LMFDB - Embedded newform 804.2.j.b.499.4

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			499.4
Character	$\chi$	$=$	804.499
Dual form			804.2.j.b.775.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32266 + 0.500561i) q^{2} +1.00000 q^{3} +(1.49888 - 1.32415i) q^{4} -3.14328i q^{5} +(-1.32266 + 0.500561i) q^{6} +(2.02612 - 3.50935i) q^{7} +(-1.31969 + 2.50168i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-1.32266 + 0.500561i) q^{2} +1.00000 q^{3} +(1.49888 - 1.32415i) q^{4} -3.14328i q^{5} +(-1.32266 + 0.500561i) q^{6} +(2.02612 - 3.50935i) q^{7} +(-1.31969 + 2.50168i) q^{8} +1.00000 q^{9} +(1.57340 + 4.15750i) q^{10} +(-0.934262 + 1.61819i) q^{11} +(1.49888 - 1.32415i) q^{12} +(1.56836 - 0.905492i) q^{13} +(-0.923236 + 5.65589i) q^{14} -3.14328i q^{15} +(0.493266 - 3.96947i) q^{16} +(3.63749 + 6.30032i) q^{17} +(-1.32266 + 0.500561i) q^{18} +(3.35356 - 1.93618i) q^{19} +(-4.16216 - 4.71139i) q^{20} +(2.02612 - 3.50935i) q^{21} +(0.425712 - 2.60797i) q^{22} +(-0.543486 + 0.313782i) q^{23} +(-1.31969 + 2.50168i) q^{24} -4.88020 q^{25} +(-1.62116 + 1.98272i) q^{26} +1.00000 q^{27} +(-1.60999 - 7.94297i) q^{28} +(4.41834 - 7.65278i) q^{29} +(1.57340 + 4.15750i) q^{30} +(-3.78697 + 6.55923i) q^{31} +(1.33454 + 5.49718i) q^{32} +(-0.934262 + 1.61819i) q^{33} +(-7.96487 - 6.51242i) q^{34} +(-11.0309 - 6.36867i) q^{35} +(1.49888 - 1.32415i) q^{36} +(-5.45660 - 9.45112i) q^{37} +(-3.46645 + 4.23957i) q^{38} +(1.56836 - 0.905492i) q^{39} +(7.86348 + 4.14816i) q^{40} +(-2.51599 - 1.45261i) q^{41} +(-0.923236 + 5.65589i) q^{42} -2.50287 q^{43} +(0.742377 + 3.66257i) q^{44} -3.14328i q^{45} +(0.561783 - 0.687076i) q^{46} +(-6.03173 - 3.48242i) q^{47} +(0.493266 - 3.96947i) q^{48} +(-4.71035 - 8.15857i) q^{49} +(6.45486 - 2.44284i) q^{50} +(3.63749 + 6.30032i) q^{51} +(1.15177 - 3.43396i) q^{52} -3.73302i q^{53} +(-1.32266 + 0.500561i) q^{54} +(5.08642 + 2.93664i) q^{55} +(6.10541 + 9.69998i) q^{56} +(3.35356 - 1.93618i) q^{57} +(-2.01329 + 12.3337i) q^{58} +14.0628i q^{59} +(-4.16216 - 4.71139i) q^{60} +(2.09861 - 1.21163i) q^{61} +(1.72560 - 10.5713i) q^{62} +(2.02612 - 3.50935i) q^{63} +(-4.51682 - 6.60290i) q^{64} +(-2.84621 - 4.92979i) q^{65} +(0.425712 - 2.60797i) q^{66} +(6.35908 + 5.15385i) q^{67} +(13.7947 + 4.62683i) q^{68} +(-0.543486 + 0.313782i) q^{69} +(17.7780 + 2.90199i) q^{70} +(-12.4110 - 7.16551i) q^{71} +(-1.31969 + 2.50168i) q^{72} +(2.30070 + 3.98493i) q^{73} +(11.9481 + 9.76928i) q^{74} -4.88020 q^{75} +(2.46279 - 7.34270i) q^{76} +(3.78586 + 6.55730i) q^{77} +(-1.62116 + 1.98272i) q^{78} +(0.726008 - 1.25748i) q^{79} +(-12.4771 - 1.55047i) q^{80} +1.00000 q^{81} +(4.05492 + 0.661904i) q^{82} +(-8.21115 + 4.74071i) q^{83} +(-1.60999 - 7.94297i) q^{84} +(19.8037 - 11.4337i) q^{85} +(3.31045 - 1.25284i) q^{86} +(4.41834 - 7.65278i) q^{87} +(-2.81525 - 4.47274i) q^{88} +4.88846 q^{89} +(1.57340 + 4.15750i) q^{90} -7.33856i q^{91} +(-0.399126 + 1.18998i) q^{92} +(-3.78697 + 6.55923i) q^{93} +(9.72111 + 1.58682i) q^{94} +(-6.08595 - 10.5412i) q^{95} +(1.33454 + 5.49718i) q^{96} +(1.88856 - 1.09036i) q^{97} +(10.3141 + 8.43322i) q^{98} +(-0.934262 + 1.61819i) 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} - 6 q^{10} - 2 q^{12} + 6 q^{13} + 10 q^{14} - 2 q^{16} - 12 q^{20} - 4 q^{21} - 22 q^{22} + 6 q^{24} - 68 q^{25} - 19 q^{26} + 68 q^{27} - 7 q^{28} - 8 q^{29} - 6 q^{30} - 2 q^{31} + 15 q^{32} - 2 q^{36} + 12 q^{37} + 4 q^{38} + 6 q^{39} + 18 q^{40} + 10 q^{42} + 4 q^{43} - 5 q^{44} + 16 q^{46} - 2 q^{48} - 46 q^{49} + 27 q^{50} + 28 q^{52} - 17 q^{56} - 4 q^{58} - 12 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} + 11 q^{74} - 68 q^{75} + 14 q^{76} - 4 q^{77} - 19 q^{78} - 6 q^{79} - 25 q^{80} + 68 q^{81} - 26 q^{82} - 12 q^{83} - 7 q^{84} - 33 q^{86} - 8 q^{87} + 22 q^{88} - 6 q^{90} + 10 q^{92} - 2 q^{93} + 16 q^{94} - 20 q^{95} + 15 q^{96} + 18 q^{97} - 32 q^{98}+O(q^{100}) $ 68 * q + 68 * q^3 - 2 * q^4 - 4 * q^7 + 6 * q^8 + 68 * q^9 - 6 * q^10 - 2 * q^12 + 6 * q^13 + 10 * q^14 - 2 * q^16 - 12 * q^20 - 4 * q^21 - 22 * q^22 + 6 * q^24 - 68 * q^25 - 19 * q^26 + 68 * q^27 - 7 * q^28 - 8 * q^29 - 6 * q^30 - 2 * q^31 + 15 * q^32 - 2 * q^36 + 12 * q^37 + 4 * q^38 + 6 * q^39 + 18 * q^40 + 10 * q^42 + 4 * q^43 - 5 * q^44 + 16 * q^46 - 2 * q^48 - 46 * q^49 + 27 * q^50 + 28 * q^52 - 17 * q^56 - 4 * q^58 - 12 * 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 + 11 * q^74 - 68 * q^75 + 14 * q^76 - 4 * q^77 - 19 * q^78 - 6 * q^79 - 25 * q^80 + 68 * q^81 - 26 * q^82 - 12 * q^83 - 7 * q^84 - 33 * q^86 - 8 * q^87 + 22 * q^88 - 6 * q^90 + 10 * q^92 - 2 * q^93 + 16 * q^94 - 20 * q^95 + 15 * q^96 + 18 * q^97 - 32 * 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 $

$2$	−1.32266	+	0.500561i	−0.935264	+	0.353950i
$2$	−1.32266	+	0.500561i	−0.935264	+	0.353950i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	1.49888	−	1.32415i	0.749439	−	0.662074i
$5$		−	3.14328i		−	1.40572i	−0.711330	−	0.702858i	$-0.751907\pi$
$5$		−	3.14328i		−	1.40572i	0.711330	−	0.702858i	$-0.248093\pi$
$6$	−1.32266	+	0.500561i	−0.539975	+	0.204353i
$7$	2.02612	−	3.50935i	0.765803	−	1.32641i	−0.174018	−	0.984742i	$-0.555675\pi$
$7$	2.02612	−	3.50935i	0.765803	−	1.32641i	0.939821	−	0.341667i	$-0.110991\pi$
$8$	−1.31969	+	2.50168i	−0.466582	+	0.884478i
$9$	1.00000			0.333333
$10$	1.57340	+	4.15750i	0.497554	+	1.31472i
$11$	−0.934262	+	1.61819i	−0.281690	+	0.487902i	−0.971801	−	0.235802i	$-0.924228\pi$
$11$	−0.934262	+	1.61819i	−0.281690	+	0.487902i	0.690111	+	0.723704i	$0.257562\pi$
$12$	1.49888	−	1.32415i	0.432689	−	0.382249i
$13$	1.56836	−	0.905492i	0.434984	−	0.251138i	−0.266483	−	0.963839i	$-0.585862\pi$
$13$	1.56836	−	0.905492i	0.434984	−	0.251138i	0.701468	+	0.712701i	$0.252528\pi$
$14$	−0.923236	+	5.65589i	−0.246745	+	1.51160i
$15$		−	3.14328i		−	0.811591i
$16$	0.493266	−	3.96947i	0.123317	−	0.992367i
$17$	3.63749	+	6.30032i	0.882221	+	1.52805i	0.848866	+	0.528609i	$0.177286\pi$
$17$	3.63749	+	6.30032i	0.882221	+	1.52805i	0.0333558	+	0.999444i	$0.489381\pi$
$18$	−1.32266	+	0.500561i	−0.311755	+	0.117983i
$19$	3.35356	−	1.93618i	0.769359	−	0.444190i	−0.0632869	−	0.997995i	$-0.520158\pi$
$19$	3.35356	−	1.93618i	0.769359	−	0.444190i	0.832646	+	0.553806i	$0.186825\pi$
$20$	−4.16216	−	4.71139i	−0.930688	−	1.05350i
$21$	2.02612	−	3.50935i	0.442136	−	0.765803i
$22$	0.425712	−	2.60797i	0.0907620	−	0.556022i
$23$	−0.543486	+	0.313782i	−0.113325	+	0.0654281i	−0.555591	−	0.831456i	$-0.687508\pi$
$23$	−0.543486	+	0.313782i	−0.113325	+	0.0654281i	0.442266	+	0.896884i	$0.354175\pi$
$24$	−1.31969	+	2.50168i	−0.269381	+	0.510654i
$25$	−4.88020			−0.976040
$26$	−1.62116	+	1.98272i	−0.317935	+	0.388843i
$27$	1.00000			0.192450
$28$	−1.60999	−	7.94297i	−0.304259	−	1.50108i
$29$	4.41834	−	7.65278i	0.820464	−	1.42109i	−0.0848728	−	0.996392i	$-0.527048\pi$
$29$	4.41834	−	7.65278i	0.820464	−	1.42109i	0.905337	−	0.424694i	$-0.139618\pi$
$30$	1.57340	+	4.15750i	0.287263	+	0.759052i
$31$	−3.78697	+	6.55923i	−0.680160	+	1.17807i	0.294771	+	0.955568i	$0.404757\pi$
$31$	−3.78697	+	6.55923i	−0.680160	+	1.17807i	−0.974932	+	0.222505i	$0.928577\pi$
$32$	1.33454	+	5.49718i	0.235915	+	0.971774i
$33$	−0.934262	+	1.61819i	−0.162634	+	0.281690i
$34$	−7.96487	−	6.51242i	−1.36596	−	1.11687i
$35$	−11.0309	−	6.36867i	−1.86456	−	1.07650i
$36$	1.49888	−	1.32415i	0.249813	−	0.220691i
$37$	−5.45660	−	9.45112i	−0.897060	−	1.55375i	−0.831234	−	0.555923i	$-0.812365\pi$
$37$	−5.45660	−	9.45112i	−0.897060	−	1.55375i	−0.0658262	−	0.997831i	$-0.520968\pi$
$38$	−3.46645	+	4.23957i	−0.562333	+	0.687749i
$39$	1.56836	−	0.905492i	0.251138	−	0.144995i
$40$	7.86348	+	4.14816i	1.24333	+	0.655882i
$41$	−2.51599	−	1.45261i	−0.392931	−	0.226859i	0.290498	−	0.956876i	$-0.406179\pi$
$41$	−2.51599	−	1.45261i	−0.392931	−	0.226859i	−0.683429	+	0.730017i	$0.739512\pi$
$42$	−0.923236	+	5.65589i	−0.142458	+	0.872722i
$43$	−2.50287			−0.381684			−0.190842	−	0.981621i	$-0.561122\pi$
$43$	−2.50287			−0.381684			−0.190842	+	0.981621i	$0.561122\pi$
$44$	0.742377	+	3.66257i	0.111918	+	0.552153i
$45$		−	3.14328i		−	0.468572i
$46$	0.561783	−	0.687076i	0.0828303	−	0.101304i
$47$	−6.03173	−	3.48242i	−0.879818	−	0.507963i	−0.00921972	−	0.999957i	$-0.502935\pi$
$47$	−6.03173	−	3.48242i	−0.879818	−	0.507963i	−0.870598	+	0.491994i	$0.836268\pi$
$48$	0.493266	−	3.96947i	0.0711968	−	0.572944i
$49$	−4.71035	−	8.15857i	−0.672908	−	1.16551i
$50$	6.45486	−	2.44284i	0.912855	−	0.345470i
$51$	3.63749	+	6.30032i	0.509351	+	0.882221i
$52$	1.15177	−	3.43396i	0.159722	−	0.476204i
$53$		−	3.73302i		−	0.512769i	−0.966575	−	0.256385i	$-0.917469\pi$
$53$		−	3.73302i		−	0.512769i	0.966575	−	0.256385i	$-0.0825314\pi$
$54$	−1.32266	+	0.500561i	−0.179992	+	0.0681177i
$55$	5.08642	+	2.93664i	0.685852	+	0.395977i
$56$	6.10541	+	9.69998i	0.815870	+	1.29621i
$57$	3.35356	−	1.93618i	0.444190	−	0.256453i
$58$	−2.01329	+	12.3337i	−0.264357	+	1.61949i
$59$			14.0628i			1.83082i	0.402522	+	0.915410i	$0.368134\pi$
$59$			14.0628i			1.83082i	−0.402522	+	0.915410i	$0.631866\pi$
$60$	−4.16216	−	4.71139i	−0.537333	−	0.608238i
$61$	2.09861	−	1.21163i	0.268699	−	0.155134i	−0.359597	−	0.933108i	$-0.617086\pi$
