914	−	0.262567i	$-0.0845690\pi$
$522$	−1.56580	+	4.11727i	−0.0685333	+	0.180208i
$523$	13.7342	−	7.92947i	0.600557	−	0.346732i	−0.168704	−	0.985667i	$-0.553958\pi$
$523$	13.7342	−	7.92947i	0.600557	−	0.346732i	0.769261	+	0.638935i	$0.220625\pi$
$524$	−11.6296	−	35.0491i	−0.508042	−	1.53113i
$525$	3.07074	−	5.31867i	0.134018	−	0.232126i
$526$	3.65898	+	22.6459i	0.159539	+	0.987408i
$527$	−15.4241			−0.671884
$528$	0.912817	+	7.75569i	0.0397253	+	0.337523i
$529$	−3.21025	+	5.56032i	−0.139576	+	0.241753i
$530$	49.1355	−	7.93900i	2.13431	−	0.344848i
$531$		−	6.93788i		−	0.301078i
$532$	−1.30892	−	3.94480i	−0.0567489	−	0.171029i
$533$	−22.6979			−0.983155
$534$	10.0085	−	1.61711i	0.433110	−	0.0699791i
$535$	−63.8134			−2.75889
$536$	−19.7166	−	12.1350i	−0.851626	−	0.524150i
$537$	4.43228			0.191267
$538$	−10.5981	+	1.71237i	−0.456917	+	0.0738257i
$539$	12.6918			0.546676
$540$	−2.33075	−	7.02438i	−0.100300	−	0.302281i
$541$			34.0628i			1.46448i	0.681049	+	0.732238i	$0.261524\pi$
$541$			34.0628i			1.46448i	−0.681049	+	0.732238i	$0.738476\pi$
$542$	−11.8393	+	1.91291i	−0.508541	+	0.0821667i
$543$	−8.33135	+	14.4303i	−0.357532	+	0.619264i
$544$	−26.5522	−	6.67400i	−1.13842	−	0.286145i
$545$	44.9462			1.92528
$546$	−0.742922	−	4.59805i	−0.0317941	−	0.196778i
$547$	15.4020	−	26.6770i	0.658541	−	1.14063i	−0.322452	−	0.946586i	$-0.604507\pi$
$547$	15.4020	−	26.6770i	0.658541	−	1.14063i	0.980993	−	0.194041i	$-0.0621596\pi$
$548$	−1.21238	−	3.65384i	−0.0517902	−	0.156084i
$549$	−6.25445	+	3.61101i	−0.266934	+	0.154114i
$550$	8.53209	−	22.4351i	0.363810	−	0.956637i
$551$		−	9.16280i		−	0.390348i
$552$	6.18211	−	9.71686i	0.263128	−	0.413577i
$553$	−2.43449	−	4.21667i	−0.103525	−	0.179311i
$554$	26.2957	−	4.24869i	1.11720	−	0.180510i
$555$	4.85727	−	2.80435i	0.206180	−	0.119038i
$556$	−42.5735	+	14.1263i	−1.80552	+	0.599088i
$557$	7.41239	−	12.8386i	0.314073	−	0.543990i	−0.665167	−	0.746695i	$-0.731640\pi$
$557$	7.41239	−	12.8386i	0.314073	−	0.543990i	0.979240	+	0.202704i	$0.0649730\pi$
$558$	1.60207	−	4.21263i	0.0678208	−	0.178335i
$559$	5.90191	−	3.40747i	0.249624	−	0.144121i
$560$	10.3850	−	1.22227i	0.438845	−	0.0516505i
$561$	−9.44880			−0.398929
$562$	22.3682	−	18.2288i	0.943545	−	0.768938i
$563$	3.46863			0.146185			0.0730927	−	0.997325i	$-0.476713\pi$
$563$	3.46863			0.146185			0.0730927	+	0.997325i	$0.476713\pi$
$564$	−2.98449	−	0.614999i	−0.125670	−	0.0258961i
$565$	−20.7770	+	35.9868i	−0.874095	+	1.51398i
$566$	−5.54415	−	34.3135i	−0.233038	−	1.44230i
$567$	0.353219	−	0.611794i	0.0148338	−	0.0256929i
$568$	−40.1799	−	1.73007i	−1.68591	−	0.0725922i
$569$	18.1953	−	31.5152i	0.762786	−	1.32118i	−0.178623	−	0.983918i	$-0.557164\pi$
$569$	18.1953	−	31.5152i	0.762786	−	1.32118i	0.941409	−	0.337267i	$-0.109502\pi$
$570$	9.72543	+	11.9338i	0.407353	+	0.499853i
$571$	−17.2734	−	9.97279i	−0.722868	−	0.417348i	0.0929392	−	0.995672i	$-0.470374\pi$
$571$	−17.2734	−	9.97279i	−0.722868	−	0.417348i	−0.815807	+	0.578324i	$0.803707\pi$
$572$	−5.73279	−	17.2774i	−0.239700	−	0.722403i
$573$	4.91644	+	8.51552i	0.205387	+	0.355741i
$574$	3.77051	−	3.07276i	0.157378	−	0.128255i
$575$	−30.6559	+	17.6992i	−1.27844	+	0.738108i
$576$	4.58072	−	6.55873i	0.190863	−	0.273281i
$577$	−22.9167	−	13.2310i	−0.954034	−	0.550812i	−0.0597025	−	0.998216i	$-0.519015\pi$
$577$	−22.9167	−	13.2310i	−0.954034	−	0.550812i	−0.894332	+	0.447404i	$0.852349\pi$
$578$	3.22927	−	8.49136i	0.134320	−	0.353194i
$579$	−15.2168			−0.632388
$580$	22.5780	+	4.65254i	0.937499	+	0.193186i
$581$			12.0617i			0.500405i
$582$	4.55153	−	3.70925i	0.188667	−	0.153753i
$583$	16.0804	+	9.28403i	0.665982	+	0.384505i
$584$	−14.8583	−	9.45320i	−0.614839	−	0.391176i
$585$	8.62598	+	14.9406i	0.356640	+	0.617719i
$586$	35.4979	−	5.73552i	1.46641	−	0.236932i
$587$	21.9442	+	38.0084i	0.905733	+	1.56878i	0.819930	+	0.572464i	$0.194012\pi$
$587$	21.9442	+	38.0084i	0.905733	+	1.56878i	0.0858036	+	0.996312i	$0.472654\pi$
$588$	−9.71620	−	8.63971i	−0.400689	−	0.356295i
$589$			9.37501i			0.386291i
$590$	−35.8429	+	5.79127i	−1.47563	+	0.238423i
$591$	13.9200	+	8.03674i	0.572594	+	0.330587i
$592$	5.56876	+	2.39683i	0.228875	+	0.0985092i
$593$	−40.5416	+	23.4067i	−1.66484	+	0.961198i	−0.694493	+	0.719499i	$0.744371\pi$
$593$	−40.5416	+	23.4067i	−1.66484	+	0.961198i	−0.970351	+	0.241699i	$0.922295\pi$
