LMFDB - Embedded newform 804.2.y.a.157.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(49,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 0, 46]))

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

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

chi := DirichletCharacter("804.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.y (of order $33$, degree $20$, 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:	$100$
Relative dimension:	$5$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			157.5
Character	$\chi$	$=$	804.157
Dual form			804.2.y.a.169.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 + 0.989821i) q^{3} +(1.26894 + 2.77859i) q^{5} +(-3.37248 + 3.21566i) q^{7} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})$	\(q+(-0.142315 + 0.989821i) q^{3} +(1.26894 + 2.77859i) q^{5} +(-3.37248 + 3.21566i) q^{7} +(-0.959493 - 0.281733i) q^{9} +(1.67110 + 0.159571i) q^{11} +(3.76402 + 0.725456i) q^{13} +(-2.93090 + 0.860589i) q^{15} +(-3.78882 - 1.95327i) q^{17} +(0.222513 + 0.212166i) q^{19} +(-2.70297 - 3.79579i) q^{21} +(-5.91001 + 2.36601i) q^{23} +(-2.83605 + 3.27297i) q^{25} +(0.415415 - 0.909632i) q^{27} +(2.96087 - 5.12839i) q^{29} +(2.69497 - 0.519413i) q^{31} +(-0.395770 + 1.63138i) q^{33} +(-13.2145 - 5.29027i) q^{35} +(-4.62971 - 8.01890i) q^{37} +(-1.25375 + 3.62247i) q^{39} +(0.484081 + 10.1621i) q^{41} +(-9.25698 + 5.94910i) q^{43} +(-0.434719 - 3.02354i) q^{45} +(4.62641 + 3.63825i) q^{47} +(0.700125 - 14.6974i) q^{49} +(2.47259 - 3.47227i) q^{51} +(4.35112 + 2.79629i) q^{53} +(1.67715 + 4.84580i) q^{55} +(-0.241673 + 0.190054i) q^{57} +(3.42100 + 3.94805i) q^{59} +(8.52901 - 0.814422i) q^{61} +(4.14183 - 2.13526i) q^{63} +(2.76057 + 11.3792i) q^{65} +(4.38873 - 6.90934i) q^{67} +(-1.50085 - 6.18657i) q^{69} +(-2.96443 + 1.52827i) q^{71} +(-12.1308 + 1.15835i) q^{73} +(-2.83605 - 3.27297i) q^{75} +(-6.14889 + 4.83554i) q^{77} +(0.311637 + 0.900416i) q^{79} +(0.841254 + 0.540641i) q^{81} +(-2.45220 + 3.44363i) q^{83} +(0.619559 - 13.0061i) q^{85} +(4.65481 + 3.66058i) q^{87} +(2.41415 + 16.7908i) q^{89} +(-15.0269 + 9.65722i) q^{91} +(0.130592 + 2.74146i) q^{93} +(-0.307166 + 0.887497i) q^{95} +(3.90414 + 6.76216i) q^{97} +(-1.55846 - 0.623911i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q - 10 q^{3} + 2 q^{5} - 3 q^{7} - 10 q^{9}+O(q^{10}) $ 100 * q - 10 * q^3 + 2 * q^5 - 3 * q^7 - 10 * q^9	$ 100 q - 10 q^{3} + 2 q^{5} - 3 q^{7} - 10 q^{9} - 13 q^{11} - 3 q^{13} - 9 q^{15} - 44 q^{17} - 16 q^{19} - 3 q^{21} - 16 q^{23} + 28 q^{25} - 10 q^{27} - 7 q^{29} + 20 q^{31} - 2 q^{33} - 19 q^{35} - 22 q^{37} - 3 q^{39} - 14 q^{41} - 27 q^{43} + 2 q^{45} + 4 q^{47} - 92 q^{49} + 22 q^{51} + 8 q^{53} - 13 q^{55} + 17 q^{57} + 22 q^{59} + 17 q^{61} - 3 q^{63} + 56 q^{65} - 14 q^{67} + 17 q^{69} - q^{71} + 26 q^{73} + 28 q^{75} + 112 q^{77} + 69 q^{79} - 10 q^{81} + 15 q^{83} + 69 q^{85} + 4 q^{87} + 73 q^{89} - 40 q^{91} - 13 q^{93} + 59 q^{95} + 29 q^{97} - 2 q^{99}+O(q^{100}) $ 100 * q - 10 * q^3 + 2 * q^5 - 3 * q^7 - 10 * q^9 - 13 * q^11 - 3 * q^13 - 9 * q^15 - 44 * q^17 - 16 * q^19 - 3 * q^21 - 16 * q^23 + 28 * q^25 - 10 * q^27 - 7 * q^29 + 20 * q^31 - 2 * q^33 - 19 * q^35 - 22 * q^37 - 3 * q^39 - 14 * q^41 - 27 * q^43 + 2 * q^45 + 4 * q^47 - 92 * q^49 + 22 * q^51 + 8 * q^53 - 13 * q^55 + 17 * q^57 + 22 * q^59 + 17 * q^61 - 3 * q^63 + 56 * q^65 - 14 * q^67 + 17 * q^69 - q^71 + 26 * q^73 + 28 * q^75 + 112 * q^77 + 69 * q^79 - 10 * q^81 + 15 * q^83 + 69 * q^85 + 4 * q^87 + 73 * q^89 - 40 * q^91 - 13 * q^93 + 59 * q^95 + 29 * q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{14}{33}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.142315	+	0.989821i	−0.0821655	+	0.571474i
$3$	−0.142315	+	0.989821i	−0.0821655	+	0.571474i
$4$		0			0
$5$	1.26894	+	2.77859i	0.567487	+	1.24262i	0.948125	+	0.317899i	$0.102977\pi$
$5$	1.26894	+	2.77859i	0.567487	+	1.24262i	−0.380638	+	0.924724i	$0.624296\pi$
$6$		0			0
$7$	−3.37248	+	3.21566i	−1.27468	+	1.21540i	−0.310373	+	0.950615i	$0.600454\pi$
$7$	−3.37248	+	3.21566i	−1.27468	+	1.21540i	−0.964306	+	0.264789i	$0.914698\pi$
$8$		0			0