$61$	2.09861	−	1.21163i	0.268699	−	0.155134i	0.628296	+	0.777974i	$0.283753\pi$
$62$	1.72560	−	10.5713i	0.219151	−	1.34255i
$63$	2.02612	−	3.50935i	0.255268	−	0.442136i
$64$	−4.51682	−	6.60290i	−0.564602	−	0.825363i
$65$	−2.84621	−	4.92979i	−0.353029	−	0.611465i
$66$	0.425712	−	2.60797i	0.0524015	−	0.321019i
$67$	6.35908	+	5.15385i	0.776885	+	0.629642i
$67$	6.35908	+	5.15385i	0.776885	+	0.629642i
$68$	13.7947	+	4.62683i	1.67285	+	0.561086i
$69$	−0.543486	+	0.313782i	−0.0654281	+	0.0377749i
$70$	17.7780	+	2.90199i	2.12488	+	0.346854i
$71$	−12.4110	−	7.16551i	−1.47292	−	0.850389i	−0.473382	−	0.880857i	$-0.656967\pi$
$71$	−12.4110	−	7.16551i	−1.47292	−	0.850389i	−0.999536	+	0.0304681i	$0.990300\pi$
$72$	−1.31969	+	2.50168i	−0.155527	+	0.294826i
$73$	2.30070	+	3.98493i	0.269276	+	0.466400i	0.968675	−	0.248331i	$-0.0798822\pi$
$73$	2.30070	+	3.98493i	0.269276	+	0.466400i	−0.699399	+	0.714732i	$0.746549\pi$
$74$	11.9481	+	9.76928i	1.38894	+	1.13566i
$75$	−4.88020			−0.563517
$76$	2.46279	−	7.34270i	0.282501	−	0.842265i
$77$	3.78586	+	6.55730i	0.431439	+	0.747274i
$78$	−1.62116	+	1.98272i	−0.183560	+	0.224499i
$79$	0.726008	−	1.25748i	0.0816822	−	0.141478i	−0.822290	−	0.569068i	$-0.807304\pi$
$79$	0.726008	−	1.25748i	0.0816822	−	0.141478i	0.903973	+	0.427590i	$0.140637\pi$
$80$	−12.4771	−	1.55047i	−1.39499	−	0.173348i
$81$	1.00000			0.111111
$82$	4.05492	+	0.661904i	0.447791	+	0.0730951i
$83$	−8.21115	+	4.74071i	−0.901291	+	0.520361i	−0.877619	−	0.479359i	$-0.840869\pi$
$83$	−8.21115	+	4.74071i	−0.901291	+	0.520361i	−0.0236721	+	0.999720i	$0.507536\pi$
$84$	−1.60999	−	7.94297i	−0.175664	−	0.866649i
$85$	19.8037	−	11.4337i	2.14801	−	1.24015i
$86$	3.31045	−	1.25284i	0.356975	−	0.135097i
$87$	4.41834	−	7.65278i	0.473695	−	0.820464i
$88$	−2.81525	−	4.47274i	−0.300107	−	0.476795i
$89$	4.88846			0.518176			0.259088	−	0.965854i	$-0.416578\pi$
$89$	4.88846			0.518176			0.259088	+	0.965854i	$0.416578\pi$
$90$	1.57340	+	4.15750i	0.165851	+	0.438239i
$91$		−	7.33856i		−	0.769290i
$92$	−0.399126	+	1.18998i	−0.0416117	+	0.124064i
$93$	−3.78697	+	6.55923i	−0.392691	+	0.680160i
$94$	9.72111	+	1.58682i	1.00266	+	0.163668i
$95$	−6.08595	−	10.5412i	−0.624405	−	1.08150i
$96$	1.33454	+	5.49718i	0.136206	+	0.561054i
$97$	1.88856	−	1.09036i	0.191755	−	0.110710i	−0.401049	−	0.916057i	$-0.631354\pi$
$97$	1.88856	−	1.09036i	0.191755	−	0.110710i	0.592804	+	0.805347i	$0.298021\pi$
$98$	10.3141	+	8.43322i	1.04188	+	0.851884i
$99$	−0.934262	+	1.61819i	−0.0938968	+	0.162634i
$100$	−7.31482	+	6.46211i	−0.731482	+	0.646211i
$101$	5.00651	+	2.89051i	0.498167	+	0.287617i	0.727956	−	0.685624i	$-0.240470\pi$
$101$	5.00651	+	2.89051i	0.498167	+	0.287617i	−0.229789	+	0.973240i	$0.573804\pi$
$102$	−7.96487	−	6.51242i	−0.788640	−	0.644825i
$103$	8.68180	+	5.01244i	0.855443	+	0.493890i	0.862484	−	0.506085i	$-0.168908\pi$
$103$	8.68180	+	5.01244i	0.855443	+	0.493890i	−0.00704068	+	0.999975i	$0.502241\pi$
$104$	0.195500	+	5.11850i	0.0191704	+	0.501911i
$105$	−11.0309	−	6.36867i	−1.07650	−	0.621519i
$106$	1.86860	+	4.93752i	0.181495	+	0.479575i
$107$			3.66590i			0.354396i	0.984175	+	0.177198i	$0.0567033\pi$
$107$			3.66590i			0.354396i	−0.984175	+	0.177198i	$0.943297\pi$
$108$	1.49888	−	1.32415i	0.144230	−	0.127416i
$109$			6.55918i			0.628256i	0.949381	+	0.314128i	$0.101712\pi$
$109$			6.55918i			0.628256i	−0.949381	+	0.314128i	$0.898288\pi$
$110$	−8.19759	−	1.33813i	−0.781609	−	0.127586i
$111$	−5.45660	−	9.45112i	−0.517918	−	0.897060i
$112$	−12.9308	−	9.77368i	−1.22185	−	0.923526i
$113$	0.372202	+	0.214891i	0.0350138	+	0.0202153i	0.517405	−	0.855741i	$-0.326898\pi$
$113$	0.372202	+	0.214891i	0.0350138	+	0.0202153i	−0.482391	+	0.875956i	$0.660232\pi$
$114$	−3.46645	+	4.23957i	−0.324663	+	0.397072i
$115$	0.986304	+	1.70833i	0.0919734	+	0.159303i
$116$	−3.51087	−	17.3211i	−0.325976	−	1.60822i
$117$	1.56836	−	0.905492i	0.144995	−	0.0837128i
$118$	−7.03929	−	18.6004i	−0.648019	−	1.71230i
$119$	29.4800			2.70243
$120$	7.86348	+	4.14816i	0.717834	+	0.378674i
$121$	3.75431	+	6.50266i	0.341301	+	0.591151i
$122$	−2.16926	+	2.65306i	−0.196395	+	0.240197i
$123$	−2.51599	−	1.45261i	−0.226859	−	0.130977i
$124$	3.00918	+	14.8460i	0.270232	+	1.33321i
$125$		−	0.376563i		−	0.0336808i
$126$	−0.923236	+	5.65589i	−0.0822484	+	0.503866i
$127$	−1.52701	−	0.881617i	−0.135500	−	0.0782309i	0.430718	−	0.902487i	$-0.358260\pi$
$127$	−1.52701	−	0.881617i	−0.135500	−	0.0782309i	−0.566218	+	0.824256i	$0.691594\pi$
$128$	9.27939	+	6.47248i	0.820190	+	0.572092i
$129$	−2.50287			−0.220365
$130$	6.23224	+	5.09575i	0.546604	+	0.446926i
$131$			6.98506i			0.610287i	0.952306	+	0.305144i	$0.0987045\pi$
$131$			6.98506i			0.610287i	−0.952306	+	0.305144i	$0.901295\pi$
$132$	0.742377	+	3.66257i	0.0646156	+	0.318786i
$133$		−	15.6917i		−	1.36065i
$134$	−10.9907	−	3.63370i	−0.949455	−	0.313904i
$135$		−	3.14328i		−	0.270530i
$136$	−20.5618	+	0.785354i	−1.76316	+	0.0673435i
$137$		−	20.0886i		−	1.71628i	−0.513414	−	0.858141i	$-0.671620\pi$
$137$		−	20.0886i		−	1.71628i	0.513414	−	0.858141i	$-0.328380\pi$
$138$	0.561783	−	0.687076i	0.0478221	−	0.0584878i
$139$	8.51721			0.722420			0.361210	−	0.932484i	$-0.382364\pi$
$139$	8.51721			0.722420			0.361210	+	0.932484i	$0.382364\pi$
$140$	−24.9670	+	5.06063i	−2.11009	+	0.427702i
$141$	−6.03173	−	3.48242i	−0.507963	−	0.293273i
$142$	20.0024	+	3.26508i	1.67856	+	0.273999i
$143$			3.38387i			0.282973i
$144$	0.493266	−	3.96947i	0.0411055	−	0.330789i
$145$	−24.0548	−	13.8881i	−1.99764	−	1.15334i
$146$	−5.03775	−	4.11908i	−0.416927	−	0.340897i
$147$	−4.71035	−	8.15857i	−0.388503	−	0.672908i
$148$	−20.6935	−	6.94071i	−1.70099	−	0.570523i
$149$	−13.0609			−1.06999			−0.534995	−	0.844855i	$-0.679686\pi$
$149$	−13.0609			−1.06999			−0.534995	+	0.844855i	$0.679686\pi$
$150$	6.45486	−	2.44284i	0.527037	−	0.199457i
$151$	−16.6270	+	9.59960i	−1.35309	+	0.781204i	−0.988680	−	0.150037i	$-0.952061\pi$
$151$	−16.6270	+	9.59960i	−1.35309	+	0.781204i	−0.364405	+	0.931241i	$0.618727\pi$
$152$	0.418031	+	10.9447i	0.0339068	+	0.887732i
$153$	3.63749	+	6.30032i	0.294074	+	0.509351i
$154$	−8.28975	−	6.77805i	−0.668007	−	0.546191i
$155$	20.6175	+	11.9035i	1.65604	+	0.956113i
$156$	1.15177	−	3.43396i	0.0922155	−	0.274937i
$157$	12.1533	+	21.0501i	0.969936	+	1.67998i	0.695725	+	0.718309i	$0.255083\pi$
$157$	12.1533	+	21.0501i	0.969936	+	1.67998i	0.274211	+	0.961669i	$0.411583\pi$
$158$	−0.330817	+	2.02664i	−0.0263184	+	0.161231i
$159$		−	3.73302i		−	0.296047i
$160$	17.2792	−	4.19482i	1.36604	−	0.331630i
$161$			2.54304i			0.200420i
$162$	−1.32266	+	0.500561i	−0.103918	+	0.0393278i
$163$	2.27493	+	1.31343i	0.178187	+	0.102876i	0.586440	−	0.809992i	$-0.300529\pi$
$163$	2.27493	+	1.31343i	0.178187	+	0.102876i	−0.408254	+	0.912868i	$0.633862\pi$
$164$	−5.69462	+	1.15426i	−0.444675	+	0.0901327i
$165$	5.08642	+	2.93664i	0.395977	+	0.228617i
$166$	8.48757	−	10.3805i	0.658764	−	0.805687i
$167$	5.03270	+	2.90563i	0.389442	+	0.224845i	0.681918	−	0.731428i	$-0.261146\pi$
$167$	5.03270	+	2.90563i	0.389442	+	0.224845i	−0.292476	+	0.956273i	$0.594479\pi$
$168$	6.10541	+	9.69998i	0.471043	+	0.748370i
$169$	−4.86017	+	8.41806i	−0.373859	+	0.647543i
$170$	−20.4703	+	25.0358i	−1.57000	+	1.92016i
$171$	3.35356	−	1.93618i	0.256453	−	0.148063i
$172$	−3.75149	+	3.31416i	−0.286048	+	0.252703i
$173$	2.25366	+	3.90346i	0.171343	+	0.296775i	0.938890	−	0.344218i	$-0.111856\pi$
$173$	2.25366	+	3.90346i	0.171343	+	0.296775i	−0.767547	+	0.640993i	$0.778523\pi$
$174$	−2.01329	+	12.3337i	−0.152627	+	0.935015i
$175$	−9.88789	+	17.1263i	−0.747454	+	1.29463i
$176$	5.96251	+	4.50672i	0.449441	+	0.339707i
$177$			14.0628i			1.05702i
$178$	−6.46579	+	2.44697i	−0.484632	+	0.183408i
$179$	18.3582			1.37216			0.686079	−	0.727527i	$-0.259331\pi$
$179$	18.3582			1.37216			0.686079	+	0.727527i	$0.259331\pi$
$180$	−4.16216	−	4.71139i	−0.310229	−	0.351166i
$181$	2.65528	−	4.59908i	0.197365	−	0.341847i	−0.750308	−	0.661088i	$-0.770095\pi$
$181$	2.65528	−	4.59908i	0.197365	−	0.341847i	0.947673	+	0.319242i	$0.103428\pi$
$182$	3.67340	+	9.70644i	0.272290	+	0.719489i
$183$	2.09861	−	1.21163i	0.155134	−	0.0895665i
$184$	−0.0677472	−	1.77373i	−0.00499439	−	0.130761i
$185$	−29.7075	+	17.1516i	−2.18414	+	1.26101i
$186$	1.72560	−	10.5713i	0.126527	−	0.775123i
$187$	−13.5935			−0.994054
$188$	−13.6521	+	2.76718i	−0.995679	+	0.201817i
$189$	2.02612	−	3.50935i	0.147379	−	0.255268i
$190$	13.3262	+	10.8960i	0.966781	+	0.790481i
$191$	4.16544	+	7.21475i	0.301400	+	0.522041i	0.976453	−	0.215728i	$-0.0692126\pi$
$191$	4.16544	+	7.21475i	0.301400	+	0.522041i	−0.675053	+	0.737769i	$0.735879\pi$
$192$	−4.51682	−	6.60290i	−0.325973	−	0.476524i
$193$	21.1039			1.51909			0.759546	−	0.650453i	$-0.225421\pi$
$193$	21.1039			1.51909			0.759546	+	0.650453i	$0.225421\pi$
$194$	−1.95214	+	2.38752i	−0.140156	+	0.171414i
$195$	−2.84621	−	4.92979i	−0.203822	−	0.353029i
$196$	−17.8634	−	5.99149i	−1.27596	−	0.427964i
$197$	4.60979	+	2.66147i	0.328434	+	0.189622i	0.655146	−	0.755503i	$-0.272607\pi$
$197$	4.60979	+	2.66147i	0.328434	+	0.189622i	−0.326712	+	0.945124i	$0.605941\pi$
$198$	0.425712	−	2.60797i	0.0302540	−	0.185341i