$594$	0.981426	−	2.58066i	0.0402684	−	0.105886i
$595$			12.6521i			0.518684i
$596$	15.3027	−	5.07757i	0.626823	−	0.207985i
$597$	12.6422	−	7.29900i	0.517413	−	0.298728i
$598$	−9.54280	+	25.0928i	−0.390234	+	1.02612i
$599$	−14.1712	+	24.5452i	−0.579018	+	1.00289i	0.416574	+	0.909102i	$0.363231\pi$
$599$	−14.1712	+	24.5452i	−0.579018	+	1.00289i	−0.995592	+	0.0937870i	$0.970103\pi$
$600$	−21.8040	+	11.3671i	−0.890144	+	0.464060i
$601$	−12.1708	−	21.0804i	−0.496456	−	0.859887i	0.503536	−	0.863975i	$-0.332032\pi$
$601$	−12.1708	−	21.0804i	−0.496456	−	0.859887i	−0.999992	+	0.00408727i	$0.998699\pi$
$602$	−0.519118	+	1.36502i	−0.0211577	+	0.0556340i
$603$	4.19794	+	7.02690i	0.170953	+	0.286158i
$604$	−0.609602	+	0.685557i	−0.0248043	+	0.0278949i
$605$	−23.0371	+	13.3005i	−0.936590	+	0.540741i
$606$	−14.7863	−	5.62326i	−0.600654	−	0.228429i
$607$	−22.2472	−	12.8444i	−0.902984	−	0.521338i	−0.0248171	−	0.999692i	$-0.507900\pi$
$607$	−22.2472	−	12.8444i	−0.902984	−	0.521338i	−0.878167	+	0.478354i	$0.841234\pi$
$608$	−4.05656	+	16.1389i	−0.164515	+	0.654518i
$609$	1.10020	+	1.90560i	0.0445823	+	0.0772188i
$610$	23.8762	+	29.2980i	0.966721	+	1.18624i
$611$	7.10314			0.287362
$612$	7.23351	+	6.43208i	0.292397	+	0.260001i
$613$	−4.99936	−	8.65914i	−0.201922	−	0.349740i	0.747226	−	0.664571i	$-0.231385\pi$
$613$	−4.99936	−	8.65914i	−0.201922	−	0.349740i	−0.949148	+	0.314831i	$0.898052\pi$
$614$	−9.97273	+	8.12723i	−0.402467	+	0.327988i
$615$	−9.00811	+	15.6025i	−0.363242	+	0.629154i
$616$	3.29126	+	2.09398i	0.132609	+	0.0843690i
$617$	−17.8103			−0.717016			−0.358508	−	0.933527i	$-0.616714\pi$
$617$	−17.8103			−0.717016			−0.358508	+	0.933527i	$0.616714\pi$
$618$	−10.6768	−	4.06041i	−0.429485	−	0.163333i
$619$	−23.2473	+	13.4218i	−0.934387	+	0.539468i	−0.888196	−	0.459464i	$-0.848041\pi$
$619$	−23.2473	+	13.4218i	−0.934387	+	0.539468i	−0.0461905	+	0.998933i	$0.514708\pi$
$620$	−23.1009	−	4.76029i	−0.927754	−	0.191178i
$621$	−3.52628	+	2.03590i	−0.141505	+	0.0816977i
$622$	3.52735	−	0.569925i	0.141434	−	0.0228519i
$623$	2.53218	−	4.38586i	0.101450	−	0.175716i
$624$	−7.37249	+	17.1291i	−0.295136	+	0.685714i
$625$	7.11029			0.284411
$626$	4.14378	+	25.6464i	0.165619	+	1.02504i
$627$			5.74313i			0.229359i
$628$	4.72374	+	4.20038i	0.188498	+	0.167613i
$629$	−3.66777	+	6.35277i	−0.146244	+	0.253301i
$630$	−3.45553	−	1.31414i	−0.137672	−	0.0523567i
$631$	7.38254	+	12.7869i	0.293894	+	0.509040i	0.974727	−	0.223399i	$-0.0717153\pi$
$631$	7.38254	+	12.7869i	0.293894	+	0.509040i	−0.680833	+	0.732439i	$0.738382\pi$
$632$	−0.838616	+	19.4763i	−0.0333584	+	0.774727i
$633$	7.89775	−	4.55977i	0.313907	−	0.181234i
$634$	−12.4988	−	15.3370i	−0.496393	−	0.609112i
$635$	−7.75396	+	13.4303i	−0.307707	+	0.532963i
$636$	−5.99041	−	18.0538i	−0.237535	−	0.715879i
$637$	26.2475	+	15.1540i	1.03996	+	0.600423i
$638$	5.43280	+	6.66646i	0.215087	+	0.263928i
$639$	12.3139	+	7.10944i	0.487131	+	0.281245i
$640$	−37.7079	−	18.1905i	−1.49053	−	0.719042i
$641$	−7.49304	−	4.32611i	−0.295957	−	0.170871i	0.344668	−	0.938725i	$-0.387991\pi$
$641$	−7.49304	−	4.32611i	−0.295957	−	0.170871i	−0.640625	+	0.767854i	$0.721325\pi$
$642$	3.88993	+	24.0753i	0.153523	+	0.950177i
$643$			38.8404i			1.53172i	0.643009	+	0.765859i	$0.277686\pi$
$643$			38.8404i			1.53172i	−0.643009	+	0.765859i	$0.722314\pi$
$644$	−1.81175	−	5.46021i	−0.0713929	−	0.215162i
$645$		−	5.40929i		−	0.212990i
$646$	−18.8197	−	7.15715i	−0.740452	−	0.281594i
$647$	−14.5991	−	25.2863i	−0.573949	−	0.994108i	−0.996155	−	0.0876086i	$-0.972078\pi$
$647$	−14.5991	−	25.2863i	−0.573949	−	0.994108i	0.422206	−	0.906500i	$-0.361256\pi$
$648$	−2.50806	+	1.30753i	−0.0985259	+	0.0513647i
$649$	−11.7302	−	6.77243i	−0.460450	−	0.265841i
$650$	44.4323	−	36.2099i	1.74278	−	1.42027i
$651$	−1.12568	−	1.94973i	−0.0441189	−	0.0764161i
$652$	31.5796	+	6.50746i	1.23675	+	0.254852i
$653$	−11.3269	+	6.53958i	−0.443256	+	0.255914i	−0.704978	−	0.709230i	$-0.749043\pi$
$653$	−11.3269	+	6.53958i	−0.443256	+	0.255914i	0.261722	+	0.965143i	$0.415710\pi$
$654$	−2.73983	−	16.9572i	−0.107136	−	0.663078i
$655$	68.3260			2.66972
$656$	−19.3410	+	2.27636i	−0.755137	+	0.0888770i
$657$	3.11313	+	5.39210i	0.121455	+	0.210366i
$658$	−1.17995	+	0.961598i	−0.0459994	+	0.0374870i
$659$	−6.10852	−	3.52675i	−0.237954	−	0.137383i	0.376282	−	0.926505i	$-0.377202\pi$