$9$	−0.959493	−	0.281733i	−0.319831	−	0.0939109i
$10$		0			0
$11$	1.67110	+	0.159571i	0.503857	+	0.0481125i	0.343890	−	0.939010i	$-0.388255\pi$
$11$	1.67110	+	0.159571i	0.503857	+	0.0481125i	0.159967	+	0.987122i	$0.448861\pi$
$12$		0			0
$13$	3.76402	+	0.725456i	1.04395	+	0.201205i	0.682273	−	0.731097i	$-0.260991\pi$
$13$	3.76402	+	0.725456i	1.04395	+	0.201205i	0.361679	+	0.932303i	$0.382204\pi$
$14$		0			0
$15$	−2.93090	+	0.860589i	−0.756754	+	0.222203i
$16$		0			0
$17$	−3.78882	−	1.95327i	−0.918923	−	0.473738i	−0.0672055	−	0.997739i	$-0.521408\pi$
$17$	−3.78882	−	1.95327i	−0.918923	−	0.473738i	−0.851717	+	0.524002i	$0.824439\pi$
$18$		0			0
$19$	0.222513	+	0.212166i	0.0510479	+	0.0486741i	0.715174	−	0.698947i	$-0.246348\pi$
$19$	0.222513	+	0.212166i	0.0510479	+	0.0486741i	−0.664126	+	0.747621i	$0.731196\pi$
$20$		0			0
$21$	−2.70297	−	3.79579i	−0.589837	−	0.828310i
$22$		0			0
$23$	−5.91001	+	2.36601i	−1.23232	+	0.493347i	−0.894163	−	0.447741i	$-0.852229\pi$
$23$	−5.91001	+	2.36601i	−1.23232	+	0.493347i	−0.338159	+	0.941089i	$0.609804\pi$
$24$		0			0
$25$	−2.83605	+	3.27297i	−0.567210	+	0.654595i
$26$		0			0
$27$	0.415415	−	0.909632i	0.0799467	−	0.175059i
$28$		0			0
$29$	2.96087	−	5.12839i	0.549821	−	0.952317i	−0.448466	−	0.893800i	$-0.648029\pi$
$29$	2.96087	−	5.12839i	0.549821	−	0.952317i	0.998286	−	0.0585172i	$-0.0186373\pi$
$30$		0			0
$31$	2.69497	−	0.519413i	0.484031	−	0.0932893i	0.0586025	−	0.998281i	$-0.481336\pi$
$31$	2.69497	−	0.519413i	0.484031	−	0.0932893i	0.425428	+	0.904992i	$0.360123\pi$
$32$		0			0
$33$	−0.395770	+	1.63138i	−0.0688946	+	0.283988i
$34$		0			0
$35$	−13.2145	−	5.29027i	−2.23365	−	0.894220i
$36$		0			0
$37$	−4.62971	−	8.01890i	−0.761120	−	1.31830i	−0.942274	−	0.334844i	$-0.891316\pi$
$37$	−4.62971	−	8.01890i	−0.761120	−	1.31830i	0.181153	−	0.983455i	$-0.442017\pi$
$38$		0			0
$39$	−1.25375	+	3.62247i	−0.200760	+	0.580059i
$40$		0			0
$41$	0.484081	+	10.1621i	0.0756008	+	1.58706i	0.644471	+	0.764628i	$0.277077\pi$
$41$	0.484081	+	10.1621i	0.0756008	+	1.58706i	−0.568871	+	0.822427i	$0.692619\pi$
$42$		0			0
$43$	−9.25698	+	5.94910i	−1.41168	+	0.907229i	−0.999992	−	0.00409679i	$-0.998696\pi$
$43$	−9.25698	+	5.94910i	−1.41168	+	0.907229i	−0.411685	+	0.911326i	$0.635060\pi$
$44$		0			0
$45$	−0.434719	−	3.02354i	−0.0648041	−	0.450723i
$46$		0			0
$47$	4.62641	+	3.63825i	0.674831	+	0.530693i	0.895727	−	0.444604i	$-0.146656\pi$
$47$	4.62641	+	3.63825i	0.674831	+	0.530693i	−0.220896	+	0.975297i	$0.570898\pi$
$48$		0			0
$49$	0.700125	−	14.6974i	0.100018	−	2.09963i
$50$		0			0
$51$	2.47259	−	3.47227i	0.346232	−	0.486215i
$52$		0			0
$53$	4.35112	+	2.79629i	0.597672	+	0.384100i	0.804216	−	0.594337i	$-0.202585\pi$
$53$	4.35112	+	2.79629i	0.597672	+	0.384100i	−0.206544	+	0.978437i	$0.566222\pi$
$54$		0			0
$55$	1.67715	+	4.84580i	0.226146	+	0.653407i
$56$		0			0
$57$	−0.241673	+	0.190054i	−0.0320104	+	0.0251732i
$58$		0			0
$59$	3.42100	+	3.94805i	0.445377	+	0.513992i	0.933400	−	0.358839i	$-0.116827\pi$
$59$	3.42100	+	3.94805i	0.445377	+	0.513992i	−0.488023	+	0.872831i	$0.662282\pi$
$60$		0			0
$61$	8.52901	−	0.814422i	1.09203	−	0.104276i	0.466533	−	0.884504i	$-0.345503\pi$
$61$	8.52901	−	0.814422i	1.09203	−	0.104276i	0.625495	+	0.780228i	$0.284897\pi$
$62$		0			0
$63$	4.14183	−	2.13526i	0.521822	−	0.269018i
$64$		0			0
$65$	2.76057	+	11.3792i	0.342407	+	1.41142i
$66$		0			0
$67$	4.38873	−	6.90934i	0.536169	−	0.844111i
$67$	4.38873	−	6.90934i	0.536169	−	0.844111i
$68$		0			0
$69$	−1.50085	−	6.18657i	−0.180681	−	0.744776i
$70$		0			0
$71$	−2.96443	+	1.52827i	−0.351813	+	0.181372i	−0.625069	−	0.780569i	$-0.714929\pi$
$71$	−2.96443	+	1.52827i	−0.351813	+	0.181372i	0.273257	+	0.961941i	$0.411899\pi$
$72$		0			0
$73$	−12.1308	+	1.15835i	−1.41981	+	0.135575i	−0.776540	−	0.630067i	$-0.783027\pi$
$73$	−12.1308	+	1.15835i	−1.41981	+	0.135575i	−0.643266	+	0.765643i	$0.722421\pi$
$74$		0			0
$75$	−2.83605	−	3.27297i	−0.327479	−	0.377931i
$76$		0			0
$77$	−6.14889	+	4.83554i	−0.700732	+	0.551061i
$78$		0			0
$79$	0.311637	+	0.900416i	0.0350619	+	0.101305i	0.961173	−	0.275945i	$-0.0889909\pi$
$79$	0.311637	+	0.900416i	0.0350619	+	0.101305i	−0.926111	+	0.377250i	$0.876870\pi$