$199$	−12.8058	+	7.39343i	−0.907779	+	0.524106i	−0.879716	−	0.475500i	$-0.842267\pi$
$199$	−12.8058	+	7.39343i	−0.907779	+	0.524106i	−0.0280631	+	0.999606i	$0.508934\pi$
$200$	6.44037	−	12.2087i	0.455403	−	0.863286i
$201$	6.35908	+	5.15385i	0.448535	+	0.363524i
$202$	−8.06881	−	1.31711i	−0.567720	−	0.0926715i
$203$	−17.9042	−	31.0110i	−1.25663	−	2.17654i
$204$	13.7947	+	4.62683i	0.965823	+	0.323943i
$205$	−4.56595	+	7.90845i	−0.318900	+	0.552350i
$206$	−13.9921	−	2.28400i	−0.974878	−	0.159134i
$207$	−0.543486	+	0.313782i	−0.0377749	+	0.0218094i
$208$	−2.82071	−	6.67220i	−0.195581	−	0.462634i
$209$			7.23559i			0.500496i
$210$	17.7780	+	2.90199i	1.22680	+	0.200256i
$211$	12.0538	−	6.95929i	0.829821	−	0.479097i	−0.0239703	−	0.999713i	$-0.507631\pi$
$211$	12.0538	−	6.95929i	0.829821	−	0.479097i	0.853791	+	0.520615i	$0.174297\pi$
$212$	−4.94306	−	5.59533i	−0.339491	−	0.384289i
$213$	−12.4110	−	7.16551i	−0.850389	−	0.490972i
$214$	−1.83501	−	4.84875i	−0.125438	−	0.331454i
$215$			7.86721i			0.536539i
$216$	−1.31969	+	2.50168i	−0.0897938	+	0.170218i
$217$	15.3458	+	26.5796i	1.04174	+	1.80434i
$218$	−3.28327	−	8.67559i	−0.222371	−	0.587585i
$219$	2.30070	+	3.98493i	0.155467	+	0.269276i
$220$	11.5125	−	2.33350i	0.776170	−	0.157324i
$221$	11.4098	+	6.58744i	0.767505	+	0.443119i
$222$	11.9481	+	9.76928i	0.801905	+	0.655671i
$223$			22.7611i			1.52420i	0.647460	+	0.762099i	$0.275831\pi$
$223$			22.7611i			1.52420i	−0.647460	+	0.762099i	$0.724169\pi$
$224$	21.9955	+	6.45461i	1.46963	+	0.431267i
$225$	−4.88020			−0.325347
$226$	−0.599864	−	0.0979186i	−0.0399024	−	0.00651345i
$227$	−8.68285	−	5.01304i	−0.576301	−	0.332727i	0.183361	−	0.983046i	$-0.441302\pi$
$227$	−8.68285	−	5.01304i	−0.576301	−	0.332727i	−0.759662	+	0.650318i	$0.774636\pi$
$228$	2.46279	−	7.34270i	0.163102	−	0.486282i
$229$	−7.45156	+	4.30216i	−0.492413	+	0.284295i	−0.725575	−	0.688143i	$-0.758426\pi$
$229$	−7.45156	+	4.30216i	−0.492413	+	0.284295i	0.233162	+	0.972438i	$0.425093\pi$
$230$	−2.15967	−	1.76584i	−0.142405	−	0.116436i
$231$	3.78586	+	6.55730i	0.249091	+	0.431439i
$232$	13.3140	+	21.1526i	0.874105	+	1.38874i
$233$	−12.1603	−	7.02078i	−0.796651	−	0.459946i	0.0456481	−	0.998958i	$-0.485465\pi$
$233$	−12.1603	−	7.02078i	−0.796651	−	0.459946i	−0.842299	+	0.539011i	$0.818798\pi$
$234$	−1.62116	+	1.98272i	−0.105978	+	0.129614i
$235$	−10.9462	+	18.9594i	−0.714053	+	1.23678i
$236$	18.6212	+	21.0784i	1.21214	+	1.37209i
$237$	0.726008	−	1.25748i	0.0471593	−	0.0816822i
$238$	−38.9922	+	14.7566i	−2.52749	+	0.956525i
$239$	−7.61571	+	13.1908i	−0.492619	+	0.853242i	−0.999964	−	0.00850144i	$-0.997294\pi$
$239$	−7.61571	+	13.1908i	−0.492619	+	0.853242i	0.507344	+	0.861743i	$0.330627\pi$
$240$	−12.4771	−	1.55047i	−0.805396	−	0.100083i
$241$	1.87229			0.120605			0.0603024	−	0.998180i	$-0.480794\pi$
$241$	1.87229			0.120605			0.0603024	+	0.998180i	$0.480794\pi$
$242$	−8.22067	−	6.72156i	−0.528444	−	0.432079i
$243$	1.00000			0.0641500
$244$	1.54118	−	4.59496i	0.0986638	−	0.294162i
$245$	−25.6447	+	14.8060i	−1.63838	+	0.945918i
$246$	4.05492	+	0.661904i	0.258533	+	0.0422014i
$247$	3.50639	−	6.07324i	0.223106	−	0.386431i
$248$	−11.4115	−	18.1300i	−0.724628	−	1.15125i
$249$	−8.21115	+	4.74071i	−0.520361	+	0.300430i
$250$	0.188493	+	0.498066i	0.0119213	+	0.0315005i
$251$	−2.42889	−	4.20697i	−0.153310	−	0.265542i	0.779132	−	0.626860i	$-0.215660\pi$
$251$	−2.42889	−	4.20697i	−0.153310	−	0.265542i	−0.932443	+	0.361318i	$0.882327\pi$
$252$	−1.60999	−	7.94297i	−0.101420	−	0.500360i
$253$		−	1.17262i		−	0.0737219i
$254$	2.46102	+	0.401723i	0.154418	+	0.0252064i
$255$	19.8037	−	11.4337i	1.24015	−	0.716003i
$256$	−15.5134	−	3.91601i	−0.969586	−	0.244751i
$257$	4.52176	−	7.83191i	0.282060	−	0.488541i	−0.689832	−	0.723969i	$-0.742316\pi$
$257$	4.52176	−	7.83191i	0.282060	−	0.488541i	0.971892	+	0.235428i	$0.0756491\pi$
$258$	3.31045	−	1.25284i	0.206100	−	0.0779982i
$259$	−44.2230			−2.74788
$260$	−10.7939	−	3.62034i	−0.669409	−	0.224524i
$261$	4.41834	−	7.65278i	0.273488	−	0.473695i
$262$	−3.49645	−	9.23888i	−0.216011	−	0.570780i
$263$		−	27.8170i		−	1.71527i	−0.514257	−	0.857636i	$-0.671932\pi$
$263$		−	27.8170i		−	1.71527i	0.514257	−	0.857636i	$-0.328068\pi$
$264$	−2.81525	−	4.47274i	−0.173267	−	0.275278i
$265$	−11.7339			−0.720808
$266$	7.85467	+	20.7549i	0.481601	+	1.27256i
$267$	4.88846			0.299169
$268$	16.3559	−	0.695377i	0.999097	−	0.0424769i
$269$	28.3773			1.73019			0.865097	−	0.501605i	$-0.167257\pi$
$269$	28.3773			1.73019			0.865097	+	0.501605i	$0.167257\pi$
$270$	1.57340	+	4.15750i	0.0957543	+	0.253017i
$271$	−11.4356			−0.694661			−0.347331	−	0.937743i	$-0.612912\pi$
$271$	−11.4356			−0.694661			−0.347331	+	0.937743i	$0.612912\pi$
$272$	26.8032	−	11.3312i	1.62518	−	0.687054i
$273$		−	7.33856i		−	0.444150i
$274$	10.0556	+	26.5704i	0.607478	+	1.60518i
$275$	4.55938	−	7.89709i	0.274941	−	0.476212i
$276$	−0.399126	+	1.18998i	−0.0240245	+	0.0716282i
$277$	−11.7684			−0.707093			−0.353547	−	0.935417i	$-0.615024\pi$
$277$	−11.7684			−0.707093			−0.353547	+	0.935417i	$0.615024\pi$
$278$	−11.2654	+	4.26338i	−0.675654	+	0.255701i
$279$	−3.78697	+	6.55923i	−0.226720	+	0.392691i
$280$	30.4897	−	19.1910i	1.82211	−	1.14688i
$281$	−0.164511	+	0.0949807i	−0.00981393	+	0.00566607i	−0.504899	−	0.863178i	$-0.668470\pi$
$281$	−0.164511	+	0.0949807i	−0.00981393	+	0.00566607i	0.495085	+	0.868845i	$0.335137\pi$
$282$	9.72111	+	1.58682i	0.578884	+	0.0944939i
$283$		−	25.3856i		−	1.50902i	−0.656290	−	0.754509i	$-0.727875\pi$
$283$		−	25.3856i		−	1.50902i	0.656290	−	0.754509i	$-0.272125\pi$
$284$	−28.0908	+	5.69381i	−1.66688	+	0.337866i
$285$	−6.08595	−	10.5412i	−0.360500	−	0.624405i
$286$	−1.69383	−	4.47572i	−0.100158	−	0.264655i
$287$	−10.1954	+	5.88632i	−0.601816	+	0.347459i
$288$	1.33454	+	5.49718i	0.0786383	+	0.323925i
$289$	−17.9627	+	31.1123i	−1.05663	+	1.83014i
$290$	38.7683	+	6.32832i	2.27655	+	0.371612i
$291$	1.88856	−	1.09036i	0.110710	−	0.0639182i
$292$	8.72509	+	2.92645i	0.510597	+	0.171258i
$293$	9.67877			0.565440			0.282720	−	0.959202i	$-0.408763\pi$
$293$	9.67877			0.565440			0.282720	+	0.959202i	$0.408763\pi$
$294$	10.3141	+	8.43322i	0.601529	+	0.491836i
$295$	44.2033			2.57362
$296$	30.8447	−	1.17811i	1.79281	−	0.0684762i
$297$	−0.934262	+	1.61819i	−0.0542114	+	0.0938968i
$298$	17.2752	−	6.53777i	1.00072	−	0.378723i
$299$	−0.568254	+	0.984245i	−0.0328630	+	0.0569204i
$300$	−7.31482	+	6.46211i	−0.422321	+	0.373090i
$301$	−5.07112	+	8.78343i	−0.292294	+	0.506269i
$302$	17.1867	−	21.0199i	0.988985	−	1.20956i
$303$	5.00651	+	2.89051i	0.287617	+	0.166056i
$304$	−6.03140	−	14.2669i	−0.345925	−	0.818263i
$305$	−3.80850	−	6.59651i	−0.218074	−	0.377715i
$306$	−7.96487	−	6.51242i	−0.455321	−	0.372290i
$307$	18.3287	−	10.5821i	1.04607	−	0.603950i	0.124525	−	0.992217i	$-0.460259\pi$
$307$	18.3287	−	10.5821i	1.04607	−	0.603950i	0.921547	+	0.388267i	$0.126926\pi$
$308$	14.3574	+	4.81555i	0.818087	+	0.274392i
$309$	8.68180	+	5.01244i	0.493890	+	0.285148i
$310$	−33.2284	−	5.42403i	−1.88725	−	0.308064i
$311$	22.5190			1.27694			0.638469	−	0.769648i	$-0.279568\pi$
$311$	22.5190			1.27694			0.638469	+	0.769648i	$0.279568\pi$
$312$	0.195500	+	5.11850i	0.0110680	+	0.289778i
$313$		−	28.6373i		−	1.61868i	−0.587344	−	0.809338i	$-0.699826\pi$
$313$		−	28.6373i		−	1.61868i	0.587344	−	0.809338i	$-0.300174\pi$
$314$	−26.6115	−	21.7587i	−1.50177	−	1.22791i
$315$	−11.0309	−	6.36867i	−0.621519	−	0.358834i
$316$	−0.576896	−	2.84615i	−0.0324529	−	0.160109i
$317$	11.5584	+	20.0198i	0.649186	+	1.12442i	0.983318	+	0.181896i	$0.0582236\pi$
$317$	11.5584	+	20.0198i	0.649186	+	1.12442i	−0.334132	+	0.942526i	$0.608443\pi$
$318$	1.86860	+	4.93752i	0.104786	+	0.276883i
$319$	8.25576	+	14.2994i	0.462234	+	0.800613i
$320$	−20.7548	+	14.1976i	−1.16023	+	0.793671i
$321$			3.66590i			0.204611i
$322$	−1.27295	−	3.36359i	−0.0709387	−	0.187446i
$323$	24.3971	+	14.0857i	1.35749	+	0.783747i
$324$	1.49888	−	1.32415i	0.0832710	−	0.0735638i
$325$	−7.65390	+	4.41898i	−0.424562	+	0.245121i
$326$	−3.66643	−	0.598487i	−0.203065	−	0.0331472i
$327$			6.55918i			0.362724i
$328$	6.95429	−	4.37721i	0.383987	−	0.241691i
$329$	−24.4421	+	14.1116i	−1.34753	+	0.777999i
$330$	−8.19759	−	1.33813i	−0.451262	−	0.0736616i
$331$	5.59150	−	9.68477i	0.307337	−	0.532323i	−0.670442	−	0.741962i	$-0.733895\pi$
$331$	5.59150	−	9.68477i	0.307337	−	0.532323i	0.977779	+	0.209639i	$0.0672288\pi$
$332$	−6.03011	+	17.9785i	−0.330945	+	0.986699i
$333$	−5.45660	−	9.45112i	−0.299020	−	0.517918i
$334$	−8.11102	−	1.32400i	−0.443815	−	0.0724460i
$335$	16.2000	−	19.9884i	0.885099	−	1.09208i
$336$	−12.9308	−	9.77368i	−0.705435	−	0.533198i
$337$	−2.03943	+	1.17747i	−0.111095	+	0.0641407i	−0.554518	−	0.832172i	$-0.687097\pi$
$337$	−2.03943	+	1.17747i	−0.111095	+	0.0641407i	0.443423	+	0.896312i	$0.353764\pi$
$338$	2.21461	−	13.5671i	0.120459	−	0.737951i
$339$	0.372202	+	0.214891i	0.0202153	+	0.0116713i
$340$	14.5434	−	43.3606i	0.788728	−	2.35156i
$341$	−7.07605	−	12.2561i	−0.383189	−	0.663704i
$342$	−3.46645	+	4.23957i	−0.187444	+	0.229250i
$343$	−9.80930			−0.529652
$344$	3.30302	−	6.26137i	0.178087	−	0.337591i
$345$	0.986304	+	1.70833i	0.0531008	+	0.0919734i