$659$	−6.10852	−	3.52675i	−0.237954	−	0.137383i	−0.614236	+	0.789122i	$0.710536\pi$
$660$	−14.1516	−	2.91615i	−0.550851	−	0.113511i
$661$		−	13.9179i		−	0.541344i	−0.962672	−	0.270672i	$-0.912754\pi$
$661$		−	13.9179i		−	0.541344i	0.962672	−	0.270672i	$-0.0872459\pi$
$662$	3.90121	−	10.2582i	0.151625	−	0.398697i
$663$	−19.5407	−	11.2818i	−0.758897	−	0.438150i
$664$	25.9231	−	40.7452i	1.00601	−	1.58122i
$665$	7.69013			0.298211
$666$	−1.35411	−	1.66159i	−0.0524705	−	0.0643853i
$667$		−	12.6827i		−	0.491077i
$668$	−35.1421	−	7.24157i	−1.35969	−	0.280185i
$669$			4.78143i			0.184861i
$670$	32.7987	−	27.5533i	1.26713	−	1.06448i
$671$			14.0996i			0.544309i
$672$	−1.09418	−	3.84350i	−0.0422090	−	0.148266i
$673$		−	16.7551i		−	0.645863i	−0.946422	−	0.322932i	$-0.895332\pi$
$673$		−	16.7551i		−	0.645863i	0.946422	−	0.322932i	$-0.104668\pi$
$674$	−20.2867	+	16.5326i	−0.781415	+	0.636811i
$675$	8.69357			0.334616
$676$	3.52589	−	17.1106i	0.135611	−	0.658099i
$677$	−24.2877	−	14.0225i	−0.933451	−	0.538928i	−0.0455498	−	0.998962i	$-0.514504\pi$
$677$	−24.2877	−	14.0225i	−0.933451	−	0.538928i	−0.887901	+	0.460034i	$0.847837\pi$
$678$	14.8435	+	5.64501i	0.570062	+	0.216795i
$679$		−	2.93299i		−	0.112558i
$680$	27.1918	−	42.7393i	1.04276	−	1.63898i
$681$	11.5826	+	6.68725i	0.443848	+	0.256256i
$682$	−5.55862	−	6.82085i	−0.212851	−	0.261184i
$683$	−1.90877	−	3.30608i	−0.0730369	−	0.126504i	0.827194	−	0.561916i	$-0.189936\pi$
$683$	−1.90877	−	3.30608i	−0.0730369	−	0.126504i	−0.900231	+	0.435413i	$0.856602\pi$
$684$	3.90952	−	4.39664i	0.149484	−	0.168110i
$685$	7.12292			0.272153
$686$	−13.3155	+	2.15143i	−0.508388	+	0.0821420i
$687$	−11.1964	+	6.46424i	−0.427169	+	0.246626i
$688$	4.68730	−	3.49542i	0.178702	−	0.133261i
$689$	22.1702	+	38.3998i	0.844616	+	1.46292i
$690$	13.4615	+	16.5183i	0.512470	+	0.628840i
$691$	−6.05845	−	3.49785i	−0.230474	−	0.133064i	0.380317	−	0.924856i	$-0.375815\pi$
$691$	−6.05845	−	3.49785i	−0.230474	−	0.133064i	−0.610791	+	0.791792i	$0.709148\pi$
$692$	−7.16329	−	6.36964i	−0.272307	−	0.242137i
$693$	−0.689592	−	1.19441i	−0.0261954	−	0.0453718i
$694$	−15.6085	+	41.0425i	−0.592491	+	1.55795i
$695$		−	82.9943i		−	3.14815i
$696$	0.378988	−	8.80176i	0.0143655	−	0.333630i
$697$		−	23.5632i		−	0.892520i
$698$	10.9024	−	1.76154i	0.412662	−	0.0666752i
$699$	−13.7454	−	7.93593i	−0.519900	−	0.300164i
$700$	−2.47900	+	12.0302i	−0.0936974	+	0.454698i
$701$	−15.3020	−	8.83462i	−0.577949	−	0.333679i	0.182369	−	0.983230i	$-0.441624\pi$
$701$	−15.3020	−	8.83462i	−0.577949	−	0.333679i	−0.760318	+	0.649551i	$0.774957\pi$
$702$	5.11094	−	4.16514i	0.192900	−	0.157203i
$703$	3.86131	+	2.22933i	0.145632	+	0.0840808i
$704$	−6.61767	−	14.1472i	−0.249413	−	0.533191i
$705$	2.81902	−	4.88269i	0.106170	−	0.183893i
$706$	21.0559	−	17.1594i	0.792450	−	0.645803i
$707$	−6.84357	+	3.95114i	−0.257379	+	0.148598i
$708$	4.36983	+	13.1697i	0.164228	+	0.494948i
$709$	−3.36268	−	5.82434i	−0.126288	−	0.218738i	0.795948	−	0.605366i	$-0.206973\pi$
$709$	−3.36268	−	5.82434i	−0.126288	−	0.218738i	−0.922236	+	0.386628i	$0.873640\pi$
$710$	26.4505	−	69.5515i	0.992669	−	2.61022i
$711$	3.44615	−	5.96891i	0.129241	−	0.223852i
$712$	−17.9799	+	9.37351i	−0.673826	+	0.351287i
$713$			12.9765i			0.485972i
$714$	4.77334	−	0.771245i	0.178638	−	0.0288631i
$715$	33.6811			1.25960
$716$	−8.41350	+	2.79168i	−0.314427	+	0.104330i
$717$	14.5156	−	25.1417i	0.542094	−	0.938934i
$718$	4.89943	+	30.3233i	0.182845	+	1.13165i
$719$	−5.39456	+	3.11455i	−0.201183	+	0.116153i	−0.597207	−	0.802087i	$-0.703723\pi$
$719$	−5.39456	+	3.11455i	−0.201183	+	0.116153i	0.396024	+	0.918240i	$0.370390\pi$
$720$	8.84862	+	11.8659i	0.329769	+	0.442215i
$721$	−4.94157	+	2.85301i	−0.184034	+	0.106252i
$722$	5.20109	−	13.6763i	0.193565	−	0.508978i
$723$	−27.2729			−1.01429
$724$	6.72589	−	32.6396i	0.249966	−	1.21304i
$725$	−13.5393	+	23.4507i	−0.502836	+	0.870937i
$726$	6.42226	+	7.88060i	0.238352	+	0.292476i
$727$	−15.1169	−	26.1832i	−0.560655	−	0.971082i	−0.997439	−	0.0715164i	$-0.977216\pi$
$727$	−15.1169	−	26.1832i	−0.560655	−	0.971082i	0.436785	−	0.899566i	$-0.356117\pi$
$728$	4.30632	+	8.26023i	0.159603	+	0.306145i
$729$	1.00000			0.0370370
$730$	25.2584	−	20.5842i	0.934857	−	0.761857i
$731$	3.53737	+	6.12691i	0.130834	+	0.226612i
$732$	9.59801	−	10.7939i	0.354753	−	0.398954i