$80$		0			0
$81$	0.841254	+	0.540641i	0.0934726	+	0.0600712i
$82$		0			0
$83$	−2.45220	+	3.44363i	−0.269163	+	0.377987i	−0.926930	−	0.375235i	$-0.877562\pi$
$83$	−2.45220	+	3.44363i	−0.269163	+	0.377987i	0.657766	+	0.753222i	$0.271501\pi$
$84$		0			0
$85$	0.619559	−	13.0061i	0.0672006	−	1.41071i
$86$		0			0
$87$	4.65481	+	3.66058i	0.499048	+	0.392456i
$88$		0			0
$89$	2.41415	+	16.7908i	0.255900	+	1.77982i	0.561314	+	0.827603i	$0.310296\pi$
$89$	2.41415	+	16.7908i	0.255900	+	1.77982i	−0.305415	+	0.952219i	$0.598795\pi$
$90$		0			0
$91$	−15.0269	+	9.65722i	−1.57525	+	1.01235i
$92$		0			0
$93$	0.130592	+	2.74146i	0.0135417	+	0.284276i
$94$		0			0
$95$	−0.307166	+	0.887497i	−0.0315145	+	0.0910553i
$96$		0			0
$97$	3.90414	+	6.76216i	0.396405	+	0.686594i	0.993279	−	0.115741i	$-0.0369243\pi$
$97$	3.90414	+	6.76216i	0.396405	+	0.686594i	−0.596874	+	0.802335i	$0.703591\pi$
$98$		0			0
$99$	−1.55846	−	0.623911i	−0.156631	−	0.0627055i
$100$		0			0
$101$	−2.67072	+	11.0088i	−0.265746	+	1.09542i	0.669892	+	0.742459i	$0.266341\pi$
$101$	−2.67072	+	11.0088i	−0.265746	+	1.09542i	−0.935638	+	0.352962i	$0.885175\pi$
$102$		0			0
$103$	−7.57904	+	1.46074i	−0.746785	+	0.143931i	−0.548427	−	0.836199i	$-0.684773\pi$
$103$	−7.57904	+	1.46074i	−0.746785	+	0.143931i	−0.198358	+	0.980130i	$0.563561\pi$
$104$		0			0
$105$	7.11704	−	12.3271i	0.694552	−	1.20300i
$106$		0			0
$107$	0.398988	−	0.873663i	0.0385717	−	0.0844602i	−0.889365	−	0.457197i	$-0.848853\pi$
$107$	0.398988	−	0.873663i	0.0385717	−	0.0844602i	0.927937	+	0.372737i	$0.121581\pi$
$108$		0			0
$109$	11.1928	−	12.9172i	1.07208	−	1.23724i	0.101912	−	0.994793i	$-0.467504\pi$
$109$	11.1928	−	12.9172i	1.07208	−	1.23724i	0.970164	−	0.242448i	$-0.0779505\pi$
$110$		0			0
$111$	8.59615	−	3.44138i	0.815911	−	0.326641i
$112$		0			0
$113$	2.53546	+	3.56056i	0.238516	+	0.334949i	0.916432	−	0.400191i	$-0.131056\pi$
$113$	2.53546	+	3.56056i	0.238516	+	0.334949i	−0.677916	+	0.735139i	$0.737117\pi$
$114$		0			0
$115$	−14.0736	−	13.4192i	−1.31237	−	1.25134i
$116$		0			0
$117$	−3.40717	−	1.75652i	−0.314993	−	0.162390i
$118$		0			0
$119$	19.0588	−	5.59616i	1.74711	−	0.512999i
$120$		0			0
$121$	−8.03409	−	1.54844i	−0.730372	−	0.140768i
$122$		0			0
$123$	−10.1276	−	0.967066i	−0.913172	−	0.0871974i
$124$		0			0
$125$	1.96146	+	0.575935i	0.175438	+	0.0515132i
$126$		0			0
$127$	−1.65982	+	1.58263i	−0.147285	+	0.140436i	−0.760140	−	0.649760i	$-0.774870\pi$
$127$	−1.65982	+	1.58263i	−0.147285	+	0.140436i	0.612855	+	0.790196i	$0.290021\pi$
$128$		0			0
$129$	−4.57114	−	10.0094i	−0.402467	−	0.881279i
$130$		0			0
$131$	0.457904	−	3.18479i	0.0400072	−	0.278256i	−0.959991	−	0.280030i	$-0.909656\pi$
$131$	0.457904	−	3.18479i	0.0400072	−	0.278256i	0.999998	+	0.00177374i	$0.000564599\pi$
$132$		0			0
$133$	−1.43267			−0.124228
$134$		0			0
$135$	3.05463			0.262901
$136$		0			0
$137$	1.86944	−	13.0022i	0.159717	−	1.11086i	−0.739438	−	0.673225i	$-0.764908\pi$
$137$	1.86944	−	13.0022i	0.159717	−	1.11086i	0.899155	−	0.437631i	$-0.144182\pi$
$138$		0			0
$139$	6.28876	+	13.7705i	0.533406	+	1.16800i	0.964110	+	0.265502i	$0.0855379\pi$
$139$	6.28876	+	13.7705i	0.533406	+	1.16800i	−0.430704	+	0.902493i	$0.641735\pi$
$140$		0			0
$141$	−4.25962	+	4.06154i	−0.358725	+	0.342044i
$142$		0			0
$143$	6.17431	+	1.81294i	0.516322	+	0.151606i
$144$		0			0
$145$	18.0068	+	1.71945i	1.49539	+	0.142792i
$146$		0			0
$147$	14.4482	+	2.78466i	1.19167	+	0.229675i
$148$		0			0
$149$	11.3851	−	3.34297i	0.932706	−	0.273867i	0.220137	−	0.975469i	$-0.429350\pi$
$149$	11.3851	−	3.34297i	0.932706	−	0.273867i	0.712569	+	0.701602i	$0.247531\pi$
$150$		0			0
$151$	9.02352	+	4.65195i	0.734324	+	0.378570i	0.784466	−	0.620172i	$-0.212937\pi$
$151$	9.02352	+	4.65195i	0.734324	+	0.378570i	−0.0501422	+	0.998742i	$0.515967\pi$
$152$		0			0
$153$	3.08504	+	2.94158i	0.249411	+	0.237813i
$154$		0			0
$155$	4.86299	+	6.82911i	0.390605	+	0.548527i
$156$		0			0
$157$	17.2904	−	6.92203i	1.37992	−	0.552438i	0.441294	−	0.897363i	$-0.354520\pi$
$157$	17.2904	−	6.92203i	1.37992	−	0.552438i	0.938631	+	0.344924i	$0.112095\pi$
$158$		0			0
$159$	−3.38706	+	3.90887i	−0.268611	+	0.309994i