$346$	−4.93476	−	4.03487i	−0.265294	−	0.216916i
$347$	5.79554	−	10.0382i	0.311121	−	0.538878i	−0.667484	−	0.744624i	$-0.732629\pi$
$347$	5.79554	−	10.0382i	0.311121	−	0.538878i	0.978605	+	0.205746i	$0.0659622\pi$
$348$	−3.51087	−	17.3211i	−0.188202	−	0.928509i
$349$	−16.4268			−0.879304			−0.439652	−	0.898168i	$-0.644898\pi$
$349$	−16.4268			−0.879304			−0.439652	+	0.898168i	$0.644898\pi$
$350$	4.50558	−	27.6019i	0.240833	−	1.47538i
$351$	1.56836	−	0.905492i	0.0837128	−	0.0483316i
$352$	−10.1423	−	2.97627i	−0.540586	−	0.158636i
$353$	25.1091	−	14.4967i	1.33642	−	0.771584i	0.350147	−	0.936695i	$-0.386132\pi$
$353$	25.1091	−	14.4967i	1.33642	−	0.771584i	0.986275	+	0.165111i	$0.0527983\pi$
$354$	−7.03929	−	18.6004i	−0.374134	−	0.988598i
$355$	−22.5232	+	39.0113i	−1.19541	+	2.07051i
$356$	7.32721	−	6.47305i	0.388341	−	0.343071i
$357$	29.4800			1.56025
$358$	−24.2817	+	9.18941i	−1.28333	+	0.485675i
$359$		−	16.0771i		−	0.848516i	−0.905541	−	0.424258i	$-0.860535\pi$
$359$		−	16.0771i		−	0.848516i	0.905541	−	0.424258i	$-0.139465\pi$
$360$	7.86348	+	4.14816i	0.414442	+	0.218627i
$361$	−2.00243	+	3.46832i	−0.105391	+	0.182543i
$362$	−1.20992	+	7.41216i	−0.0635920	+	0.389574i
$363$	3.75431	+	6.50266i	0.197050	+	0.341301i
$364$	−9.71733	−	10.9996i	−0.509327	−	0.576535i
$365$	12.5257	−	7.23173i	0.655627	−	0.378526i
$366$	−2.16926	+	2.65306i	−0.113389	+	0.138678i
$367$	3.79571	−	6.57436i	0.198134	−	0.343179i	−0.749789	−	0.661677i	$-0.769845\pi$
$367$	3.79571	−	6.57436i	0.198134	−	0.343179i	0.947924	+	0.318498i	$0.103178\pi$
$368$	0.977465	+	2.31213i	0.0509539	+	0.120528i
$369$	−2.51599	−	1.45261i	−0.130977	−	0.0756197i
$370$	30.7076	−	37.5562i	1.59641	−	1.95246i
$371$	−13.1005	−	7.56355i	−0.680142	−	0.392680i
$372$	3.00918	+	14.8460i	0.156019	+	0.769729i
$373$	2.90432	+	1.67681i	0.150380	+	0.0868220i	0.573302	−	0.819344i	$-0.305662\pi$
$373$	2.90432	+	1.67681i	0.150380	+	0.0868220i	−0.422922	+	0.906166i	$0.638996\pi$
$374$	17.9796	−	6.80437i	0.929703	−	0.351845i
$375$		−	0.376563i		−	0.0194456i
$376$	16.6719	−	10.4937i	0.859790	−	0.541173i
$377$		−	16.0031i		−	0.824200i
$378$	−0.923236	+	5.65589i	−0.0474861	+	0.290907i
$379$	−9.02457	−	15.6310i	−0.463561	−	0.802911i	0.535574	−	0.844488i	$-0.320095\pi$
$379$	−9.02457	−	15.6310i	−0.463561	−	0.802911i	−0.999135	+	0.0415769i	$0.986762\pi$
$380$	−23.0801	−	7.74122i	−1.18399	−	0.397116i
$381$	−1.52701	−	0.881617i	−0.0782309	−	0.0451666i
$382$	−9.12089	−	7.45763i	−0.466665	−	0.381565i
$383$	2.02414	+	3.50592i	0.103429	+	0.179144i	0.913095	−	0.407746i	$-0.133685\pi$
$383$	2.02414	+	3.50592i	0.103429	+	0.179144i	−0.809666	+	0.586890i	$0.800352\pi$
$384$	9.27939	+	6.47248i	0.473537	+	0.330297i
$385$	20.6114	−	11.9000i	1.05046	−	0.606481i
$386$	−27.9134	+	10.5638i	−1.42075	+	0.537683i
$387$	−2.50287			−0.127228
$388$	1.38692	−	4.13506i	0.0704104	−	0.209926i
$389$	6.54654	+	11.3389i	0.331923	+	0.574907i	0.982889	−	0.184200i	$-0.0589694\pi$
$389$	6.54654	+	11.3389i	0.331923	+	0.574907i	−0.650966	+	0.759107i	$0.725636\pi$
$390$	6.23224	+	5.09575i	0.315582	+	0.258033i
$391$	−3.95385	−	2.28276i	−0.199955	−	0.115444i
$392$	26.6264	−	1.01699i	1.34483	−	0.0513657i
$393$			6.98506i			0.352350i
$394$	−7.42943	−	1.21274i	−0.374289	−	0.0610969i
$395$	−3.95262	−	2.28204i	−0.198878	−	0.114822i
$396$	0.742377	+	3.66257i	0.0373059	+	0.184051i
$397$	1.91018			0.0958692			0.0479346	−	0.998850i	$-0.484736\pi$
$397$	1.91018			0.0958692			0.0479346	+	0.998850i	$0.484736\pi$
$398$	13.2369	−	16.1891i	0.663506	−	0.811487i
$399$		−	15.6917i		−	0.785570i
$400$	−2.40724	+	19.3718i	−0.120362	+	0.968590i
$401$		−	0.717734i		−	0.0358419i	−0.999839	−	0.0179210i	$-0.994295\pi$
$401$		−	0.717734i		−	0.0358419i	0.999839	−	0.0179210i	$-0.00570473\pi$
$402$	−10.9907	−	3.63370i	−0.548168	−	0.181232i
$403$			13.7163i			0.683257i
$404$	11.3316	−	2.29684i	0.563769	−	0.114272i
$405$		−	3.14328i		−	0.156191i
$406$	39.2041	+	32.0549i	1.94567	+	1.59086i
$407$	20.3916			1.01077
$408$	−20.5618	+	0.785354i	−1.01796	+	0.0388808i
$409$	−18.3698	−	10.6058i	−0.908328	−	0.524423i	−0.0284352	−	0.999596i	$-0.509052\pi$
$409$	−18.3698	−	10.6058i	−0.908328	−	0.524423i	−0.879893	+	0.475172i	$0.842386\pi$
$410$	2.08055	−	12.7458i	0.102751	−	0.629468i
$411$		−	20.0886i		−	0.990896i
$412$	19.6502	−	3.98295i	0.968094	−	0.196226i
$413$	49.3513	+	28.4930i	2.42842	+	1.40205i
$414$	0.561783	−	0.687076i	0.0276101	−	0.0337680i
$415$	14.9014	+	25.8099i	0.731480	+	1.26696i
$416$	7.07069	+	7.41314i	0.346669	+	0.363459i
$417$	8.51721			0.417090
$418$	−3.62185	−	9.57025i	−0.177151	−	0.468096i
$419$	−24.3289	+	14.0463i	−1.18855	+	0.686208i	−0.957976	−	0.286848i	$-0.907393\pi$
$419$	−24.3289	+	14.0463i	−1.18855	+	0.686208i	−0.230571	+	0.973056i	$0.574059\pi$
$420$	−24.9670	+	5.06063i	−1.21826	+	0.246934i
$421$	19.1695	+	33.2025i	0.934264	+	1.61819i	0.775942	+	0.630805i	$0.217275\pi$
$421$	19.1695	+	33.2025i	0.934264	+	1.61819i	0.158322	+	0.987388i	$0.449392\pi$
$422$	−12.4596	+	15.2385i	−0.606525	+	0.741798i
$423$	−6.03173	−	3.48242i	−0.293273	−	0.169321i
$424$	9.33882	+	4.92644i	0.453533	+	0.239249i
$425$	−17.7517	−	30.7468i	−0.861083	−	1.49144i
$426$	20.0024	+	3.26508i	0.969119	+	0.158194i
$427$		−	9.81967i		−	0.475207i
$428$	4.85419	+	5.49473i	0.234636	+	0.265598i
$429$			3.38387i			0.163375i
$430$	−3.93802	−	10.4057i	−0.189908	−	0.501806i
$431$	−31.0841	−	17.9464i	−1.49727	−	0.864450i	−0.497275	−	0.867593i	$-0.665666\pi$
$431$	−31.0841	−	17.9464i	−1.49727	−	0.864450i	−0.999995	+	0.00314323i	$0.998999\pi$
$432$	0.493266	−	3.96947i	0.0237323	−	0.190981i
$433$	19.3801	+	11.1891i	0.931347	+	0.537714i	0.887237	−	0.461313i	$-0.152622\pi$
$433$	19.3801	+	11.1891i	0.931347	+	0.537714i	0.0441099	+	0.999027i	$0.485955\pi$
$434$	−33.6020	−	27.4744i	−1.61295	−	1.31881i
$435$	−24.0548	−	13.8881i	−1.15334	−	0.665881i
$436$	8.68533	+	9.83141i	0.415952	+	0.470839i
$437$	−1.21508	+	2.10457i	−0.0581249	+	0.100675i
$438$	−5.03775	−	4.11908i	−0.240713	−	0.196817i
$439$	−5.92371	+	3.42006i	−0.282723	+	0.163230i	−0.634656	−	0.772795i	$-0.718858\pi$
$439$	−5.92371	+	3.42006i	−0.282723	+	0.163230i	0.351932	+	0.936025i	$0.385525\pi$
$440$	−14.0591	+	8.84913i	−0.670239	+	0.421866i
$441$	−4.71035	−	8.15857i	−0.224303	−	0.388503i
$442$	−18.3887	−	3.00167i	−0.874662	−	0.142775i
$443$	18.5472	−	32.1247i	0.881206	−	1.52629i	0.0312039	−	0.999513i	$-0.490066\pi$
$443$	18.5472	−	32.1247i	0.881206	−	1.52629i	0.850002	−	0.526780i	$-0.176601\pi$
$444$	−20.6935	−	6.94071i	−0.982068	−	0.329392i
$445$		−	15.3658i		−	0.728409i
$446$	−11.3933	−	30.1053i	−0.539490	−	1.42553i
$447$	−13.0609			−0.617759
$448$	−32.3235	+	2.47279i	−1.52714	+	0.116828i
$449$	−11.1349	+	19.2862i	−0.525487	+	0.910171i	0.474072	+	0.880486i	$0.342784\pi$
$449$	−11.1349	+	19.2862i	−0.525487	+	0.910171i	−0.999559	+	0.0296847i	$0.990550\pi$
$450$	6.45486	−	2.44284i	0.304285	−	0.115157i
$451$	4.70118	−	2.71423i	0.221370	−	0.127808i
$452$	0.842433	−	0.170755i	0.0396247	−	0.00803166i
$453$	−16.6270	+	9.59960i	−0.781204	+	0.451028i
$454$	13.9938	+	2.28427i	0.656762	+	0.107206i
$455$	−23.0671			−1.08140
$456$	0.418031	+	10.9447i	0.0195761	+	0.512532i
$457$	−10.6263	+	18.4054i	−0.497079	+	0.860966i	−0.999994	−	0.00336952i	$-0.998927\pi$
$457$	−10.6263	+	18.4054i	−0.497079	+	0.860966i	0.502915	+	0.864336i	$0.332261\pi$
$458$	7.70241	−	9.42027i	0.359910	−	0.440180i
$459$	3.63749	+	6.30032i	0.169784	+	0.294074i
$460$	3.74043	+	1.25456i	0.174398	+	0.0584943i
$461$	−35.1560			−1.63738			−0.818689	−	0.574237i	$-0.805299\pi$
$461$	−35.1560			−1.63738			−0.818689	+	0.574237i	$0.805299\pi$
$462$	−8.28975	−	6.77805i	−0.385674	−	0.315343i
$463$	7.07547	+	12.2551i	0.328825	+	0.569542i	0.982279	−	0.187425i	$-0.0600140\pi$
$463$	7.07547	+	12.2551i	0.328825	+	0.569542i	−0.653454	+	0.756966i	$0.726681\pi$
$464$	−28.1981	−	21.3133i	−1.30906	−	0.989445i
$465$	20.6175	+	11.9035i	0.956113	+	0.552012i
$466$	19.5984	+	3.19913i	0.907877	+	0.148197i
$467$	8.68690	−	5.01538i	0.401982	−	0.232084i	−0.285357	−	0.958421i	$-0.592112\pi$
$467$	8.68690	−	5.01538i	0.401982	−	0.232084i	0.687339	+	0.726337i	$0.258779\pi$
$468$	1.15177	−	3.43396i	0.0532407	−	0.158735i
$469$	30.9709	−	11.8739i	1.43010	−	0.548286i
$470$	4.98782	−	30.5562i	0.230071	−	1.40945i
$471$	12.1533	+	21.0501i	0.559993	+	0.969936i
$472$	−35.1806	−	18.5586i	−1.61932	−	0.854228i
$473$	2.33833	−	4.05011i	0.107517	−	0.186224i
$474$	−0.330817	+	2.02664i	−0.0151949	+	0.0930865i
$475$	−16.3660	+	9.44893i	−0.750925	+	0.433547i
$476$	44.1869	−	39.0359i	2.02531	−	1.78921i
$477$		−	3.73302i		−	0.170923i
$478$	3.47022	−	21.2591i	0.158724	−	0.972369i
$479$	−29.7525	+	17.1776i	−1.35943	+	0.784865i	−0.989546	−	0.144215i	$-0.953934\pi$
$479$	−29.7525	+	17.1776i	−1.35943	+	0.784865i	−0.369880	+	0.929080i	$0.620601\pi$
$480$	17.2792	−	4.19482i	0.788683	−	0.191467i
$481$	−17.1158	−	9.88182i	−0.780414	−	0.450572i
$482$	−2.47641	+	0.937195i	−0.112797	+	0.0426881i
$483$			2.54304i			0.115713i
$484$	14.2377	+	4.77542i	0.647169	+	0.217065i
$485$	−3.42731	−	5.93628i	−0.155626	−	0.269553i
$486$	−1.32266	+	0.500561i	−0.0599972	+	0.0227059i
$487$	1.95720	+	3.38997i	0.0886891	+	0.153614i	0.906957	−	0.421223i	$-0.138399\pi$