$733$	−0.846063	−	0.488475i	−0.0312501	−	0.0180422i	0.484294	−	0.874906i	$-0.339077\pi$
$733$	−0.846063	−	0.488475i	−0.0312501	−	0.0180422i	−0.515544	+	0.856863i	$0.672410\pi$
$734$	14.5163	−	38.1706i	0.535807	−	1.40890i
$735$	20.8337	−	12.0283i	0.768461	−	0.443671i
$736$	−5.61491	+	22.3387i	−0.206968	+	0.823415i
$737$	15.9785	−	0.238316i	0.588577	−	0.00877847i
$738$	6.43558	+	2.44746i	0.236897	+	0.0900921i
$739$	−3.34084	−	5.78650i	−0.122895	−	0.212860i	0.798013	−	0.602640i	$-0.205884\pi$
$739$	−3.34084	−	5.78650i	−0.122895	−	0.212860i	−0.920908	+	0.389780i	$0.872551\pi$
$740$	−7.45391	+	8.38266i	−0.274011	+	0.308153i
$741$	−6.85727	+	11.8771i	−0.251908	+	0.436318i
$742$	−8.88128	−	3.37756i	−0.326042	−	0.123994i
$743$	6.22953	−	3.59662i	0.228539	−	0.131947i	−0.381359	−	0.924427i	$-0.624544\pi$
$743$	6.22953	−	3.59662i	0.228539	−	0.131947i	0.609898	+	0.792480i	$0.291210\pi$
$744$	−0.387765	+	9.00561i	−0.0142162	+	0.330162i
$745$			29.8316i			1.09295i
$746$	−28.8063	−	10.9551i	−1.05468	−	0.401094i
$747$	−14.7865	+	8.53701i	−0.541011	+	0.312353i
$748$	17.9360	−	5.95134i	0.655806	−	0.217602i
$749$	10.5501	+	6.09113i	0.385494	+	0.222565i
$750$	−3.08314	−	19.0820i	−0.112580	−	0.696775i
$751$		−	6.57827i		−	0.240045i	−0.992771	−	0.120022i	$-0.961703\pi$
$751$		−	6.57827i		−	0.240045i	0.992771	−	0.120022i	$-0.0382966\pi$
$752$	6.05261	−	0.712370i	0.220716	−	0.0259775i
$753$	8.32086	+	14.4122i	0.303229	+	0.525208i
$754$	3.27564	+	20.2734i	0.119292	+	0.738313i
$755$	−0.848696	−	1.46998i	−0.0308872	−	0.0534982i
$756$	−0.285154	+	1.38380i	−0.0103709	+	0.0503284i
$757$	−19.6906	−	11.3684i	−0.715666	−	0.413190i	0.0974896	−	0.995237i	$-0.468919\pi$
$757$	−19.6906	−	11.3684i	−0.715666	−	0.413190i	−0.813155	+	0.582047i	$0.802252\pi$
$758$	3.81583	+	4.68232i	0.138597	+	0.170069i
$759$			7.94938i			0.288544i
$760$	−25.9777	−	16.5276i	−0.942309	−	0.599520i
$761$	17.2590			0.625637			0.312819	−	0.949813i	$-0.398727\pi$
$761$	17.2590			0.625637			0.312819	+	0.949813i	$0.398727\pi$
$762$	5.53960	+	2.10671i	0.200678	+	0.0763181i
$763$	−7.43087	−	4.29021i	−0.269016	−	0.155316i
$764$	−14.6960	−	13.0678i	−0.531684	−	0.472777i
$765$	−15.5102	+	8.95483i	−0.560773	+	0.323763i
$766$	−31.4809	−	38.6295i	−1.13745	−	1.39574i
$767$	−16.1725	−	28.0116i	−0.583955	−	1.01144i
$768$	−4.56426	+	15.3352i	−0.164698	+	0.553360i
$769$	−17.9769	−	10.3790i	−0.648264	−	0.374275i	0.139527	−	0.990218i	$-0.455442\pi$
$769$	−17.9769	−	10.3790i	−0.648264	−	0.374275i	−0.787791	+	0.615943i	$0.788775\pi$
$770$	−5.59501	+	4.55963i	−0.201630	+	0.164318i
$771$	−12.7014	+	21.9995i	−0.457431	+	0.792294i
$772$	28.8850	−	9.58431i	1.03959	−	0.344947i
$773$	−3.60995	+	6.25261i	−0.129841	+	0.224891i	−0.923615	−	0.383322i	$-0.874780\pi$
$773$	−3.60995	+	6.25261i	−0.129841	+	0.224891i	0.793774	+	0.608213i	$0.208113\pi$
$774$	−2.04080	+	0.329739i	−0.0733551	+	0.0118522i
$775$	13.8528	−	23.9938i	0.497608	−	0.861883i
$776$	−6.30359	+	9.90780i	−0.226286	+	0.355669i
$777$	−1.07072			−0.0384120
$778$	19.2069	+	23.5683i	0.688601	+	0.844966i
$779$	−14.3221			−0.513142
$780$	−25.7845	−	22.9277i	−0.923233	−	0.820944i
$781$	24.0405	−	13.8798i	0.860238	−	0.496658i
$782$	−26.0494	−	9.90660i	−0.931524	−	0.354259i
$783$	−1.55739	+	2.69748i	−0.0556565	+	0.0963999i
$784$	23.8853	+	10.2804i	0.853048	+	0.367158i
$785$	−10.1287	+	5.84783i	−0.361510	+	0.208718i
$786$	−4.16502	−	25.7779i	−0.148561	−	0.919466i
$787$	−26.2497	−	45.4658i	−0.935699	−	1.62068i	−0.773382	−	0.633940i	$-0.781436\pi$
$787$	−26.2497	−	45.4658i	−0.935699	−	1.62068i	−0.162318	−	0.986739i	$-0.551897\pi$
$788$	−31.4854	−	6.48805i	−1.12162	−	0.231127i
$789$			16.2207i			0.577474i
$790$	−33.7136	−	12.8213i	−1.19948	−	0.456162i
$791$	6.87004	−	3.96642i	0.244271	−	0.141030i
$792$	−0.237545	+	5.51684i	−0.00844080	+	0.196032i
$793$	−16.8348	+	29.1588i	−0.597822	+	1.03546i
$794$	35.4962	−	5.73525i	1.25971	−	0.203536i
$795$	35.1947			1.24823
$796$	−19.4006	+	21.8179i	−0.687637	+	0.773316i
$797$	11.5294	−	19.9695i	0.408392	−	0.707356i	−0.586317	−	0.810081i	$-0.699423\pi$
$797$	11.5294	−	19.9695i	0.408392	−	0.707356i	0.994710	+	0.102725i	$0.0327562\pi$
$798$	−0.468775	−	2.90131i	−0.0165945	−	0.102705i
$799$			7.37393i			0.260871i
$800$	34.2295	−	35.3107i	1.21019	−	1.24842i
$801$	7.16886			0.253299
$802$	−4.76423	−	29.4864i	−0.168231	−	1.04120i