$160$		0			0
$161$	12.3231	−	26.9839i	0.971199	−	2.12663i
$162$		0			0
$163$	3.68144	−	6.37645i	0.288353	−	0.499442i	−0.685064	−	0.728483i	$-0.740226\pi$
$163$	3.68144	−	6.37645i	0.288353	−	0.499442i	0.973417	+	0.229041i	$0.0735590\pi$
$164$		0			0
$165$	−5.03516	+	0.970447i	−0.391986	+	0.0755492i
$166$		0			0
$167$	5.84568	−	24.0962i	0.452352	−	1.86462i	−0.0480748	−	0.998844i	$-0.515309\pi$
$167$	5.84568	−	24.0962i	0.452352	−	1.86462i	0.500427	−	0.865779i	$-0.333176\pi$
$168$		0			0
$169$	1.57280	+	0.629656i	0.120985	+	0.0484351i
$170$		0			0
$171$	−0.153726	−	0.266260i	−0.0117557	−	0.0203614i
$172$		0			0
$173$	−6.95034	+	20.0817i	−0.528424	+	1.52678i	0.292798	+	0.956174i	$0.405414\pi$
$173$	−6.95034	+	20.0817i	−0.528424	+	1.52678i	−0.821223	+	0.570608i	$0.806708\pi$
$174$		0			0
$175$	−0.960235	−	20.1578i	−0.0725869	−	1.52379i
$176$		0			0
$177$	−4.39472	+	2.82432i	−0.330328	+	0.212289i
$178$		0			0
$179$	3.05733	+	21.2642i	0.228516	+	1.58936i	0.704367	+	0.709836i	$0.251231\pi$
$179$	3.05733	+	21.2642i	0.228516	+	1.58936i	−0.475851	+	0.879526i	$0.657860\pi$
$180$		0			0
$181$	20.2756	+	15.9449i	1.50707	+	1.18517i	0.929494	+	0.368836i	$0.120244\pi$
$181$	20.2756	+	15.9449i	1.50707	+	1.18517i	0.577576	+	0.816337i	$0.303999\pi$
$182$		0			0
$183$	−0.407673	+	8.55810i	−0.0301360	+	0.632633i
$184$		0			0
$185$	16.4064	−	23.0396i	1.20622	−	1.69390i
$186$		0			0
$187$	−6.01982	−	3.86870i	−0.440213	−	0.282907i
$188$		0			0
$189$	1.52408	+	4.40355i	0.110861	+	0.320311i
$190$		0			0
$191$	−4.93517	+	3.88106i	−0.357096	+	0.280824i	−0.780549	−	0.625095i	$-0.785060\pi$
$191$	−4.93517	+	3.88106i	−0.357096	+	0.280824i	0.423453	+	0.905918i	$0.360818\pi$
$192$		0			0
$193$	0.738416	+	0.852178i	0.0531524	+	0.0613411i	0.781703	−	0.623651i	$-0.214351\pi$
$193$	0.738416	+	0.852178i	0.0531524	+	0.0613411i	−0.728551	+	0.684992i	$0.759806\pi$
$194$		0			0
$195$	−11.6563	+	1.11304i	−0.834724	+	0.0797065i
$196$		0			0
$197$	−4.48839	+	2.31393i	−0.319784	+	0.164860i	−0.610644	−	0.791906i	$-0.709089\pi$
$197$	−4.48839	+	2.31393i	−0.319784	+	0.164860i	0.290859	+	0.956766i	$0.406059\pi$
$198$		0			0
$199$	−1.78641	−	7.36367i	−0.126635	−	0.521997i	−0.999425	−	0.0339012i	$-0.989207\pi$
$199$	−1.78641	−	7.36367i	−0.126635	−	0.521997i	0.872790	−	0.488096i	$-0.162308\pi$
$200$		0			0
$201$	6.21443	+	5.32736i	0.438332	+	0.375763i
$202$		0			0
$203$	6.50563	+	26.8166i	0.456605	+	1.88215i
$204$		0			0
$205$	−27.6221	+	14.2402i	−1.92921	+	0.994576i
$206$		0			0
$207$	6.33720	−	0.605129i	0.440466	−	0.0420594i
$208$		0			0
$209$	0.337986	+	0.390057i	0.0233790	+	0.0269808i
$210$		0			0
$211$	10.2340	−	8.04809i	0.704536	−	0.554053i	−0.200341	−	0.979726i	$-0.564205\pi$
$211$	10.2340	−	8.04809i	0.704536	−	0.554053i	0.904877	+	0.425673i	$0.139963\pi$
$212$		0			0
$213$	−1.09083	−	3.15175i	−0.0747424	−	0.215954i
$214$		0			0
$215$	−28.2767	−	18.1723i	−1.92845	−	1.23934i
$216$		0			0
$217$	−7.41849	+	10.4178i	−0.503600	+	0.707207i
$218$		0			0
$219$	0.579834	−	12.1722i	0.0391815	−	0.822522i
$220$		0			0
$221$	−12.8442	−	10.1008i	−0.863993	−	0.679452i
$222$		0			0
$223$	−1.58749	−	11.0413i	−0.106306	−	0.739377i	−0.971345	−	0.237672i	$-0.923616\pi$
$223$	−1.58749	−	11.0413i	−0.106306	−	0.739377i	0.865039	−	0.501705i	$-0.167294\pi$
$224$		0			0
$225$	3.64327	−	2.34139i	0.242885	−	0.156093i
$226$		0			0
$227$	0.542532	+	11.3891i	0.0360091	+	0.755924i	0.942602	+	0.333918i	$0.108371\pi$
$227$	0.542532	+	11.3891i	0.0360091	+	0.755924i	−0.906593	+	0.422006i	$0.861326\pi$
$228$		0			0
$229$	5.53309	−	15.9868i	0.365637	−	1.05644i	−0.600770	−	0.799422i	$-0.705139\pi$
$229$	5.53309	−	15.9868i	0.365637	−	1.05644i	0.966407	−	0.257017i	$-0.0827396\pi$
$230$		0			0
$231$	−3.91125	−	6.77448i	−0.257341	−	0.445728i
$232$		0			0
$233$	16.9117	+	6.77041i	1.10792	+	0.443544i	0.852205	−	0.523208i	$-0.175265\pi$
$233$	16.9117	+	6.77041i	1.10792	+	0.443544i	0.255715	+	0.966752i	$0.417689\pi$
$234$		0			0
$235$	−4.23857	+	17.4716i	−0.276494	+	1.13972i
$236$		0			0
$237$	−0.935602	+	0.180323i	−0.0607739	+	0.0117132i
$238$		0			0
$239$	−6.25249	+	10.8296i	−0.404440	+	0.700510i	−0.994256	−	0.107027i	$-0.965867\pi$