$487$	1.95720	+	3.38997i	0.0886891	+	0.153614i	−0.818268	+	0.574837i	$0.805066\pi$
$488$	0.261598	+	6.84903i	0.0118420	+	0.310041i
$489$	2.27493	+	1.31343i	0.102876	+	0.0593955i
$490$	26.5080	−	32.4200i	1.19751	−	1.46459i
$491$			34.4636i			1.55532i	0.628684	+	0.777661i	$0.283594\pi$
$491$			34.4636i			1.55532i	−0.628684	+	0.777661i	$0.716406\pi$
$492$	−5.69462	+	1.15426i	−0.256733	+	0.0520381i
$493$	64.2866			2.89532
$494$	−1.59774	+	9.78801i	−0.0718858	+	0.440384i
$495$	5.08642	+	2.93664i	0.228617	+	0.131992i
$496$	24.1687	+	18.2677i	1.08521	+	0.820245i
$497$	−50.2925	+	29.0364i	−2.25593	+	1.30246i
$498$	8.48757	−	10.3805i	0.380337	−	0.465163i
$499$	19.3059	+	33.4388i	0.864251	+	1.49693i	0.867789	+	0.496932i	$0.165540\pi$
$499$	19.3059	+	33.4388i	0.864251	+	1.49693i	−0.00353889	+	0.999994i	$0.501126\pi$
$500$	−0.498625	−	0.564422i	−0.0222992	−	0.0252417i
$501$	5.03270	+	2.90563i	0.224845	+	0.129814i
$502$	5.31846	+	4.34859i	0.237374	+	0.194087i
$503$	−6.50316	+	11.2638i	−0.289961	+	0.502228i	−0.973800	−	0.227405i	$-0.926976\pi$
$503$	−6.50316	+	11.2638i	−0.289961	+	0.502228i	0.683839	+	0.729633i	$0.260309\pi$
$504$	6.10541	+	9.69998i	0.271957	+	0.432071i
$505$	9.08569	−	15.7369i	0.404308	−	0.700282i
$506$	0.586967	+	1.55098i	0.0260939	+	0.0689494i
$507$	−4.86017	+	8.41806i	−0.215848	+	0.373859i
$508$	−3.45619	+	0.700545i	−0.153343	+	0.0310817i
$509$	18.6072			0.824749			0.412375	−	0.911014i	$-0.364699\pi$
$509$	18.6072			0.824749			0.412375	+	0.911014i	$0.364699\pi$
$510$	−20.4703	+	25.0358i	−0.906442	+	1.10860i
$511$	18.6460			0.824850
$512$	22.4792	−	2.58583i	0.993449	−	0.114279i
$513$	3.35356	−	1.93618i	0.148063	−	0.0854843i
$514$	−2.06041	+	12.6224i	−0.0908809	+	0.556750i
$515$	15.7555	−	27.2893i	0.694270	−	1.20251i
$516$	−3.75149	+	3.31416i	−0.165150	+	0.145898i
$517$	11.2704	−	6.50698i	0.495673	−	0.286177i
$518$	58.4922	−	22.1363i	2.57000	−	0.972614i
$519$	2.25366	+	3.90346i	0.0989249	+	0.171343i
$520$	16.0889	−	0.614513i	0.705544	−	0.0269482i
$521$		−	28.3049i		−	1.24006i	−0.784577	−	0.620031i	$-0.787120\pi$
$521$		−	28.3049i		−	1.24006i	0.784577	−	0.620031i	$-0.212880\pi$
$522$	−2.01329	+	12.3337i	−0.0881191	+	0.539831i
$523$	13.9278	−	8.04122i	0.609021	−	0.351618i	−0.163561	−	0.986533i	$-0.552298\pi$
$523$	13.9278	−	8.04122i	0.609021	−	0.351618i	0.772582	+	0.634915i	$0.218965\pi$
$524$	9.24925	+	10.4697i	0.404055	+	0.457373i
$525$	−9.88789	+	17.1263i	−0.431543	+	0.747454i
$526$	13.9241	+	36.7926i	0.607121	+	1.60423i
$527$	−55.1003			−2.40021
$528$	5.96251	+	4.50672i	0.259485	+	0.196130i
$529$	−11.3031	+	19.5775i	−0.491438	+	0.851196i
$530$	15.5200	−	5.87354i	0.674146	−	0.255130i
$531$			14.0628i			0.610274i
$532$	−20.7782	−	23.5200i	−0.900848	−	1.01972i
$533$	−5.26130			−0.227892
$534$	−6.46579	+	2.44697i	−0.279802	+	0.105891i
$535$	11.5229			0.498180
$536$	−21.2853	+	9.10689i	−0.919385	+	0.393358i
$537$	18.3582			0.792216
$538$	−37.5336	+	14.2046i	−1.61819	+	0.612402i
$539$	17.6028			0.758207
$540$	−4.16216	−	4.71139i	−0.179111	−	0.202746i
$541$		−	35.5470i		−	1.52828i	−0.645049	−	0.764142i	$-0.723163\pi$
$541$		−	35.5470i		−	1.52828i	0.645049	−	0.764142i	$-0.276837\pi$
$542$	15.1254	−	5.72420i	0.649692	−	0.245876i
$543$	2.65528	−	4.59908i	0.113949	−	0.197365i
$544$	−29.7796	+	28.4040i	−1.27679	+	1.21781i
$545$	20.6173			0.883150
$546$	3.67340	+	9.70644i	0.157207	+	0.415397i
$547$	−3.78761	+	6.56033i	−0.161946	+	0.280499i	−0.935567	−	0.353150i	$-0.885110\pi$
$547$	−3.78761	+	6.56033i	−0.161946	+	0.280499i	0.773620	+	0.633649i	$0.218444\pi$
$548$	−26.6002	−	30.1103i	−1.13631	−	1.28625i
$549$	2.09861	−	1.21163i	0.0895665	−	0.0517112i
$550$	−2.07756	+	12.7274i	−0.0885874	+	0.542700i
$551$		−	34.2187i		−	1.45777i
$552$	−0.0677472	−	1.77373i	−0.00288351	−	0.0754948i
$553$	−2.94196	−	5.09563i	−0.125105	−	0.216688i
$554$	15.5656	−	5.89079i	0.661319	−	0.250276i
$555$	−29.7075	+	17.1516i	−1.26101	+	0.728046i
$556$	12.7663	−	11.2780i	0.541410	−	0.478296i
$557$	−15.2481	+	26.4105i	−0.646083	+	1.11905i	0.337967	+	0.941158i	$0.390261\pi$
$557$	−15.2481	+	26.4105i	−0.646083	+	1.11905i	−0.984050	+	0.177891i	$0.943073\pi$
$558$	1.72560	−	10.5713i	0.0730503	−	0.447517i
$559$	−3.92539	+	2.26633i	−0.166026	+	0.0958554i
$560$	−30.7214	+	40.6452i	−1.29822	+	1.71757i
$561$	−13.5935			−0.573917
$562$	0.170050	−	0.207976i	0.00717311	−	0.00877292i
$563$	31.9971			1.34852			0.674258	−	0.738496i	$-0.264464\pi$
$563$	31.9971			1.34852			0.674258	+	0.738496i	$0.264464\pi$
$564$	−13.6521	+	2.76718i	−0.574855	+	0.116519i
$565$	0.675463	−	1.16994i	0.0284169	−	0.0492196i
$566$	12.7070	+	33.5766i	0.534117	+	1.41133i
$567$	2.02612	−	3.50935i	0.0850892	−	0.147379i
$568$	34.3046	−	21.5922i	1.43939	−	0.905987i
$569$	3.32706	−	5.76263i	0.139477	−	0.241582i	−0.787822	−	0.615904i	$-0.788791\pi$
$569$	3.32706	−	5.76263i	0.139477	−	0.241582i	0.927299	+	0.374322i	$0.122124\pi$
$570$	13.3262	+	10.8960i	0.558171	+	0.456384i
$571$	−10.4964	−	6.06010i	−0.439261	−	0.253607i	0.264023	−	0.964516i	$-0.414950\pi$
$571$	−10.4964	−	6.06010i	−0.439261	−	0.253607i	−0.703284	+	0.710909i	$0.748284\pi$
$572$	4.48074	+	5.07200i	0.187349	+	0.212071i
$573$	4.16544	+	7.21475i	0.174014	+	0.301400i
$574$	10.5386	−	12.8890i	0.439874	−	0.537978i
$575$	2.65232	−	1.53132i	0.110610	−	0.0638604i
$576$	−4.51682	−	6.60290i	−0.188201	−	0.275121i
$577$	2.06577	+	1.19267i	0.0859990	+	0.0496516i	0.542383	−	0.840131i	$-0.317522\pi$
$577$	2.06577	+	1.19267i	0.0859990	+	0.0496516i	−0.456384	+	0.889783i	$0.650856\pi$
$578$	8.18499	−	50.1425i	0.340451	−	2.08565i
$579$	21.1039			0.877048
$580$	−54.4451	+	11.0356i	−2.26071	+	0.458230i
$581$			38.4211i			1.59397i
$582$	−1.95214	+	2.38752i	−0.0809188	+	0.0989661i
$583$	6.04072	+	3.48761i	0.250181	+	0.144442i
$584$	−13.0052	+	0.496733i	−0.538160	+	0.0205549i
$585$	−2.84621	−	4.92979i	−0.117676	−	0.203822i
$586$	−12.8018	+	4.84482i	−0.528836	+	0.200138i
$587$	11.4631	+	19.8546i	0.473132	+	0.819489i	0.999527	−	0.0307515i	$-0.00979006\pi$
$587$	11.4631	+	19.8546i	0.473132	+	0.819489i	−0.526395	+	0.850240i	$0.676457\pi$
$588$	−17.8634	−	5.99149i	−0.736674	−	0.247085i
$589$			29.3290i			1.20848i
$590$	−58.4661	+	22.1265i	−2.40701	+	0.910932i
$591$	4.60979	+	2.66147i	0.189622	+	0.109478i
$592$	−40.2075	+	16.9979i	−1.65252	+	0.698610i
$593$	26.0828	−	15.0589i	1.07109	−	0.618396i	0.142613	−	0.989778i	$-0.454449\pi$
$593$	26.0828	−	15.0589i	1.07109	−	0.618396i	0.928480	+	0.371383i	$0.121116\pi$
$594$	0.425712	−	2.60797i	0.0174672	−	0.107006i
$595$		−	92.6640i		−	3.79885i
$596$	−19.5767	+	17.2945i	−0.801891	+	0.708412i
$597$	−12.8058	+	7.39343i	−0.524106	+	0.302593i
$598$	0.258934	−	1.58627i	0.0105886	−	0.0648675i
$599$	−13.7306	+	23.7821i	−0.561016	+	0.971708i	0.436392	+	0.899757i	$0.356256\pi$
$599$	−13.7306	+	23.7821i	−0.561016	+	0.971708i	−0.997408	+	0.0719518i	$0.977077\pi$
$600$	6.44037	−	12.2087i	0.262927	−	0.498418i
$601$	−9.04377	−	15.6643i	−0.368903	−	0.638959i	0.620491	−	0.784213i	$-0.286933\pi$
$601$	−9.04377	−	15.6643i	−0.368903	−	0.638959i	−0.989394	+	0.145254i	$0.953600\pi$
$602$	2.31074	−	14.1559i	0.0941786	−	0.576952i
$603$	6.35908	+	5.15385i	0.258962	+	0.209881i
$604$	−12.2105	+	36.4052i	−0.496839	+	1.48131i
$605$	20.4397	−	11.8008i	0.830990	−	0.479773i
$606$	−8.06881	−	1.31711i	−0.327773	−	0.0535039i
$607$	9.00353	+	5.19819i	0.365442	+	0.210988i	0.671465	−	0.741036i	$-0.265665\pi$
$607$	9.00353	+	5.19819i	0.365442	+	0.210988i	−0.306023	+	0.952024i	$0.598999\pi$
$608$	15.1190	+	15.8512i	0.613155	+	0.642852i
$609$	−17.9042	−	31.0110i	−0.725514	−	1.25663i
$610$	8.33932	+	6.81858i	0.337649	+	0.276076i
$611$	−12.6132			−0.510276
$612$	13.7947	+	4.62683i	0.557618	+	0.187029i
$613$	2.48491	+	4.30399i	0.100365	+	0.173837i	0.911835	−	0.410557i	$-0.134666\pi$
$613$	2.48491	+	4.30399i	0.100365	+	0.173837i	−0.811470	+	0.584394i	$0.801332\pi$
$614$	−18.9457	+	23.1711i	−0.764585	+	0.935110i
$615$	−4.56595	+	7.90845i	−0.184117	+	0.318900i
$616$	−21.4004	+	0.817387i	−0.862249	+	0.0329335i
$617$	−12.7043			−0.511456			−0.255728	−	0.966749i	$-0.582315\pi$
$617$	−12.7043			−0.511456			−0.255728	+	0.966749i	$0.582315\pi$
$618$	−13.9921	−	2.28400i	−0.562846	−	0.0918759i
$619$	−29.0492	+	16.7715i	−1.16758	+	0.674105i	−0.953110	−	0.302624i	$-0.902137\pi$
$619$	−29.0492	+	16.7715i	−1.16758	+	0.674105i	−0.214475	+	0.976730i	$0.568804\pi$
$620$	46.6651	−	9.45869i	1.87412	−	0.379870i
$621$	−0.543486	+	0.313782i	−0.0218094	+	0.0125916i
$622$	−29.7851	+	11.2722i	−1.19427	+	0.451972i
$623$	9.90463	−	17.1553i	0.396821	−	0.687313i
$624$	−2.82071	−	6.67220i	−0.112919	−	0.267102i
$625$	−25.5846			−1.02339
$626$	14.3347	+	37.8775i	0.572930	+	1.51389i
$627$			7.23559i			0.288961i
$628$	46.0896	+	15.4588i	1.83918	+	0.616871i
$629$	39.6967	−	68.7567i	1.58281	−	2.74151i
$630$	17.7780	+	2.90199i	0.708294	+	0.115618i
$631$	−2.02430	−	3.50619i	−0.0805862	−	0.139579i	0.822916	−	0.568164i	$-0.192346\pi$
$631$	−2.02430	−	3.50619i	−0.0805862	−	0.139579i	−0.903502	+	0.428584i	$0.859013\pi$
$632$	2.18771	+	3.47573i	0.0870225	+	0.138257i
$633$	12.0538	−	6.95929i	0.479097	−	0.276607i
$634$	−25.3090	−	20.6937i	−1.00515	−	0.821853i