$803$	12.1556			0.428961
$804$	−12.3946	−	10.6946i	−0.437122	−	0.377170i
$805$	10.6443			0.375163
$806$	−3.35150	−	20.7429i	−0.118052	−	0.730638i
$807$	−7.59119			−0.267223
$808$	31.6097	+	1.36106i	1.11203	+	0.0478819i
$809$		−	0.137142i		−	0.00482166i	−0.999997	−	0.00241083i	$-0.999233\pi$
$809$		−	0.137142i		−	0.00482166i	0.999997	−	0.00241083i	$-0.000767392\pi$
$810$	−0.834732	−	5.16627i	−0.0293295	−	0.181524i
$811$	19.6482	−	34.0316i	0.689940	−	1.19501i	−0.281917	−	0.959439i	$-0.590970\pi$
$811$	19.6482	−	34.0316i	0.689940	−	1.19501i	0.971857	−	0.235573i	$-0.0756965\pi$
$812$	−3.28868	−	2.92431i	−0.115410	−	0.102623i
$813$	−8.48021			−0.297414
$814$	−4.13114	+	0.667483i	−0.144796	+	0.0233953i
$815$	−29.8288	+	51.6650i	−1.04486	+	1.80974i
$816$	−17.7821	−	7.65355i	−0.622499	−	0.267928i
$817$	3.72403	−	2.15007i	0.130287	−	0.0752215i
$818$	−51.4545	−	19.5682i	−1.79907	−	0.684186i
$819$		−	3.29348i		−	0.115083i
$820$	7.27224	−	35.2909i	0.253958	−	1.23241i
$821$	12.5570	+	21.7494i	0.438242	+	0.759058i	0.997554	−	0.0698993i	$-0.0222678\pi$
$821$	12.5570	+	21.7494i	0.438242	+	0.759058i	−0.559312	+	0.828958i	$0.688934\pi$
$822$	−0.434199	−	2.68732i	−0.0151444	−	0.0937309i
$823$	2.45501	−	1.41740i	0.0855763	−	0.0494075i	−0.456601	−	0.889671i	$-0.650933\pi$
$823$	2.45501	−	1.41740i	0.0855763	−	0.0494075i	0.542178	+	0.840264i	$0.317600\pi$
$824$	22.8246	+	0.982784i	0.795131	+	0.0342369i
$825$	8.48625	−	14.6986i	0.295453	−	0.511740i
$826$	6.47863	+	2.46383i	0.225421	+	0.0857276i
$827$	−18.1816	+	10.4971i	−0.632235	+	0.365021i	−0.781617	−	0.623759i	$-0.785605\pi$
$827$	−18.1816	+	10.4971i	−0.632235	+	0.365021i	0.149382	+	0.988780i	$0.452271\pi$
$828$	5.41138	−	6.08563i	0.188058	−	0.211490i
$829$	−23.3424			−0.810717			−0.405358	−	0.914158i	$-0.632853\pi$
$829$	−23.3424			−0.810717			−0.405358	+	0.914158i	$0.632853\pi$
$830$	56.4473	+	69.2651i	1.95931	+	2.40423i
$831$	18.8350			0.653380
$832$	3.20591	−	37.1586i	0.111145	−	1.28824i
$833$	−15.7317	+	27.2481i	−0.545071	+	0.944090i
$834$	−31.3119	+	5.05916i	−1.08424	+	0.175185i
$835$	33.1938	−	57.4933i	1.14872	−	1.98964i
$836$	−3.61732	−	10.9018i	−0.125108	−	0.377047i
$837$	1.59346	−	2.75995i	0.0550779	−	0.0953978i
$838$	−12.7794	+	10.4146i	−0.441459	+	0.359765i
$839$	−10.0771	−	5.81802i	−0.347900	−	0.200860i	0.315860	−	0.948806i	$-0.397707\pi$
$839$	−10.0771	−	5.81802i	−0.347900	−	0.200860i	−0.663760	+	0.747946i	$0.731040\pi$
$840$	7.38712	+	0.318076i	0.254880	+	0.0109747i
$841$	9.64908	+	16.7127i	0.332727	+	0.576300i
$842$	17.9304	+	22.0020i	0.617923	+	0.758238i
$843$	17.6702	−	10.2019i	0.608593	−	0.351371i
$844$	−12.1198	+	13.6299i	−0.417180	+	0.469161i
$845$	27.9933	+	16.1619i	0.962998	+	0.555987i
$846$	−2.01397	−	0.765914i	−0.0692417	−	0.0263327i
$847$	5.07823			0.174490
$848$	22.7424	+	30.4972i	0.780976	+	1.04728i
$849$		−	24.5780i		−	0.843514i
$850$	37.5903	+	46.1262i	1.28934	+	1.58212i
$851$	5.34465	+	3.08574i	0.183212	+	0.105778i
$852$	−27.8526	−	5.73945i	−0.954213	−	0.196630i
$853$	5.39495	+	9.34432i	0.184719	+	0.319944i	0.943482	−	0.331424i	$-0.107529\pi$
$853$	5.39495	+	9.34432i	0.184719	+	0.319944i	−0.758762	+	0.651367i	$0.774196\pi$
$854$	−1.15086	−	7.12282i	−0.0393816	−	0.243738i
$855$	5.44289	+	9.42736i	0.186143	+	0.322409i
$856$	−22.5479	−	43.2505i	−0.770670	−	1.47827i
$857$		−	37.2685i		−	1.27307i	−0.771249	−	0.636533i	$-0.780368\pi$
$857$		−	37.2685i		−	1.27307i	0.771249	−	0.636533i	$-0.219632\pi$
$858$	−2.05313	−	12.7071i	−0.0700928	−	0.433814i
$859$	−16.6826	−	9.63168i	−0.569202	−	0.328629i	0.187629	−	0.982240i	$-0.439920\pi$
$859$	−16.6826	−	9.63168i	−0.569202	−	0.328629i	−0.756830	+	0.653611i	$0.773253\pi$
$860$	3.40704	+	10.2681i	0.116179	+	0.350139i
$861$	2.97859	−	1.71969i	0.101510	−	0.0586068i
$862$	9.64195	+	3.66684i	0.328406	+	0.124893i
$863$			41.3733i			1.40836i	0.710020	+	0.704182i	$0.248686\pi$
$863$			41.3733i			1.40836i	−0.710020	+	0.704182i	$0.751314\pi$
$864$	3.93733	−	4.06170i	0.133951	−	0.138182i
$865$	15.3597	−	8.86790i	0.522244	−	0.301518i
$866$	−2.27037	−	0.863425i	−0.0771505	−	0.0293404i
$867$	3.21192	−	5.56320i	0.109082	−	0.188936i
$868$	3.36484	+	2.99204i	0.114210	+	0.101556i
$869$	−6.72794	−	11.6531i	−0.228230	−	0.395306i
$870$	15.2359	+	5.79422i	0.516545	+	0.196442i
$871$	33.3291	+	18.5854i	1.12931	+	0.629743i
$872$	15.8813	+	30.4630i	0.537810	+	1.03161i