$239$	−6.25249	+	10.8296i	−0.404440	+	0.700510i	0.589816	+	0.807537i	$0.299200\pi$
$240$		0			0
$241$	7.79523	−	17.0692i	0.502135	−	1.09952i	−0.473634	−	0.880722i	$-0.657058\pi$
$241$	7.79523	−	17.0692i	0.502135	−	1.09952i	0.975770	−	0.218801i	$-0.0702145\pi$
$242$		0			0
$243$	−0.654861	+	0.755750i	−0.0420093	+	0.0484814i
$244$		0			0
$245$	41.7265	−	16.7048i	2.66581	−	1.06723i
$246$		0			0
$247$	0.683627	+	0.960019i	0.0434981	+	0.0610846i
$248$		0			0
$249$	−3.05959	−	2.91731i	−0.193894	−	0.184877i
$250$		0			0
$251$	−10.8169	−	5.57648i	−0.682754	−	0.351984i	0.0817051	−	0.996657i	$-0.473963\pi$
$251$	−10.8169	−	5.57648i	−0.682754	−	0.351984i	−0.764459	+	0.644673i	$0.776994\pi$
$252$		0			0
$253$	−10.2538	+	3.01078i	−0.644650	+	0.189286i
$254$		0			0
$255$	12.7856	+	2.46422i	0.800665	+	0.154315i
$256$		0			0
$257$	−14.0180	−	1.33855i	−0.874417	−	0.0834967i	−0.351811	−	0.936071i	$-0.614434\pi$
$257$	−14.0180	−	1.33855i	−0.874417	−	0.0834967i	−0.522606	+	0.852574i	$0.675040\pi$
$258$		0			0
$259$	41.3997	+	12.1560i	2.57245	+	0.755339i
$260$		0			0
$261$	−4.28577	+	4.08647i	−0.265283	+	0.252946i
$262$		0			0
$263$	1.81149	+	3.96660i	0.111701	+	0.244591i	0.957224	−	0.289348i	$-0.0934384\pi$
$263$	1.81149	+	3.96660i	0.111701	+	0.244591i	−0.845523	+	0.533939i	$0.820711\pi$
$264$		0			0
$265$	−2.24845	+	15.6383i	−0.138121	+	0.960652i
$266$		0			0
$267$	−16.9635			−1.03815
$268$		0			0
$269$	−10.9729			−0.669027			−0.334514	−	0.942391i	$-0.608572\pi$
$269$	−10.9729			−0.669027			−0.334514	+	0.942391i	$0.608572\pi$
$270$		0			0
$271$	−2.49905	+	17.3813i	−0.151806	+	1.05584i	0.761383	+	0.648302i	$0.224521\pi$
$271$	−2.49905	+	17.3813i	−0.151806	+	1.05584i	−0.913190	+	0.407535i	$0.866388\pi$
$272$		0			0
$273$	−7.42037	−	16.2483i	−0.449101	−	0.983394i
$274$		0			0
$275$	−5.26160	+	5.01693i	−0.317287	+	0.302532i
$276$		0			0
$277$	−8.60493	−	2.52663i	−0.517020	−	0.151811i	0.0128046	−	0.999918i	$-0.495924\pi$
$277$	−8.60493	−	2.52663i	−0.517020	−	0.151811i	−0.529825	+	0.848107i	$0.677742\pi$
$278$		0			0
$279$	−2.73214	−	0.260888i	−0.163569	−	0.0156189i
$280$		0			0
$281$	6.33882	+	1.22171i	0.378142	+	0.0728810i	0.374781	−	0.927113i	$-0.377718\pi$
$281$	6.33882	+	1.22171i	0.378142	+	0.0728810i	0.00336136	+	0.999994i	$0.498930\pi$
$282$		0			0
$283$	12.6723	−	3.72094i	0.753293	−	0.221187i	0.117528	−	0.993070i	$-0.462503\pi$
$283$	12.6723	−	3.72094i	0.753293	−	0.221187i	0.635765	+	0.771883i	$0.280685\pi$
$284$		0			0
$285$	−0.834749	−	0.430343i	−0.0494463	−	0.0254913i
$286$		0			0
$287$	−34.3104	−	32.7149i	−2.02528	−	1.93110i
$288$		0			0
$289$	0.678892	+	0.953371i	0.0399348	+	0.0560806i
$290$		0			0
$291$	−7.24895	+	2.90204i	−0.424941	+	0.170121i
$292$		0			0
$293$	−11.3534	+	13.1025i	−0.663274	+	0.765459i	−0.983308	−	0.181947i	$-0.941760\pi$
$293$	−11.3534	+	13.1025i	−0.663274	+	0.765459i	0.320034	+	0.947406i	$0.396306\pi$
$294$		0			0
$295$	−6.62896	+	14.5154i	−0.385953	+	0.845119i
$296$		0			0
$297$	0.839352	−	1.45380i	0.0487042	−	0.0843581i
$298$		0			0
$299$	−23.9619	+	4.61827i	−1.38575	+	0.267081i
$300$		0			0
$301$	12.0888	−	49.8305i	0.696784	−	2.87218i
$302$		0			0
$303$	−10.5167	−	4.21025i	−0.604169	−	0.241873i
$304$		0			0
$305$	13.0857	+	22.6652i	0.749287	+	1.29780i
$306$		0			0
$307$	0.400152	−	1.15616i	0.0228379	−	0.0659858i	−0.933006	−	0.359861i	$-0.882824\pi$
$307$	0.400152	−	1.15616i	0.0228379	−	0.0659858i	0.955844	+	0.293876i	$0.0949452\pi$
$308$		0			0
$309$	−0.367262	−	7.70978i	−0.0208928	−	0.438594i
$310$		0			0
$311$	14.8371	−	9.53524i	0.841336	−	0.540694i	−0.0475253	−	0.998870i	$-0.515133\pi$
$311$	14.8371	−	9.53524i	0.841336	−	0.540694i	0.888861	+	0.458176i	$0.151497\pi$
$312$		0			0
$313$	−2.08115	−	14.4747i	−0.117634	−	0.818161i	−0.960149	−	0.279489i	$-0.909835\pi$
$313$	−2.08115	−	14.4747i	−0.117634	−	0.818161i	0.842515	−	0.538673i	$-0.181074\pi$
$314$		0			0
$315$	11.1887	+	8.79893i	0.630414	+	0.495763i
$316$		0			0
$317$	−0.183664	+	3.85558i	−0.0103156	+	0.216551i	0.987824	+	0.155577i	$0.0497237\pi$
$317$	−0.183664	+	3.85558i	−0.0103156	+	0.216551i	−0.998139	+	0.0609739i	$0.980579\pi$
$318$		0			0