$635$	−2.77117	+	4.79981i	−0.109971	+	0.190475i
$636$	−4.94306	−	5.59533i	−0.196005	−	0.221869i
$637$	−14.7750	−	8.53037i	−0.585409	−	0.337986i
$638$	−18.0773	−	14.7808i	−0.715688	−	0.585177i
$639$	−12.4110	−	7.16551i	−0.490972	−	0.283463i
$640$	20.3448	−	29.1677i	0.804199	−	1.15295i
$641$	1.95122	+	1.12654i	0.0770686	+	0.0444956i	0.538039	−	0.842920i	$-0.319165\pi$
$641$	1.95122	+	1.12654i	0.0770686	+	0.0444956i	−0.460971	+	0.887415i	$0.652499\pi$
$642$	−1.83501	−	4.84875i	−0.0724219	−	0.191365i
$643$			5.18604i			0.204517i	0.994758	+	0.102259i	$0.0326070\pi$
$643$			5.18604i			0.204517i	−0.994758	+	0.102259i	$0.967393\pi$
$644$	3.36737	+	3.81171i	0.132693	+	0.150202i
$645$			7.86721i			0.309771i
$646$	−39.3199	−	6.41836i	−1.54702	−	0.252527i
$647$	12.9463	+	22.4236i	0.508970	+	0.881562i	0.999946	+	0.0103890i	$0.00330699\pi$
$647$	12.9463	+	22.4236i	0.508970	+	0.881562i	−0.490976	+	0.871173i	$0.663360\pi$
$648$	−1.31969	+	2.50168i	−0.0518425	+	0.0982753i
$649$	−22.7563	−	13.1383i	−0.893262	−	0.515725i
$650$	7.91157	−	9.67607i	0.310317	−	0.379527i
$651$	15.3458	+	26.5796i	0.601447	+	1.04174i
$652$	5.14903	−	1.04367i	0.201651	−	0.0408734i
$653$	−36.9411	+	21.3280i	−1.44562	+	0.834628i	−0.998216	−	0.0597050i	$-0.980984\pi$
$653$	−36.9411	+	21.3280i	−1.44562	+	0.834628i	−0.447402	+	0.894333i	$0.647651\pi$
$654$	−3.28327	−	8.67559i	−0.128386	−	0.339242i
$655$	21.9560			0.857891
$656$	−7.00713	+	9.27062i	−0.273582	+	0.361957i
$657$	2.30070	+	3.98493i	0.0897588	+	0.155467i
$658$	25.2649	−	30.8997i	0.984928	−	1.20459i
$659$	32.0427	+	18.4998i	1.24821	+	0.720652i	0.970751	−	0.240087i	$-0.0771760\pi$
$659$	32.0427	+	18.4998i	1.24821	+	0.720652i	0.277454	+	0.960739i	$0.410509\pi$
$660$	11.5125	−	2.33350i	0.448122	−	0.0908313i
$661$			25.8331i			1.00479i	0.864638	+	0.502395i	$0.167548\pi$
$661$			25.8331i			1.00479i	−0.864638	+	0.502395i	$0.832452\pi$
$662$	−2.54786	+	15.6086i	−0.0990254	+	0.606645i
$663$	11.4098	+	6.58744i	0.443119	+	0.255835i
$664$	−1.02354	−	26.7980i	−0.0397212	−	1.03996i
$665$	−49.3235			−1.91268
$666$	11.9481	+	9.76928i	0.462980	+	0.378552i
$667$			5.54558i			0.214726i
$668$	11.3909	−	2.30885i	0.440727	−	0.0893323i
$669$			22.7611i			0.879997i
$670$	−11.4217	+	34.5469i	−0.441260	+	1.33466i
$671$			4.52793i			0.174799i
$672$	21.9955	+	6.45461i	0.848494	+	0.248992i
$673$		−	8.71971i		−	0.336120i	−0.985777	−	0.168060i	$-0.946250\pi$
$673$		−	8.71971i		−	0.336120i	0.985777	−	0.168060i	$-0.0537503\pi$
$674$	2.10809	−	2.57825i	0.0812005	−	0.0993106i
$675$	−4.88020			−0.187839
$676$	3.86196	+	19.0532i	0.148537	+	0.732816i
$677$	−28.6454	−	16.5384i	−1.10093	−	0.635623i	−0.164466	−	0.986383i	$-0.552590\pi$
$677$	−28.6454	−	16.5384i	−1.10093	−	0.635623i	−0.936466	+	0.350759i	$0.885923\pi$
$678$	−0.599864	−	0.0979186i	−0.0230377	−	0.00376054i
$679$		−	8.83684i		−	0.339127i
$680$	2.46859	+	64.6314i	0.0946659	+	2.47850i
$681$	−8.68285	−	5.01304i	−0.332727	−	0.192100i
$682$	15.4941	+	12.6687i	0.593301	+	0.485108i
$683$	−13.5254	−	23.4267i	−0.517535	−	0.896396i	−0.999793	−	0.0203671i	$-0.993517\pi$
$683$	−13.5254	−	23.4267i	−0.517535	−	0.896396i	0.482258	−	0.876029i	$-0.339817\pi$
$684$	2.46279	−	7.34270i	0.0941670	−	0.280755i
$685$	−63.1440			−2.41261
$686$	12.9744	−	4.91015i	0.495365	−	0.187471i
$687$	−7.45156	+	4.30216i	−0.284295	+	0.164138i
$688$	−1.23458	+	9.93505i	−0.0470679	+	0.378770i
$689$	−3.38022	−	5.85471i	−0.128776	−	0.223047i
$690$	−2.15967	−	1.76584i	−0.0822173	−	0.0672243i
$691$	−7.22794	−	4.17306i	−0.274964	−	0.158751i	0.356177	−	0.934418i	$-0.384080\pi$
$691$	−7.22794	−	4.17306i	−0.274964	−	0.158751i	−0.631141	+	0.775668i	$0.717413\pi$
$692$	8.54672	+	2.86662i	0.324898	+	0.108973i
$693$	3.78586	+	6.55730i	0.143813	+	0.249091i
$694$	−2.64083	+	16.1782i	−0.100245	+	0.614114i
$695$		−	26.7720i		−	1.01552i
$696$	13.3140	+	21.1526i	0.504665	+	0.801787i
$697$		−	21.1354i		−	0.800560i
$698$	21.7271	−	8.22260i	0.822382	−	0.311230i
$699$	−12.1603	−	7.02078i	−0.459946	−	0.265550i
$700$	7.85705	+	38.7633i	0.296969	+	1.46511i
$701$	−22.8985	−	13.2205i	−0.864866	−	0.499330i	0.000773032	−	1.00000i	$-0.499754\pi$
$701$	−22.8985	−	13.2205i	−0.864866	−	0.499330i	−0.865639	+	0.500669i	$0.833087\pi$
$702$	−1.62116	+	1.98272i	−0.0611866	+	0.0748330i
$703$	−36.5981	−	21.1299i	−1.38032	−	0.796930i
$704$	14.9046	−	1.14022i	0.561740	−	0.0429738i
$705$	−10.9462	+	18.9594i	−0.412258	+	0.714053i
$706$	−25.9544	+	31.7429i	−0.976806	+	1.19466i
$707$	20.2876	−	11.7131i	0.762995	−	0.440515i
$708$	18.6212	+	21.0784i	0.699828	+	0.792175i
$709$	3.22465	+	5.58526i	0.121104	+	0.209759i	0.920203	−	0.391440i	$-0.128023\pi$
$709$	3.22465	+	5.58526i	0.121104	+	0.209759i	−0.799099	+	0.601199i	$0.794690\pi$
$710$	10.2631	−	62.8731i	0.385166	−	2.35958i
$711$	0.726008	−	1.25748i	0.0272274	−	0.0471593i
$712$	−6.45127	+	12.2294i	−0.241772	+	0.458315i
$713$		−	4.75314i		−	0.178006i
$714$	−38.9922	+	14.7566i	−1.45924	+	0.552250i
$715$	10.6364			0.397780
$716$	27.5167	−	24.3090i	1.02835	−	0.908470i
$717$	−7.61571	+	13.1908i	−0.284414	+	0.492619i
$718$	8.04757	+	21.2646i	0.300332	+	0.793587i
$719$	−1.98014	+	1.14323i	−0.0738468	+	0.0426355i	−0.536469	−	0.843920i	$-0.680242\pi$
$719$	−1.98014	+	1.14323i	−0.0738468	+	0.0426355i	0.462622	+	0.886556i	$0.346909\pi$
$720$	−12.4771	−	1.55047i	−0.464996	−	0.0577827i
$721$	35.1808	−	20.3116i	1.31020	−	0.756445i
$722$	0.912441	−	5.58975i	0.0339575	−	0.208029i
$723$	1.87229			0.0696312
$724$	−2.10992	−	10.4094i	−0.0784146	−	0.386863i
$725$	−21.5624	+	37.3471i	−0.800806	+	1.38704i
$726$	−8.22067	−	6.72156i	−0.305098	−	0.249461i
$727$	−24.7885	−	42.9349i	−0.919353	−	1.59237i	−0.800400	−	0.599467i	$-0.795379\pi$
$727$	−24.7885	−	42.9349i	−0.919353	−	1.59237i	−0.118954	−	0.992900i	$-0.537954\pi$
$728$	18.3587	+	9.68464i	0.680420	+	0.358937i
$729$	1.00000			0.0370370
$730$	−12.9474	+	15.8350i	−0.479205	+	0.586081i
$731$	−9.10416	−	15.7689i	−0.336729	−	0.583232i
$732$	1.54118	−	4.59496i	0.0569635	−	0.169834i
$733$	24.0051	+	13.8593i	0.886648	+	0.511906i	0.872845	−	0.487998i	$-0.162273\pi$
$733$	24.0051	+	13.8593i	0.886648	+	0.511906i	0.0138033	+	0.999905i	$0.495606\pi$
$734$	−1.72958	+	10.5956i	−0.0638398	+	0.391093i
$735$	−25.6447	+	14.8060i	−0.945918	+	0.546126i
$736$	−2.45022	−	2.56889i	−0.0903163	−	0.0946905i
$737$	−14.2809	+	5.47515i	−0.526045	+	0.201680i
$738$	4.05492	+	0.661904i	0.149264	+	0.0243650i
$739$	22.6623	+	39.2522i	0.833645	+	1.44392i	0.895129	+	0.445807i	$0.147083\pi$
$739$	22.6623	+	39.2522i	0.833645	+	1.44392i	−0.0614842	+	0.998108i	$0.519583\pi$
$740$	−21.8166	+	65.0453i	−0.801994	+	2.39111i
$741$	3.50639	−	6.07324i	0.128810	−	0.223106i
$742$	21.1135	+	3.44646i	0.775101	+	0.126523i
$743$	6.31070	−	3.64348i	0.231517	−	0.133666i	−0.379755	−	0.925087i	$-0.623992\pi$
$743$	6.31070	−	3.64348i	0.231517	−	0.133666i	0.611272	+	0.791421i	$0.290658\pi$
$744$	−11.4115	−	18.1300i	−0.418364	−	0.664677i
$745$			41.0540i			1.50410i
$746$	−4.68079	−	0.764066i	−0.171376	−	0.0279744i
$747$	−8.21115	+	4.74071i	−0.300430	+	0.173454i
$748$	−20.3750	+	17.9998i	−0.744982	+	0.658137i
$749$	12.8649	+	7.42756i	0.470074	+	0.271397i
$750$	0.188493	+	0.498066i	0.00688279	+	0.0181868i
$751$			46.9172i			1.71203i	0.516948	+	0.856017i	$0.327068\pi$
$751$			46.9172i			1.71203i	−0.516948	+	0.856017i	$0.672932\pi$
$752$	−16.7986	+	22.2250i	−0.612582	+	0.810463i
$753$	−2.42889	−	4.20697i	−0.0885139	−	0.153310i
$754$	8.01051	+	21.1667i	0.291726	+	0.770845i
$755$	30.1742	+	52.2633i	1.09815	+	1.90205i
$756$	−1.60999	−	7.94297i	−0.0585546	−	0.288883i
$757$	−28.3909	−	16.3915i	−1.03188	−	0.595759i	−0.114361	−	0.993439i	$-0.536482\pi$
$757$	−28.3909	−	16.3915i	−1.03188	−	0.595759i	−0.917524	+	0.397680i	$0.869815\pi$
$758$	19.7607	+	16.1572i	0.717743	+	0.586857i
$759$		−	1.17262i		−	0.0425633i
$760$	34.4022	−	1.31399i	1.24790	−	0.0476633i
$761$	8.25537			0.299257			0.149629	−	0.988742i	$-0.452192\pi$
$761$	8.25537			0.299257			0.149629	+	0.988742i	$0.452192\pi$
$762$	2.46102	+	0.401723i	0.0891533	+	0.0145529i
$763$	23.0185	+	13.2897i	0.833324	+	0.481120i
$764$	15.7969	+	5.29837i	0.571511	+	0.191688i
$765$	19.8037	−	11.4337i	0.716003	−	0.413385i
$766$	−4.43219	−	3.62394i	−0.160141	−	0.130938i
$767$	12.7338	+	22.0555i	0.459789	+	0.796378i
$768$	−15.5134	−	3.91601i	−0.559791	−	0.141307i
$769$	−11.8707	−	6.85356i	−0.428069	−	0.247146i	0.270455	−	0.962733i	$-0.412826\pi$
$769$	−11.8707	−	6.85356i	−0.428069	−	0.247146i	−0.698524	+	0.715587i	$0.746159\pi$
$770$	−21.3053	+	26.0570i	−0.767789	+	0.939028i
$771$	4.52176	−	7.83191i	0.162847	−	0.282060i
$772$	31.6322	−	27.9447i	1.13847	−	1.00575i
$773$	12.0932	−	20.9461i	0.434963	−	0.753379i	−0.562329	−	0.826913i	$-0.690095\pi$
$773$	12.0932	−	20.9461i	0.434963	−	0.753379i	0.997293	+	0.0735347i	$0.0234280\pi$
$774$	3.31045	−	1.25284i	0.118992	−	0.0450323i
$775$	18.4812	−	32.0104i	0.663864	−	1.14985i
$776$	0.235415	+	6.16353i	0.00845091	+	0.221258i
$777$	−44.2230			−1.58649
$778$	−14.3347	−	11.7207i	−0.513924	−	0.420206i
$779$	−11.2500			−0.403074
$780$	−10.7939	−	3.62034i	−0.386483	−	0.129629i
$781$	23.1903	−	13.3889i	0.829814	−	0.479093i
$782$	6.37228	+	1.04018i	0.227872	+	0.0371966i