$873$	3.59557	−	2.07590i	0.121691	−	0.0702586i
$874$	−6.02139	+	15.8332i	−0.203677	+	0.535567i
$875$	−8.36198	−	4.82779i	−0.282687	−	0.163209i
$876$	−9.30567	−	8.27466i	−0.314409	−	0.279575i
$877$	−20.0320	−	34.6965i	−0.676434	−	1.17162i	−0.976048	−	0.217557i	$-0.930191\pi$
$877$	−20.0320	−	34.6965i	−0.676434	−	1.17162i	0.299614	−	0.954061i	$-0.403142\pi$
$878$	−34.0104	+	27.7166i	−1.14779	+	0.935390i
$879$	25.4264			0.857610
$880$	28.6998	−	3.37786i	0.967470	−	0.113868i
$881$	3.38725	+	5.86690i	0.114120	+	0.197661i	0.917427	−	0.397903i	$-0.130262\pi$
$881$	3.38725	+	5.86690i	0.114120	+	0.197661i	−0.803308	+	0.595564i	$0.796929\pi$
$882$	−5.80799	−	7.12684i	−0.195565	−	0.239973i
$883$	−9.77871	+	16.9372i	−0.329080	+	0.569983i	−0.982330	−	0.187159i	$-0.940072\pi$
$883$	−9.77871	+	16.9372i	−0.329080	+	0.569983i	0.653250	+	0.757143i	$0.273405\pi$
$884$	44.1986	+	9.10780i	1.48656	+	0.306329i
$885$	−25.6735			−0.863005
$886$	−20.2233	+	53.1770i	−0.679414	+	1.78652i
$887$	−26.8496	+	15.5017i	−0.901523	+	0.520495i	−0.877694	−	0.479222i	$-0.840919\pi$
$887$	−26.8496	+	15.5017i	−0.901523	+	0.520495i	−0.0238290	+	0.999716i	$0.507586\pi$
$888$	3.61696	+	2.30120i	0.121377	+	0.0772232i
$889$	2.56390	−	1.48027i	0.0859903	−	0.0496465i
$890$	−5.98408	−	37.0363i	−0.200587	−	1.24146i
$891$	0.976153	−	1.69075i	0.0327023	−	0.0566421i
$892$	−3.01159	−	9.07627i	−0.100835	−	0.303896i
$893$	4.48199			0.149984
$894$	11.2548	−	1.81847i	0.376416	−	0.0608189i
$895$		−	16.4016i		−	0.548244i
$896$	4.49785	+	6.60669i	0.150263	+	0.220714i
$897$	−9.49152	+	16.4398i	−0.316913	+	0.548909i
$898$	−13.3772	+	35.1753i	−0.446403	+	1.17382i
$899$	4.96326	+	8.59662i	0.165534	+	0.286713i
$900$	−16.5024	+	5.47565i	−0.550081	+	0.182522i
$901$	−39.8638	+	23.0154i	−1.32805	+	0.766753i
$902$	10.4201	−	8.49185i	0.346953	−	0.282748i
$903$	−0.516328	+	0.894307i	−0.0171823	+	0.0297607i
$904$	−31.7320	−	1.36632i	−1.05539	−	0.0454432i
$905$	53.3991	+	30.8300i	1.77505	+	1.02482i
$906$	−0.502857	+	0.409801i	−0.0167063	+	0.0136147i
$907$	−32.8700	−	18.9775i	−1.09143	−	0.630137i	−0.157473	−	0.987523i	$-0.550335\pi$
$907$	−32.8700	−	18.9775i	−1.09143	−	0.630137i	−0.933957	+	0.357386i	$0.883668\pi$
$908$	−26.1985	−	5.39861i	−0.869429	−	0.179159i
$909$	−9.68743	−	5.59304i	−0.321312	−	0.185509i
$910$	−17.0150	+	2.74917i	−0.564041	+	0.0911341i
$911$		−	20.5539i		−	0.680982i	−0.940248	−	0.340491i	$-0.889407\pi$
$911$		−	20.5539i		−	0.680982i	0.940248	−	0.340491i	$-0.110593\pi$
$912$	−4.65195	+	10.8083i	−0.154042	+	0.357898i
$913$			33.3337i			1.10318i
$914$	−11.8627	+	31.1929i	−0.392383	+	1.03177i
$915$	13.3625	+	23.1445i	0.441750	+	0.765133i
$916$	17.1818	−	19.3227i	0.567704	−	0.638439i
$917$	−11.2962	−	6.52187i	−0.373034	−	0.215371i
$918$	4.32392	+	5.30578i	0.142711	+	0.175117i
$919$	−5.83669	−	10.1094i	−0.192535	−	0.333480i	0.753555	−	0.657385i	$-0.228337\pi$
$919$	−5.83669	−	10.1094i	−0.192535	−	0.333480i	−0.946090	+	0.323905i	$0.895004\pi$
$920$	−35.9571	−	22.8768i	−1.18547	−	0.754225i
$921$	−7.87815	+	4.54845i	−0.259594	+	0.149877i
$922$	−56.3017	+	9.09687i	−1.85420	+	0.299589i
$923$	66.2897			2.18195
$924$	2.06130	+	1.83292i	0.0678119	+	0.0602988i
$925$	−6.58827	−	11.4112i	−0.216621	−	0.375199i
$926$	−12.4821	−	15.3165i	−0.410187	−	0.503331i
$927$	−6.99504	−	4.03859i	−0.229747	−	0.132645i
$928$	4.82439	+	16.9465i	0.158368	+	0.556296i
$929$		−	5.17859i		−	0.169904i	−0.996385	−	0.0849521i	$-0.972926\pi$
$929$		−	5.17859i		−	0.169904i	0.996385	−	0.0849521i	$-0.0270737\pi$
$930$	−15.5888	−	5.92841i	−0.511175	−	0.194400i
$931$	16.5618	+	9.56198i	0.542792	+	0.313381i
$932$	31.0905	+	6.40667i	1.01840	+	0.209857i
$933$	2.52656			0.0827158
$934$	−21.3465	+	17.3963i	−0.698480	+	0.569223i
$935$			34.9651i			1.14348i
$936$	−7.07834	+	11.1255i	−0.231363	+	0.363649i
$937$			16.5063i			0.539238i	0.962967	+	0.269619i	$0.0868977\pi$
$937$			16.5063i			0.539238i	−0.962967	+	0.269619i	$0.913102\pi$
$938$	−8.05257	+	1.42462i	−0.262926	+	0.0465154i
$939$			18.3699i			0.599480i
$940$	−2.27579	+	11.0440i	−0.0742282	+	0.360217i
$941$			24.3490i			0.793756i	0.917871	+	0.396878i	$0.129906\pi$
$941$			24.3490i			0.793756i	−0.917871	+	0.396878i	$0.870094\pi$
$942$	2.82368	+	3.46487i	0.0920004	+	0.112891i
$943$	−19.8240			−0.645558
$944$	−16.5899	−	22.2468i	−0.539955	−	0.724072i