$319$	5.76627	−	8.09759i	0.322849	−	0.453378i
$320$		0			0
$321$	0.807988	+	0.519263i	0.0450975	+	0.0289824i
$322$		0			0
$323$	−0.428643	−	1.23848i	−0.0238504	−	0.0689111i
$324$		0			0
$325$	−13.0494	+	10.2621i	−0.723848	+	0.569240i
$326$		0			0
$327$	11.1928	+	12.9172i	0.618963	+	0.714322i
$328$		0			0
$329$	−27.3018	+	2.60701i	−1.50520	+	0.143729i
$330$		0			0
$331$	−6.42826	+	3.31400i	−0.353329	+	0.182154i	−0.625749	−	0.780025i	$-0.715206\pi$
$331$	−6.42826	+	3.31400i	−0.353329	+	0.182154i	0.272420	+	0.962179i	$0.412176\pi$
$332$		0			0
$333$	2.18299	+	8.99842i	0.119627	+	0.493110i
$334$		0			0
$335$	24.7673	+	3.42695i	1.35318	+	0.187234i
$336$		0			0
$337$	4.25279	+	17.5302i	0.231664	+	0.954933i	0.962262	+	0.272125i	$0.0877264\pi$
$337$	4.25279	+	17.5302i	0.231664	+	0.954933i	−0.730598	+	0.682808i	$0.760758\pi$
$338$		0			0
$339$	−3.88515	+	2.00293i	−0.211012	+	0.108784i
$340$		0			0
$341$	4.58646	−	0.437953i	0.248371	−	0.0237165i
$342$		0			0
$343$	23.5399	+	27.1665i	1.27104	+	1.46685i
$344$		0			0
$345$	15.2855	−	12.0206i	0.822942	−	0.647169i
$346$		0			0
$347$	6.21649	+	17.9614i	0.333718	+	0.964216i	0.979631	+	0.200805i	$0.0643557\pi$
$347$	6.21649	+	17.9614i	0.333718	+	0.964216i	−0.645913	+	0.763411i	$0.723523\pi$
$348$		0			0
$349$	−10.5390	−	6.77304i	−0.564142	−	0.362552i	0.227273	−	0.973831i	$-0.427019\pi$
$349$	−10.5390	−	6.77304i	−0.564142	−	0.362552i	−0.791415	+	0.611279i	$0.790655\pi$
$350$		0			0
$351$	2.22353	−	3.12251i	0.118683	−	0.166667i
$352$		0			0
$353$	−0.735637	+	15.4429i	−0.0391540	+	0.821944i	0.890828	+	0.454340i	$0.150125\pi$
$353$	−0.735637	+	15.4429i	−0.0391540	+	0.821944i	−0.929982	+	0.367604i	$0.880178\pi$
$354$		0			0
$355$	−8.00810	−	6.29764i	−0.425026	−	0.334244i
$356$		0			0
$357$	2.82685	+	19.6612i	0.149613	+	1.04058i
$358$		0			0
$359$	−8.03064	+	5.16098i	−0.423841	+	0.272386i	−0.735126	−	0.677931i	$-0.762877\pi$
$359$	−8.03064	+	5.16098i	−0.423841	+	0.272386i	0.311285	+	0.950317i	$0.399241\pi$
$360$		0			0
$361$	−0.899559	−	18.8841i	−0.0473452	−	0.993898i
$362$		0			0
$363$	2.67605	−	7.73195i	0.140456	−	0.405822i
$364$		0			0
$365$	−18.6119	−	32.2367i	−0.974190	−	1.68735i
$366$		0			0
$367$	11.1984	+	4.48318i	0.584554	+	0.234020i	0.645040	−	0.764149i	$-0.276841\pi$
$367$	11.1984	+	4.48318i	0.584554	+	0.234020i	−0.0604859	+	0.998169i	$0.519265\pi$
$368$		0			0
$369$	2.39853	−	9.88686i	0.124862	−	0.514689i
$370$		0			0
$371$	−23.6660	+	4.56124i	−1.22868	+	0.236808i
$372$		0			0
$373$	−2.65693	+	4.60194i	−0.137571	+	0.238279i	−0.926577	−	0.376106i	$-0.877263\pi$
$373$	−2.65693	+	4.60194i	−0.137571	+	0.238279i	0.789006	+	0.614386i	$0.210596\pi$
$374$		0			0
$375$	−0.849217	+	1.85953i	−0.0438534	+	0.0960255i
$376$		0			0
$377$	14.8652	−	17.1554i	0.765598	−	0.883547i
$378$		0			0
$379$	−24.0595	+	9.63199i	−1.23586	+	0.494762i	−0.895301	−	0.445463i	$-0.853039\pi$
$379$	−24.0595	+	9.63199i	−1.23586	+	0.494762i	−0.340555	+	0.940225i	$0.610615\pi$
$380$		0			0
$381$	−1.33031	−	1.86816i	−0.0681537	−	0.0957085i
$382$		0			0
$383$	−15.0155	−	14.3172i	−0.767255	−	0.731576i	0.201529	−	0.979483i	$-0.435409\pi$
$383$	−15.0155	−	14.3172i	−0.767255	−	0.731576i	−0.968784	+	0.247906i	$0.920258\pi$
$384$		0			0
$385$	−21.2386	−	10.9492i	−1.08242	−	0.558025i
$386$		0			0
$387$	10.5581	−	3.10013i	0.536697	−	0.157588i
$388$		0			0
$389$	−9.87934	−	1.90409i	−0.500902	−	0.0965410i	−0.0674595	−	0.997722i	$-0.521489\pi$
$389$	−9.87934	−	1.90409i	−0.500902	−	0.0965410i	−0.433443	+	0.901181i	$0.642701\pi$
$390$		0			0
$391$	27.0134	+	2.57947i	1.36613	+	0.130449i
$392$		0			0
$393$	3.08721	+	0.906486i	0.155729	+	0.0457262i
$394$		0			0
$395$	−2.10644	+	2.00849i	−0.105986	+	0.101058i
$396$		0			0
$397$	0.493650	+	1.08094i	0.0247756	+	0.0542509i	0.921615	−	0.388105i	$-0.126870\pi$
$397$	0.493650	+	1.08094i	0.0247756	+	0.0542509i	−0.896840	+	0.442356i	$0.854143\pi$
$398$		0			0
$399$	0.203891	−	1.41809i	0.0102073	−	0.0709933i
$400$		0			0
$401$	24.7319			1.23505			0.617525	−	0.786551i	$-0.288135\pi$
$401$	24.7319			1.23505			0.617525	+	0.786551i	$0.288135\pi$
$402$		0			0
$403$	10.5207			0.524075
$404$		0			0
$405$	−0.434719	+	3.02354i	−0.0216014	+	0.150241i