$783$	4.41834	−	7.65278i	0.157898	−	0.273488i
$784$	−34.7087	+	14.6733i	−1.23959	+	0.524045i
$785$	66.1662	−	38.2011i	2.36157	−	1.36346i
$786$	−3.49645	−	9.23888i	−0.124714	−	0.329540i
$787$	−24.2313	−	41.9698i	−0.863752	−	1.49606i	−0.868281	−	0.496072i	$-0.834775\pi$
$787$	−24.2313	−	41.9698i	−0.863752	−	1.49606i	0.00452974	−	0.999990i	$-0.498558\pi$
$788$	10.4337	−	2.11484i	0.371685	−	0.0753379i
$789$		−	27.8170i		−	0.990313i
$790$	6.37028	+	1.03985i	0.226645	+	0.0369962i
$791$	1.50826	−	0.870792i	0.0536274	−	0.0309618i
$792$	−2.81525	−	4.47274i	−0.100036	−	0.158932i
$793$	2.19425	−	3.80055i	0.0779200	−	0.134961i
$794$	−2.52653	+	0.956162i	−0.0896630	+	0.0339329i
$795$	−11.7339			−0.416159
$796$	−9.40433	+	28.0386i	−0.333327	+	0.993802i
$797$	0.165324	−	0.286349i	0.00585608	−	0.0101430i	−0.863083	−	0.505063i	$-0.831469\pi$
$797$	0.165324	−	0.286349i	0.00585608	−	0.0101430i	0.868939	+	0.494920i	$0.164803\pi$
$798$	7.85467	+	20.7549i	0.278052	+	0.734715i
$799$		−	50.6691i		−	1.79254i
$800$	−6.51281	−	26.8274i	−0.230263	−	0.948490i
$801$	4.88846			0.172725
$802$	0.359270	+	0.949321i	0.0126863	+	0.0335217i
$803$	−8.59781			−0.303410
$804$	16.3559	−	0.695377i	0.576829	−	0.0245240i
$805$	7.99350			0.281734
$806$	−6.86584	−	18.1420i	−0.241839	−	0.639026i
$807$	28.3773			0.998928
$808$	−13.8382	+	8.71011i	−0.486826	+	0.306421i
$809$			52.3857i			1.84178i	0.389817	+	0.920892i	$0.372538\pi$
$809$			52.3857i			1.84178i	−0.389817	+	0.920892i	$0.627462\pi$
$810$	1.57340	+	4.15750i	0.0552837	+	0.146080i
$811$	4.90019	−	8.48737i	0.172069	−	0.298032i	−0.767074	−	0.641558i	$-0.778288\pi$
$811$	4.90019	−	8.48737i	0.172069	−	0.298032i	0.939143	+	0.343526i	$0.111622\pi$
$812$	−67.8993	−	22.7738i	−2.38280	−	0.799205i
$813$	−11.4356			−0.401063
$814$	−26.9712	+	10.2072i	−0.945340	+	0.357763i
$815$	4.12849	−	7.15075i	0.144615	−	0.250480i
$816$	26.8032	−	11.3312i	0.938299	−	0.396671i
$817$	−8.39351	+	4.84599i	−0.293652	+	0.169540i
$818$	29.6059	+	4.83271i	1.03515	+	0.168972i
$819$		−	7.33856i		−	0.256430i
$820$	3.62816	+	17.8998i	0.126701	+	0.625088i
$821$	−0.331997	−	0.575036i	−0.0115868	−	0.0200689i	0.860174	−	0.510001i	$-0.170355\pi$
$821$	−0.331997	−	0.575036i	−0.0115868	−	0.0200689i	−0.871761	+	0.489932i	$0.837022\pi$
$822$	10.0556	+	26.5704i	0.350728	+	0.926749i
$823$	−30.9660	+	17.8782i	−1.07941	+	0.623195i	−0.930736	−	0.365692i	$-0.880832\pi$
$823$	−30.9660	+	17.8782i	−1.07941	+	0.623195i	−0.148669	+	0.988887i	$0.547499\pi$
$824$	−23.9968	+	15.1042i	−0.835969	+	0.526180i
$825$	4.55938	−	7.89709i	0.158737	−	0.274941i
$826$	−79.5376	−	12.9833i	−2.76747	−	0.451746i
$827$	−0.826546	+	0.477207i	−0.0287418	+	0.0165941i	−0.514302	−	0.857609i	$-0.671949\pi$
$827$	−0.826546	+	0.477207i	−0.0287418	+	0.0165941i	0.485560	+	0.874203i	$0.338616\pi$
$828$	−0.399126	+	1.18998i	−0.0138706	+	0.0413546i
$829$	−9.78843			−0.339966			−0.169983	−	0.985447i	$-0.554371\pi$
$829$	−9.78843			−0.339966			−0.169983	+	0.985447i	$0.554371\pi$
$830$	−32.6290	−	26.6788i	−1.13257	−	0.926035i
$831$	−11.7684			−0.408240
$832$	−13.0629	−	6.26578i	−0.452873	−	0.217227i
$833$	34.2677	−	59.3535i	1.18731	−	2.05648i
$834$	−11.2654	+	4.26338i	−0.390089	+	0.147629i
$835$	9.13321	−	15.8192i	0.316068	−	0.547445i
$836$	9.58098	+	10.8453i	0.331365	+	0.375091i
$837$	−3.78697	+	6.55923i	−0.130897	+	0.226720i
$838$	25.1480	−	30.7567i	0.868722	−	1.06247i
$839$	−6.65466	−	3.84207i	−0.229745	−	0.132643i	0.380710	−	0.924695i	$-0.375680\pi$
$839$	−6.65466	−	3.84207i	−0.229745	−	0.132643i	−0.610454	+	0.792052i	$0.709013\pi$
$840$	30.4897	−	19.1910i	1.05200	−	0.662153i
$841$	−24.5434	−	42.5104i	−0.846323	−	1.46587i
$842$	−41.9747	−	34.3203i	−1.44654	−	1.18275i
$843$	−0.164511	+	0.0949807i	−0.00566607	+	0.00327131i
$844$	8.85211	−	26.3922i	0.304702	−	0.908457i
$845$	26.4603	+	15.2769i	0.910262	+	0.525540i
$846$	9.72111	+	1.58682i	0.334219	+	0.0545561i
$847$	30.4268			1.04548
$848$	−14.8181	−	1.84137i	−0.508855	−	0.0632329i
$849$		−	25.3856i		−	0.871232i
$850$	38.8702	+	31.7819i	1.33324	+	1.09011i
$851$	5.93118	+	3.42437i	0.203318	+	0.117386i
$852$	−28.0908	+	5.69381i	−0.962375	+	0.195067i
$853$	−13.9172	−	24.1052i	−0.476515	−	0.825348i	0.523123	−	0.852257i	$-0.324767\pi$
$853$	−13.9172	−	24.1052i	−0.476515	−	0.825348i	−0.999638	+	0.0269093i	$0.991433\pi$
$854$	4.91534	+	12.9881i	0.168200	+	0.444444i
$855$	−6.08595	−	10.5412i	−0.208135	−	0.360500i
$856$	−9.17091	−	4.83786i	−0.313455	−	0.165355i
$857$			22.2953i			0.761592i	0.924659	+	0.380796i	$0.124350\pi$
$857$			22.2953i			0.761592i	−0.924659	+	0.380796i	$0.875650\pi$
$858$	−1.69383	−	4.47572i	−0.0578265	−	0.152798i
$859$	3.49725	+	2.01914i	0.119325	+	0.0688920i	0.558474	−	0.829522i	$-0.311387\pi$
$859$	3.49725	+	2.01914i	0.119325	+	0.0688920i	−0.439150	+	0.898414i	$0.644720\pi$
$860$	10.4173	+	11.7920i	0.355228	+	0.402103i
$861$	−10.1954	+	5.88632i	−0.347459	+	0.200605i
$862$	50.0971	+	8.17759i	1.70632	+	0.278530i
$863$			10.3501i			0.352322i	0.984361	+	0.176161i	$0.0563680\pi$
$863$			10.3501i			0.352322i	−0.984361	+	0.176161i	$0.943632\pi$
$864$	1.33454	+	5.49718i	0.0454019	+	0.187018i
$865$	12.2697	−	7.08389i	0.417181	−	0.240860i
$866$	−31.2342	−	5.09849i	−1.06138	−	0.173254i
$867$	−17.9627	+	31.1123i	−0.610045	+	1.05663i
$868$	58.1967	+	19.5195i	1.97533	+	0.662537i
$869$	1.35656	+	2.34963i	0.0460182	+	0.0797059i
$870$	38.7683	+	6.32832i	1.31437	+	0.214550i
$871$	14.6401	+	2.32498i	0.496060	+	0.0787790i
$872$	−16.4090	−	8.65611i	−0.555678	−	0.293133i
$873$	1.88856	−	1.09036i	0.0639182	−	0.0369032i
$874$	0.553669	−	3.39186i	0.0187281	−	0.114731i
$875$	−1.32149	−	0.762963i	−0.0446746	−	0.0257929i
$876$	8.72509	+	2.92645i	0.294794	+	0.0988756i
$877$	15.5723	+	26.9720i	0.525839	+	0.910780i	0.999547	+	0.0300981i	$0.00958197\pi$
$877$	15.5723	+	26.9720i	0.525839	+	0.910780i	−0.473708	+	0.880682i	$0.657085\pi$
$878$	6.12313	−	7.48876i	0.206646	−	0.252733i
$879$	9.67877			0.326457
$880$	14.1659	−	18.7418i	0.477532	−	0.631787i
$881$	11.0849	+	19.1996i	0.373459	+	0.646850i	0.990095	−	0.140398i	$-0.0448384\pi$
$881$	11.0849	+	19.1996i	0.373459	+	0.646850i	−0.616636	+	0.787248i	$0.711505\pi$
$882$	10.3141	+	8.43322i	0.347293	+	0.283961i
$883$	15.0761	−	26.1126i	0.507352	−	0.878759i	−0.492612	−	0.870249i	$-0.663958\pi$
$883$	15.0761	−	26.1126i	0.507352	−	0.878759i	0.999964	−	0.00851011i	$-0.00270888\pi$
$884$	25.8246	−	5.23447i	0.868575	−	0.176054i
$885$	44.2033			1.48588
$886$	−8.45135	+	51.7743i	−0.283929	+	1.73939i
$887$	−0.569415	+	0.328752i	−0.0191191	+	0.0110384i	−0.509529	−	0.860453i	$-0.670180\pi$
$887$	−0.569415	+	0.328752i	−0.0191191	+	0.0110384i	0.490410	+	0.871492i	$0.336847\pi$
$888$	30.8447	−	1.17811i	1.03508	−	0.0395348i
$889$	−6.18781	+	3.57253i	−0.207532	+	0.119819i
$890$	7.69152	+	20.3238i	0.257820	+	0.681255i
$891$	−0.934262	+	1.61819i	−0.0312989	+	0.0542114i
$892$	30.1391	+	34.1162i	1.00913	+	1.14229i
$893$	−26.9703			−0.902528
$894$	17.2752	−	6.53777i	0.577768	−	0.218656i
$895$		−	57.7050i		−	1.92887i
$896$	41.5154	−	19.4506i	1.38693	−	0.649798i
$897$	−0.568254	+	0.984245i	−0.0189735	+	0.0328630i
$898$	5.07379	−	31.0828i	0.169315	−	1.03725i
$899$	33.4642	+	57.9618i	1.11609	+	1.93313i
$900$	−7.31482	+	6.46211i	−0.243827	+	0.215404i
$901$	23.5192	−	13.5788i	0.783538	−	0.452376i
$902$	−4.85945	+	5.94324i	−0.161802	+	0.197888i
$903$	−5.07112	+	8.78343i	−0.168756	+	0.292294i
$904$	−1.02878	+	0.647541i	−0.0342168	+	0.0215369i
$905$	−14.4562	−	8.34628i	−0.480540	−	0.277440i
$906$	17.1867	−	21.0199i	0.570991	−	0.698338i
$907$	−14.3152	−	8.26487i	−0.475327	−	0.274430i	0.243140	−	0.969991i	$-0.421823\pi$
$907$	−14.3152	−	8.26487i	−0.475327	−	0.274430i	−0.718467	+	0.695561i	$0.755156\pi$
$908$	−19.6525	+	3.98343i	−0.652192	+	0.132195i
$909$	5.00651	+	2.89051i	0.166056	+	0.0958723i
$910$	30.5100	−	11.5465i	1.01140	−	0.382763i
$911$		−	19.3823i		−	0.642165i	−0.947051	−	0.321082i	$-0.895953\pi$
$911$		−	19.3823i		−	0.642165i	0.947051	−	0.321082i	$-0.104047\pi$
$912$	−6.03140	−	14.2669i	−0.199720	−	0.472424i
$913$		−	17.7163i		−	0.586322i
$914$	4.84206	−	29.6632i	0.160161	−	0.981172i
$915$	−3.80850	−	6.59651i	−0.125905	−	0.218074i
$916$	−5.47228	+	16.3154i	−0.180809	+	0.539075i
$917$	24.5130	+	14.1526i	0.809491	+	0.467360i
$918$	−7.96487	−	6.51242i	−0.262880	−	0.214942i
$919$	−15.6638	−	27.1305i	−0.516700	−	0.894951i	−0.999812	−	0.0193924i	$-0.993827\pi$
$919$	−15.6638	−	27.1305i	−0.516700	−	0.894951i	0.483112	−	0.875559i	$-0.339507\pi$
$920$	−5.57531	+	0.212948i	−0.183813	+	0.00702070i
$921$	18.3287	−	10.5821i	0.603950	−	0.348691i
$922$	46.4996	−	17.5977i	1.53138	−	0.579550i
$923$	−25.9532			−0.854261
$924$	14.3574	+	4.81555i	0.472323	+	0.158420i
$925$	26.6293	+	46.1233i	0.875567	+	1.51653i
$926$	−15.4929	−	12.6676i	−0.509128	−	0.416284i
$927$	8.68180	+	5.01244i	0.285148	+	0.164630i
$928$	47.9652	+	14.0755i	1.57453	+	0.462050i
$929$			14.8164i			0.486112i	0.970012	+	0.243056i	$0.0781498\pi$
$929$			14.8164i			0.486112i	−0.970012	+	0.243056i	$0.921850\pi$
$930$	−33.2284	−	5.42403i	−1.08960	−	0.177861i
$931$	−31.5929	−	18.2402i	−1.03541	−	0.597797i
$932$	−27.5234	+	5.57881i	−0.901559	+	0.182740i