$945$	−2.26393	−	1.30708i	−0.0736457	−	0.0425194i
$946$	−1.43463	+	3.77235i	−0.0466438	+	0.122650i
$947$			54.5898i			1.77393i	0.461836	+	0.886965i	$0.347191\pi$
$947$			54.5898i			1.77393i	−0.461836	+	0.886965i	$0.652809\pi$
$948$	−2.78208	+	13.5009i	−0.0903576	+	0.438490i
$949$	25.1384	+	14.5137i	0.816028	+	0.471134i
$950$	28.0362	−	22.8480i	0.909616	−	0.741287i
$951$	−6.99505	−	12.1158i	−0.226830	−	0.392881i
$952$	−8.57514	+	4.47049i	−0.277922	+	0.144890i
$953$	52.4774			1.69991			0.849955	−	0.526856i	$-0.176629\pi$
$953$	52.4774			1.69991			0.849955	+	0.526856i	$0.176629\pi$
$954$	−2.14540	−	13.2781i	−0.0694598	−	0.429896i
$955$	31.5115	−	18.1932i	1.01969	−	0.588718i
$956$	−11.7184	+	56.8674i	−0.379000	+	1.83922i
$957$	3.04050	+	5.26630i	0.0982853	+	0.170235i
$958$	−30.0839	+	24.5167i	−0.971965	+	0.792099i
$959$	−1.17762	−	0.679898i	−0.0380273	−	0.0219551i
$960$	−24.2705	−	16.9509i	−0.783326	−	0.547087i
$961$	10.4218	+	18.0511i	0.336187	+	0.582292i
$962$	−9.34042	−	3.55217i	−0.301147	−	0.114526i
$963$			17.2446i			0.555700i
$964$	51.7703	−	17.1779i	1.66741	−	0.553262i
$965$			56.3095i			1.81267i
$966$	−0.648857	−	4.01586i	−0.0208766	−	0.129208i
$967$	6.79569	+	3.92349i	0.218535	+	0.126171i	0.605272	−	0.796019i	$-0.293065\pi$
$967$	6.79569	+	3.92349i	0.218535	+	0.126171i	−0.386737	+	0.922190i	$0.626398\pi$
$968$	−17.1545	−	10.9141i	−0.551368	−	0.350794i
$969$	−12.3299	−	7.11869i	−0.396095	−	0.228685i
$970$	−13.7260	−	16.8429i	−0.440715	−	0.540791i
$971$	7.22968	+	4.17406i	0.232012	+	0.133952i	0.611500	−	0.791245i	$-0.290567\pi$
$971$	7.22968	+	4.17406i	0.232012	+	0.133952i	−0.379488	+	0.925197i	$0.623900\pi$
$972$	−1.89823	+	0.629851i	−0.0608858	+	0.0202025i
$973$	−7.92199	+	13.7213i	−0.253967	+	0.439884i
$974$	14.9918	+	18.3961i	0.480370	+	0.589450i
$975$	35.1001	−	20.2651i	1.12410	−	0.649002i
$976$	−11.4207	+	26.5347i	−0.365568	+	0.849354i
$977$	21.4255	+	37.1101i	0.685463	+	1.18726i	0.973291	+	0.229574i	$0.0737334\pi$
$977$	21.4255	+	37.1101i	0.685463	+	1.18726i	−0.287828	+	0.957682i	$0.592933\pi$
$978$	21.3103	+	8.10433i	0.681429	+	0.259148i
$979$	6.99791	−	12.1207i	0.223654	−	0.387380i
$980$	−31.9711	+	35.9546i	−1.02128	+	1.14853i
$981$		−	12.1460i		−	0.387793i
$982$	0.986881	+	6.10794i	0.0314926	+	0.194912i
$983$	27.5810			0.879697			0.439849	−	0.898072i	$-0.355032\pi$
$983$	27.5810			0.879697			0.439849	+	0.898072i	$0.355032\pi$
$984$	−13.7578	−	0.592385i	−0.438582	−	0.0188845i
$985$	29.7398	−	51.5109i	0.947589	−	1.64127i
$986$	−21.0463	+	3.40052i	−0.670249	+	0.108294i
$987$	−0.932127	+	0.538164i	−0.0296699	+	0.0171299i
$988$	5.53587	−	26.8646i	0.176119	−	0.854678i
$989$	5.15464	−	2.97603i	0.163908	−	0.0946322i
$990$	−9.54968	−	3.63175i	−0.303509	−	0.115425i
$991$	−30.3147			−0.962979			−0.481490	−	0.876452i	$-0.659904\pi$
$991$	−30.3147			−0.962979			−0.481490	+	0.876452i	$0.659904\pi$
$992$	−4.93612	−	17.3390i	−0.156722	−	0.550513i
$993$	3.88024	−	6.72078i	0.123136	−	0.213277i
$994$	−11.0119	+	8.97406i	−0.349275	+	0.284640i
$995$	−27.0098	−	46.7824i	−0.856269	−	1.48310i
$996$	22.6912	−	25.5185i	0.718999	−	0.808586i
$997$	−15.6299			−0.495005			−0.247502	−	0.968887i	$-0.579610\pi$
$997$	−15.6299			−0.495005			−0.247502	+	0.968887i	$0.579610\pi$
$998$	−10.3848	−	12.7429i	−0.328725	−	0.403371i
$999$	−0.757833	−	1.31260i	−0.0239768	−	0.0415290i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.j.a.499.2	✓	68
4.3	odd	2		804.2.j.b.499.10	yes	68
67.38	odd	6		804.2.j.b.775.10	yes	68
268.239	even	6	inner	804.2.j.a.775.2	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.j.a.499.2	✓	68	1.1	even	1	trivial
804.2.j.a.775.2	yes	68	268.239	even	6	inner
804.2.j.b.499.10	yes	68	4.3	odd	2
804.2.j.b.775.10	yes	68	67.38	odd	6