$406$		0			0
$407$	−6.45715	−	14.1392i	−0.320069	−	0.700853i
$408$		0			0
$409$	−28.0888	+	26.7826i	−1.38890	+	1.32432i	−0.500144	+	0.865942i	$0.666720\pi$
$409$	−28.0888	+	26.7826i	−1.38890	+	1.32432i	−0.888759	+	0.458374i	$0.848432\pi$
$410$		0			0
$411$	12.6038	+	3.70082i	0.621702	+	0.182548i
$412$		0			0
$413$	−24.2329	−	2.31396i	−1.19242	−	0.113862i
$414$		0			0
$415$	−12.6801	−	2.44389i	−0.622442	−	0.119966i
$416$		0			0
$417$	−14.5253	+	4.26501i	−0.711306	+	0.208858i
$418$		0			0
$419$	30.0076	+	15.4700i	1.46597	+	0.755758i	0.992172	−	0.124877i	$-0.0398536\pi$
$419$	30.0076	+	15.4700i	1.46597	+	0.755758i	0.473795	+	0.880635i	$0.342884\pi$
$420$		0			0
$421$	0.592394	+	0.564847i	0.0288715	+	0.0275289i	0.704377	−	0.709826i	$-0.251226\pi$
$421$	0.592394	+	0.564847i	0.0288715	+	0.0275289i	−0.675506	+	0.737355i	$0.736075\pi$
$422$		0			0
$423$	−3.41399	−	4.79428i	−0.165994	−	0.233106i
$424$		0			0
$425$	17.1383	−	6.86113i	0.831328	−	0.332814i
$426$		0			0
$427$	−26.1450	+	30.1730i	−1.26525	+	1.46017i
$428$		0			0
$429$	−2.67318	+	5.85346i	−0.129063	+	0.282608i
$430$		0			0
$431$	1.54263	−	2.67191i	0.0743057	−	0.128701i	−0.826478	−	0.562968i	$-0.809659\pi$
$431$	1.54263	−	2.67191i	0.0743057	−	0.128701i	0.900784	+	0.434267i	$0.142993\pi$
$432$		0			0
$433$	−16.2337	+	3.12880i	−0.780143	+	0.150360i	−0.563750	−	0.825946i	$-0.690642\pi$
$433$	−16.2337	+	3.12880i	−0.780143	+	0.150360i	−0.216394	+	0.976306i	$0.569430\pi$
$434$		0			0
$435$	−4.26459	+	17.5789i	−0.204471	+	0.842842i
$436$		0			0
$437$	−1.81704	−	0.727433i	−0.0869208	−	0.0347978i
$438$		0			0
$439$	−8.51180	−	14.7429i	−0.406246	−	0.703639i	0.588220	−	0.808701i	$-0.299829\pi$
$439$	−8.51180	−	14.7429i	−0.406246	−	0.703639i	−0.994466	+	0.105062i	$0.966496\pi$
$440$		0			0
$441$	−4.81251	+	13.9048i	−0.229167	+	0.662135i
$442$		0			0
$443$	−1.13313	−	23.7874i	−0.0538369	−	1.13017i	−0.850576	−	0.525852i	$-0.823747\pi$
$443$	−1.13313	−	23.7874i	−0.0538369	−	1.13017i	0.796739	−	0.604323i	$-0.206556\pi$
$444$		0			0
$445$	−43.5913	+	28.0145i	−2.06643	+	1.32801i
$446$		0			0
$447$	1.68868	+	11.7450i	0.0798716	+	0.555519i
$448$		0			0
$449$	15.8227	+	12.4431i	0.746718	+	0.587226i	0.917337	−	0.398111i	$-0.130334\pi$
$449$	15.8227	+	12.4431i	0.746718	+	0.587226i	−0.170619	+	0.985337i	$0.554577\pi$
$450$		0			0
$451$	−0.812629	+	17.0592i	−0.0382652	+	0.803286i
$452$		0			0
$453$	−5.88878	+	8.26963i	−0.276679	+	0.388541i
$454$		0			0
$455$	−45.9017	−	29.4992i	−2.15191	−	1.38295i
$456$		0			0
$457$	6.38801	+	18.4569i	0.298818	+	0.863379i	0.990046	+	0.140742i	$0.0449488\pi$
$457$	6.38801	+	18.4569i	0.298818	+	0.863379i	−0.691228	+	0.722637i	$0.742930\pi$
$458$		0			0
$459$	−3.35069	+	2.63501i	−0.156397	+	0.122992i
$460$		0			0
$461$	−10.2109	−	11.7841i	−0.475571	−	0.548838i	0.466382	−	0.884584i	$-0.345557\pi$
$461$	−10.2109	−	11.7841i	−0.475571	−	0.548838i	−0.941953	+	0.335745i	$0.891012\pi$
$462$		0			0
$463$	−2.72105	+	0.259829i	−0.126458	+	0.0120753i	−0.158093	−	0.987424i	$-0.550535\pi$
$463$	−2.72105	+	0.259829i	−0.126458	+	0.0120753i	0.0316351	+	0.999499i	$0.489929\pi$
$464$		0			0
$465$	−7.45168	+	3.84161i	−0.345563	+	0.178150i
$466$		0			0
$467$	0.0570286	+	0.235075i	0.00263897	+	0.0108780i	0.973116	−	0.230316i	$-0.0739761\pi$
$467$	0.0570286	+	0.235075i	0.00263897	+	0.0108780i	−0.970477	+	0.241194i	$0.922461\pi$
$468$		0			0
$469$	7.41715	+	37.4143i	0.342492	+	1.72763i
$470$		0			0
$471$	4.39090	+	18.0995i	0.202322	+	0.833982i
$472$		0			0
$473$	−16.4187	+	8.46442i	−0.754932	+	0.389194i
$474$		0			0
$475$	−1.32547	+	0.126567i	−0.0608167	+	0.00580729i
$476$		0			0
$477$	−3.38706	−	3.90887i	−0.155083	−	0.178975i
$478$		0			0
$479$	24.3721	−	19.1664i	1.11359	−	0.875736i	0.120454	−	0.992719i	$-0.461565\pi$
$479$	24.3721	−	19.1664i	1.11359	−	0.875736i	0.993134	+	0.116983i	$0.0373224\pi$
$480$		0			0
$481$	−11.6090	−	33.5420i	−0.529324	−	1.52938i
$482$		0			0
$483$	24.9555	+	16.0379i	1.13551	+	0.729750i
$484$		0			0
$485$	−13.8352	+	19.4288i	−0.628222	+	0.882215i
$486$		0			0
$487$	0.997950	−	20.9496i	0.0452214	−	0.949315i	−0.856273	−	0.516524i	$-0.827226\pi$