$933$	22.5190			0.737241
$934$	−8.97934	+	10.9820i	−0.293813	+	0.359341i
$935$			42.7281i			1.39736i
$936$	0.195500	+	5.11850i	0.00639013	+	0.167304i
$937$		−	6.07853i		−	0.198577i	−0.995059	−	0.0992885i	$-0.968343\pi$
$937$		−	6.07853i		−	0.198577i	0.995059	−	0.0992885i	$-0.0316567\pi$
$938$	−35.0205	+	31.2080i	−1.14346	+	1.01898i
$939$		−	28.6373i		−	0.934543i
$940$	8.69802	+	42.9122i	0.283698	+	1.39964i
$941$		−	21.1508i		−	0.689496i	−0.938695	−	0.344748i	$-0.887964\pi$
$941$		−	21.1508i		−	0.689496i	0.938695	−	0.344748i	$-0.112036\pi$
$942$	−26.6115	−	21.7587i	−0.867050	−	0.708937i
$943$	1.82321			0.0593718
$944$	55.8219	+	6.93670i	1.81685	+	0.225770i
$945$	−11.0309	−	6.36867i	−0.358834	−	0.207173i
$946$	−1.06550	+	6.52741i	−0.0346424	+	0.212224i
$947$		−	28.0752i		−	0.912322i	−0.889897	−	0.456161i	$-0.849224\pi$
$947$		−	28.0752i		−	0.912322i	0.889897	−	0.456161i	$-0.150776\pi$
$948$	−0.576896	−	2.84615i	−0.0187367	−	0.0924387i
$949$	7.21664	+	4.16653i	0.234262	+	0.135251i
$950$	16.9170	−	20.6900i	0.548860	−	0.671271i
$951$	11.5584	+	20.0198i	0.374808	+	0.649186i
$952$	−38.9046	+	73.7496i	−1.26091	+	2.39024i
$953$	−26.2947			−0.851768			−0.425884	−	0.904778i	$-0.640037\pi$
$953$	−26.2947			−0.851768			−0.425884	+	0.904778i	$0.640037\pi$
$954$	1.86860	+	4.93752i	0.0604982	+	0.159858i
$955$	22.6780	−	13.0931i	0.733842	−	0.423684i
$956$	6.05155	+	29.8557i	0.195721	+	0.965603i
$957$	8.25576	+	14.2994i	0.266871	+	0.462234i
$958$	30.7541	−	37.6131i	0.993620	−	1.21523i
$959$	−70.4978	−	40.7019i	−2.27649	−	1.31433i
$960$	−20.7548	+	14.1976i	−0.669857	+	0.458226i
$961$	−13.1823	−	22.8325i	−0.425237	−	0.736531i
$962$	27.5849	+	4.50281i	0.889374	+	0.145177i
$963$			3.66590i			0.118132i
$964$	2.80633	−	2.47919i	0.0903859	−	0.0798492i
$965$		−	66.3355i		−	2.13541i
$966$	−1.27295	−	3.36359i	−0.0409565	−	0.108222i
$967$	31.7410	+	18.3257i	1.02072	+	0.589314i	0.914313	−	0.405009i	$-0.132732\pi$
$967$	31.7410	+	18.3257i	1.02072	+	0.589314i	0.106409	+	0.994322i	$0.466065\pi$
$968$	−21.2221	+	0.810575i	−0.682105	+	0.0260529i
$969$	24.3971	+	14.0857i	0.783747	+	0.452497i
$970$	7.50465	+	6.13612i	0.240960	+	0.197019i
$971$	37.8112	+	21.8303i	1.21342	+	0.700567i	0.963502	−	0.267700i	$-0.0862637\pi$
$971$	37.8112	+	21.8303i	1.21342	+	0.700567i	0.249916	+	0.968268i	$0.419597\pi$
$972$	1.49888	−	1.32415i	0.0480765	−	0.0424721i
$973$	17.2569	−	29.8899i	0.553232	−	0.958225i
$974$	−4.28560	−	3.50409i	−0.137319	−	0.112278i
$975$	−7.65390	+	4.41898i	−0.245121	+	0.141521i
$976$	−3.77437	−	8.92802i	−0.120815	−	0.285779i
$977$	0.214926	+	0.372263i	0.00687609	+	0.0119097i	0.869443	−	0.494033i	$-0.164478\pi$
$977$	0.214926	+	0.372263i	0.00687609	+	0.0119097i	−0.862567	+	0.505943i	$0.831145\pi$
$978$	−3.66643	−	0.598487i	−0.117239	−	0.0191375i
$979$	−4.56710	+	7.91046i	−0.145965	+	0.252819i
$980$	−18.8329	+	56.1496i	−0.601596	+	1.79363i
$981$			6.55918i			0.209419i
$982$	−17.2512	−	45.5838i	−0.550506	−	1.45464i
$983$	−48.8806			−1.55905			−0.779524	−	0.626372i	$-0.784539\pi$
$983$	−48.8806			−1.55905			−0.779524	+	0.626372i	$0.784539\pi$
$984$	6.95429	−	4.37721i	0.221695	−	0.139540i
$985$	8.36573	−	14.4899i	0.266554	−	0.461685i
$986$	−85.0296	+	32.1794i	−2.70789	+	1.02480i
$987$	−24.4421	+	14.1116i	−0.777999	+	0.449178i
$988$	−2.78622	−	13.7460i	−0.0886416	−	0.437319i
$989$	1.36027	−	0.785354i	0.0432542	−	0.0249728i
$990$	−8.19759	−	1.33813i	−0.260536	−	0.0425286i
$991$	45.0902			1.43234			0.716169	−	0.697927i	$-0.245894\pi$
$991$	45.0902			1.43234			0.716169	+	0.697927i	$0.245894\pi$
$992$	−41.1111	−	12.0641i	−1.30528	−	0.383037i
$993$	5.59150	−	9.68477i	0.177441	−	0.307337i
$994$	51.9856	−	63.5799i	1.64888	−	2.01663i
$995$	23.2396	+	40.2522i	0.736745	+	1.27608i
$996$	−6.03011	+	17.9785i	−0.191071	+	0.569671i
$997$	22.3360			0.707389			0.353694	−	0.935361i	$-0.384925\pi$
$997$	22.3360			0.707389			0.353694	+	0.935361i	$0.384925\pi$
$998$	−42.2734	−	34.5645i	−1.33814	−	1.09412i
$999$	−5.45660	−	9.45112i	−0.172639	−	0.299020i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.j.b.499.4	yes	68
4.3	odd	2		804.2.j.a.499.8	✓	68
67.38	odd	6		804.2.j.a.775.8	yes	68
268.239	even	6	inner	804.2.j.b.775.4	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.j.a.499.8	✓	68	4.3	odd	2
804.2.j.a.775.8	yes	68	67.38	odd	6
804.2.j.b.499.4	yes	68	1.1	even	1	trivial
804.2.j.b.775.4	yes	68	268.239	even	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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32266 + 0.500561i) q^{2} +1.00000 q^{3} +(1.49888 - 1.32415i) q^{4} -3.14328i q^{5} +(-1.32266 + 0.500561i) q^{6} +(2.02612 - 3.50935i) q^{7} +(-1.31969 + 2.50168i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-1.32266 + 0.500561i) q^{2} +1.00000 q^{3} +(1.49888 - 1.32415i) q^{4} -3.14328i q^{5} +(-1.32266 + 0.500561i) q^{6} +(2.02612 - 3.50935i) q^{7} +(-1.31969 + 2.50168i) q^{8} +1.00000 q^{9} +(1.57340 + 4.15750i) q^{10} +(-0.934262 + 1.61819i) q^{11} +(1.49888 - 1.32415i) q^{12} +(1.56836 - 0.905492i) q^{13} +(-0.923236 + 5.65589i) q^{14} -3.14328i q^{15} +(0.493266 - 3.96947i) q^{16} +(3.63749 + 6.30032i) q^{17} +(-1.32266 + 0.500561i) q^{18} +(3.35356 - 1.93618i) q^{19} +(-4.16216 - 4.71139i) q^{20} +(2.02612 - 3.50935i) q^{21} +(0.425712 - 2.60797i) q^{22} +(-0.543486 + 0.313782i) q^{23} +(-1.31969 + 2.50168i) q^{24} -4.88020 q^{25} +(-1.62116 + 1.98272i) q^{26} +1.00000 q^{27} +(-1.60999 - 7.94297i) q^{28} +(4.41834 - 7.65278i) q^{29} +(1.57340 + 4.15750i) q^{30} +(-3.78697 + 6.55923i) q^{31} +(1.33454 + 5.49718i) q^{32} +(-0.934262 + 1.61819i) q^{33} +(-7.96487 - 6.51242i) q^{34} +(-11.0309 - 6.36867i) q^{35} +(1.49888 - 1.32415i) q^{36} +(-5.45660 - 9.45112i) q^{37} +(-3.46645 + 4.23957i) q^{38} +(1.56836 - 0.905492i) q^{39} +(7.86348 + 4.14816i) q^{40} +(-2.51599 - 1.45261i) q^{41} +(-0.923236 + 5.65589i) q^{42} -2.50287 q^{43} +(0.742377 + 3.66257i) q^{44} -3.14328i q^{45} +(0.561783 - 0.687076i) q^{46} +(-6.03173 - 3.48242i) q^{47} +(0.493266 - 3.96947i) q^{48} +(-4.71035 - 8.15857i) q^{49} +(6.45486 - 2.44284i) q^{50} +(3.63749 + 6.30032i) q^{51} +(1.15177 - 3.43396i) q^{52} -3.73302i q^{53} +(-1.32266 + 0.500561i) q^{54} +(5.08642 + 2.93664i) q^{55} +(6.10541 + 9.69998i) q^{56} +(3.35356 - 1.93618i) q^{57} +(-2.01329 + 12.3337i) q^{58} +14.0628i q^{59} +(-4.16216 - 4.71139i) q^{60} +(2.09861 - 1.21163i) q^{61} +(1.72560 - 10.5713i) q^{62} +(2.02612 - 3.50935i) q^{63} +(-4.51682 - 6.60290i) q^{64} +(-2.84621 - 4.92979i) q^{65} +(0.425712 - 2.60797i) q^{66} +(6.35908 + 5.15385i) q^{67} +(13.7947 + 4.62683i) q^{68} +(-0.543486 + 0.313782i) q^{69} +(17.7780 + 2.90199i) q^{70} +(-12.4110 - 7.16551i) q^{71} +(-1.31969 + 2.50168i) q^{72} +(2.30070 + 3.98493i) q^{73} +(11.9481 + 9.76928i) q^{74} -4.88020 q^{75} +(2.46279 - 7.34270i) q^{76} +(3.78586 + 6.55730i) q^{77} +(-1.62116 + 1.98272i) q^{78} +(0.726008 - 1.25748i) q^{79} +(-12.4771 - 1.55047i) q^{80} +1.00000 q^{81} +(4.05492 + 0.661904i) q^{82} +(-8.21115 + 4.74071i) q^{83} +(-1.60999 - 7.94297i) q^{84} +(19.8037 - 11.4337i) q^{85} +(3.31045 - 1.25284i) q^{86} +(4.41834 - 7.65278i) q^{87} +(-2.81525 - 4.47274i) q^{88} +4.88846 q^{89} +(1.57340 + 4.15750i) q^{90} -7.33856i q^{91} +(-0.399126 + 1.18998i) q^{92} +(-3.78697 + 6.55923i) q^{93} +(9.72111 + 1.58682i) q^{94} +(-6.08595 - 10.5412i) q^{95} +(1.33454 + 5.49718i) q^{96} +(1.88856 - 1.09036i) q^{97} +(10.3141 + 8.43322i) q^{98} +(-0.934262 + 1.61819i) 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	\( 68 q + 68 q^{3} - 2 q^{4} - 4 q^{7} + 6 q^{8} + 68 q^{9} - 6 q^{10} - 2 q^{12} + 6 q^{13} + 10 q^{14} - 2 q^{16} - 12 q^{20} - 4 q^{21} - 22 q^{22} + 6 q^{24} - 68 q^{25} - 19 q^{26} + 68 q^{27} - 7 q^{28} - 8 q^{29} - 6 q^{30} - 2 q^{31} + 15 q^{32} - 2 q^{36} + 12 q^{37} + 4 q^{38} + 6 q^{39} + 18 q^{40} + 10 q^{42} + 4 q^{43} - 5 q^{44} + 16 q^{46} - 2 q^{48} - 46 q^{49} + 27 q^{50} + 28 q^{52} - 17 q^{56} - 4 q^{58} - 12 q^{60} + 6 q^{61} - 34 q^{62} - 4 q^{63} + 16 q^{64} - 22 q^{66} + 18 q^{67} + 34 q^{68} - 56 q^{70} + 36 q^{71} + 6 q^{72} + 6 q^{73} + 11 q^{74} - 68 q^{75} + 14 q^{76} - 4 q^{77} - 19 q^{78} - 6 q^{79} - 25 q^{80} + 68 q^{81} - 26 q^{82} - 12 q^{83} - 7 q^{84} - 33 q^{86} - 8 q^{87} + 22 q^{88} - 6 q^{90} + 10 q^{92} - 2 q^{93} + 16 q^{94} - 20 q^{95} + 15 q^{96} + 18 q^{97} - 32 q^{98}+O(q^{100}) \) 68 * q + 68 * q^3 - 2 * q^4 - 4 * q^7 + 6 * q^8 + 68 * q^9 - 6 * q^10 - 2 * q^12 + 6 * q^13 + 10 * q^14 - 2 * q^16 - 12 * q^20 - 4 * q^21 - 22 * q^22 + 6 * q^24 - 68 * q^25 - 19 * q^26 + 68 * q^27 - 7 * q^28 - 8 * q^29 - 6 * q^30 - 2 * q^31 + 15 * q^32 - 2 * q^36 + 12 * q^37 + 4 * q^38 + 6 * q^39 + 18 * q^40 + 10 * q^42 + 4 * q^43 - 5 * q^44 + 16 * q^46 - 2 * q^48 - 46 * q^49 + 27 * q^50 + 28 * q^52 - 17 * q^56 - 4 * q^58 - 12 * 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 + 11 * q^74 - 68 * q^75 + 14 * q^76 - 4 * q^77 - 19 * q^78 - 6 * q^79 - 25 * q^80 + 68 * q^81 - 26 * q^82 - 12 * q^83 - 7 * q^84 - 33 * q^86 - 8 * q^87 + 22 * q^88 - 6 * q^90 + 10 * q^92 - 2 * q^93 + 16 * q^94 - 20 * q^95 + 15 * q^96 + 18 * q^97 - 32 * q^98

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