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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39611 + 0.225574i) q^{2} -1.00000 q^{3} +(1.89823 - 0.629851i) q^{4} +3.70048i q^{5} +(1.39611 - 0.225574i) q^{6} +(0.353219 - 0.611794i) q^{7} +(-2.50806 + 1.30753i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-1.39611 + 0.225574i) q^{2} -1.00000 q^{3} +(1.89823 - 0.629851i) q^{4} +3.70048i q^{5} +(1.39611 - 0.225574i) q^{6} +(0.353219 - 0.611794i) q^{7} +(-2.50806 + 1.30753i) q^{8} +1.00000 q^{9} +(-0.834732 - 5.16627i) q^{10} +(0.976153 - 1.69075i) q^{11} +(-1.89823 + 0.629851i) q^{12} +(4.03748 - 2.33104i) q^{13} +(-0.355127 + 0.933807i) q^{14} -3.70048i q^{15} +(3.20658 - 2.39121i) q^{16} +(2.41991 + 4.19141i) q^{17} +(-1.39611 + 0.225574i) q^{18} +(2.54760 - 1.47086i) q^{19} +(2.33075 + 7.02438i) q^{20} +(-0.353219 + 0.611794i) q^{21} +(-0.981426 + 2.58066i) q^{22} +(3.52628 - 2.03590i) q^{23} +(2.50806 - 1.30753i) q^{24} -8.69357 q^{25} +(-5.11094 + 4.16514i) q^{26} -1.00000 q^{27} +(0.285154 - 1.38380i) q^{28} +(1.55739 - 2.69748i) q^{29} +(0.834732 + 5.16627i) q^{30} +(-1.59346 + 2.75995i) q^{31} +(-3.93733 + 4.06170i) q^{32} +(-0.976153 + 1.69075i) q^{33} +(-4.32392 - 5.30578i) q^{34} +(2.26393 + 1.30708i) q^{35} +(1.89823 - 0.629851i) q^{36} +(0.757833 + 1.31260i) q^{37} +(-3.22494 + 2.62815i) q^{38} +(-4.03748 + 2.33104i) q^{39} +(-4.83850 - 9.28103i) q^{40} +(-4.21634 - 2.43431i) q^{41} +(0.355127 - 0.933807i) q^{42} +1.46178 q^{43} +(0.788047 - 3.82426i) q^{44} +3.70048i q^{45} +(-4.46382 + 3.63777i) q^{46} +(1.31947 + 0.761798i) q^{47} +(-3.20658 + 2.39121i) q^{48} +(3.25047 + 5.62998i) q^{49} +(12.1372 - 1.96104i) q^{50} +(-2.41991 - 4.19141i) q^{51} +(6.19588 - 6.96787i) q^{52} +9.51083i q^{53} +(1.39611 - 0.225574i) q^{54} +(6.25658 + 3.61224i) q^{55} +(-0.0859553 + 1.99626i) q^{56} +(-2.54760 + 1.47086i) q^{57} +(-1.56580 + 4.11727i) q^{58} -6.93788i q^{59} +(-2.33075 - 7.02438i) q^{60} +(-6.25445 + 3.61101i) q^{61} +(1.60207 - 4.21263i) q^{62} +(0.353219 - 0.611794i) q^{63} +(4.58072 - 6.55873i) q^{64} +(8.62598 + 14.9406i) q^{65} +(0.981426 - 2.58066i) q^{66} +(4.19794 + 7.02690i) q^{67} +(7.23351 + 6.43208i) q^{68} +(-3.52628 + 2.03590i) q^{69} +(-3.45553 - 1.31414i) q^{70} +(12.3139 + 7.10944i) q^{71} +(-2.50806 + 1.30753i) q^{72} +(3.11313 + 5.39210i) q^{73} +(-1.35411 - 1.66159i) q^{74} +8.69357 q^{75} +(3.90952 - 4.39664i) q^{76} +(-0.689592 - 1.19441i) q^{77} +(5.11094 - 4.16514i) q^{78} +(3.44615 - 5.96891i) q^{79} +(8.84862 + 11.8659i) q^{80} +1.00000 q^{81} +(6.43558 + 2.44746i) q^{82} +(-14.7865 + 8.53701i) q^{83} +(-0.285154 + 1.38380i) q^{84} +(-15.5102 + 8.95483i) q^{85} +(-2.04080 + 0.329739i) q^{86} +(-1.55739 + 2.69748i) q^{87} +(-0.237545 + 5.51684i) q^{88} +7.16886 q^{89} +(-0.834732 - 5.16627i) q^{90} -3.29348i q^{91} +(5.41138 - 6.08563i) q^{92} +(1.59346 - 2.75995i) q^{93} +(-2.01397 - 0.765914i) q^{94} +(5.44289 + 9.42736i) q^{95} +(3.93733 - 4.06170i) q^{96} +(3.59557 - 2.07590i) q^{97} +(-5.80799 - 7.12684i) q^{98} +(0.976153 - 1.69075i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 68 q^{3} - 2 q^{4} + 4 q^{7} - 6 q^{8} + 68 q^{9}+O(q^{10}) \) 68 * q - 68 * q^3 - 2 * q^4 + 4 * q^7 - 6 * q^8 + 68 * q^9	\( 68 q - 68 q^{3} - 2 q^{4} + 4 q^{7} - 6 q^{8} + 68 q^{9} + 18 q^{10} + 2 q^{12} + 6 q^{13} + 10 q^{14} - 2 q^{16} - 36 q^{20} - 4 q^{21} - 22 q^{22} + 6 q^{24} - 68 q^{25} - q^{26} - 68 q^{27} + q^{28} - 8 q^{29} - 18 q^{30} + 2 q^{31} + 15 q^{32} - 2 q^{36} + 12 q^{37} - 22 q^{38} - 6 q^{39} + 18 q^{40} - 10 q^{42} - 4 q^{43} - 31 q^{44} + 32 q^{46} + 2 q^{48} - 46 q^{49} - 9 q^{50} - 28 q^{52} - 11 q^{56} + 4 q^{58} + 36 q^{60} + 6 q^{61} - 34 q^{62} + 4 q^{63} + 16 q^{64} + 22 q^{66} - 18 q^{67} + 34 q^{68} + 56 q^{70} - 36 q^{71} - 6 q^{72} + 6 q^{73} - 53 q^{74} + 68 q^{75} + 14 q^{76} - 4 q^{77} + q^{78} + 6 q^{79} + 55 q^{80} + 68 q^{81} - 26 q^{82} + 12 q^{83} - q^{84} - 21 q^{86} + 8 q^{87} - 50 q^{88} + 18 q^{90} + 10 q^{92} - 2 q^{93} - 16 q^{94} + 20 q^{95} - 15 q^{96} + 18 q^{97} - 70 q^{98}+O(q^{100}) \) 68 * q - 68 * q^3 - 2 * q^4 + 4 * q^7 - 6 * q^8 + 68 * q^9 + 18 * q^10 + 2 * q^12 + 6 * q^13 + 10 * q^14 - 2 * q^16 - 36 * q^20 - 4 * q^21 - 22 * q^22 + 6 * q^24 - 68 * q^25 - q^26 - 68 * q^27 + q^28 - 8 * q^29 - 18 * q^30 + 2 * q^31 + 15 * q^32 - 2 * q^36 + 12 * q^37 - 22 * q^38 - 6 * q^39 + 18 * q^40 - 10 * q^42 - 4 * q^43 - 31 * q^44 + 32 * q^46 + 2 * q^48 - 46 * q^49 - 9 * q^50 - 28 * q^52 - 11 * q^56 + 4 * q^58 + 36 * q^60 + 6 * q^61 - 34 * q^62 + 4 * q^63 + 16 * q^64 + 22 * q^66 - 18 * q^67 + 34 * q^68 + 56 * q^70 - 36 * q^71 - 6 * q^72 + 6 * q^73 - 53 * q^74 + 68 * q^75 + 14 * q^76 - 4 * q^77 + q^78 + 6 * q^79 + 55 * q^80 + 68 * q^81 - 26 * q^82 + 12 * q^83 - q^84 - 21 * q^86 + 8 * q^87 - 50 * q^88 + 18 * q^90 + 10 * q^92 - 2 * q^93 - 16 * q^94 + 20 * q^95 - 15 * q^96 + 18 * q^97 - 70 * q^98

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