$487$	0.997950	−	20.9496i	0.0452214	−	0.949315i	0.901494	−	0.432791i	$-0.142471\pi$
$488$		0			0
$489$	5.78762	+	4.55144i	0.261725	+	0.205823i
$490$		0			0
$491$	0.886186	+	6.16356i	0.0399930	+	0.278158i	0.999998	−	0.00182421i	$-0.000580664\pi$
$491$	0.886186	+	6.16356i	0.0399930	+	0.278158i	−0.960005	+	0.279982i	$0.909672\pi$
$492$		0			0
$493$	−21.2353	+	13.6471i	−0.956391	+	0.614635i
$494$		0			0
$495$	−0.243992	−	5.12201i	−0.0109666	−	0.230217i
$496$		0			0
$497$	5.08309	−	14.6866i	0.228008	−	0.658785i
$498$		0			0
$499$	−17.6798	−	30.6224i	−0.791458	−	1.37084i	−0.925064	−	0.379810i	$-0.875989\pi$
$499$	−17.6798	−	30.6224i	−0.791458	−	1.37084i	0.133607	−	0.991034i	$-0.457344\pi$
$500$		0			0
$501$	23.0190	+	9.21543i	1.02841	+	0.411715i
$502$		0			0
$503$	−1.12551	+	4.63943i	−0.0501842	+	0.206862i	−0.991384	−	0.130989i	$-0.958185\pi$
$503$	−1.12551	+	4.63943i	−0.0501842	+	0.206862i	0.941200	+	0.337851i	$0.109700\pi$
$504$		0			0
$505$	−33.9780	+	6.54873i	−1.51200	+	0.291415i
$506$		0			0
$507$	−0.847080	+	1.46719i	−0.0376202	+	0.0651600i
$508$		0			0
$509$	0.351316	−	0.769275i	0.0155718	−	0.0340975i	−0.901686	−	0.432391i	$-0.857670\pi$
$509$	0.351316	−	0.769275i	0.0155718	−	0.0340975i	0.917258	+	0.398293i	$0.130397\pi$
$510$		0			0
$511$	37.1862	−	42.9151i	1.64502	−	1.89845i
$512$		0			0
$513$	0.285428	−	0.114268i	0.0126019	−	0.00504506i
$514$		0			0
$515$	−13.6761	−	19.2055i	−0.602643	−	0.846293i
$516$		0			0
$517$	7.15065	+	6.81813i	0.314485	+	0.299861i
$518$		0			0
$519$	−18.8881	−	9.73752i	−0.829098	−	0.427429i
$520$		0			0
$521$	8.38736	−	2.46275i	0.367457	−	0.107895i	−0.0927907	−	0.995686i	$-0.529579\pi$
$521$	8.38736	−	2.46275i	0.367457	−	0.107895i	0.460248	+	0.887791i	$0.347761\pi$
$522$		0			0
$523$	42.2483	+	8.14269i	1.84739	+	0.356055i	0.987899	−	0.155098i	$-0.0495694\pi$
$523$	42.2483	+	8.14269i	1.84739	+	0.356055i	0.859490	+	0.511153i	$0.170782\pi$
$524$		0			0
$525$	20.0893	+	1.91829i	0.876769	+	0.0837212i
$526$		0			0
$527$	−11.2253	−	3.29604i	−0.488982	−	0.143578i
$528$		0			0
$529$	12.6843	−	12.0945i	0.551493	−	0.525847i
$530$		0			0
$531$	−2.17014	−	4.75193i	−0.0941759	−	0.206216i
$532$		0			0
$533$	−5.55007	+	38.6016i	−0.240400	+	1.67202i
$534$		0			0
$535$	2.93384			0.126841
$536$		0			0
$537$	−21.4829			−0.927054
$538$		0			0
$539$	3.51527	−	24.4492i	0.151413	−	1.05310i
$540$		0			0
$541$	15.5982	+	34.1554i	0.670621	+	1.46845i	0.872284	+	0.489000i	$0.162638\pi$
$541$	15.5982	+	34.1554i	0.670621	+	1.46845i	−0.201663	+	0.979455i	$0.564635\pi$
$542$		0			0
$543$	−18.6681	+	17.8000i	−0.801124	+	0.763871i
$544$		0			0
$545$	50.0945	+	14.7091i	2.14581	+	0.630068i
$546$		0			0
$547$	−2.15290	−	0.205577i	−0.0920515	−	0.00878986i	0.0489286	−	0.998802i	$-0.484419\pi$
$547$	−2.15290	−	0.205577i	−0.0920515	−	0.00878986i	−0.140980	+	0.990012i	$0.545025\pi$
$548$		0			0
$549$	−8.41297	−	1.62147i	−0.359057	−	0.0692026i
$550$		0			0
$551$	1.74690	−	0.512936i	0.0744204	−	0.0218518i
$552$		0			0
$553$	−3.94642	−	2.03452i	−0.167819	−	0.0865167i
$554$		0			0
$555$	20.4702	+	19.5183i	0.868911	+	0.828505i
$556$		0			0
$557$	0.0858078	+	0.120500i	0.00363579	+	0.00510576i	0.816390	−	0.577501i	$-0.195972\pi$
$557$	0.0858078	+	0.120500i	0.00363579	+	0.00510576i	−0.812754	+	0.582607i	$0.802033\pi$
$558$		0			0
$559$	−39.1593	+	15.6770i	−1.65626	+	0.663067i
$560$		0			0
$561$	4.68603	−	5.40797i	0.197844	−	0.228325i
$562$		0			0
$563$	16.4041	−	35.9199i	0.691349	−	1.51384i	−0.158805	−	0.987310i	$-0.550764\pi$
$563$	16.4041	−	35.9199i	0.691349	−	1.51384i	0.850154	−	0.526533i	$-0.176509\pi$
$564$		0			0
$565$	−6.67598	+	11.5631i	−0.280860	+	0.486465i
$566$		0			0
$567$	−4.57563	+	0.881880i	−0.192158	+	0.0370355i
$568$		0			0
$569$	−7.18854	+	29.6316i	−0.301359	+	1.24222i	0.596743	+	0.802433i	$0.296461\pi$
$569$	−7.18854	+	29.6316i	−0.301359	+	1.24222i	−0.898102	+	0.439787i	$0.855054\pi$
$570$		0			0
$571$	−28.3504	−	11.3498i	−1.18643	−	0.474975i	−0.307325	−	0.951605i	$-0.599434\pi$
$571$	−28.3504	−	11.3498i	−1.18643	−	0.474975i	−0.879104	+	0.476630i	$0.841858\pi$
$572$		0			0
$573$	−3.13921	−	5.43727i	−0.131142	−	0.227145i
$574$		0			0
$575$	9.01718	−	26.0534i	0.376043	−	1.08650i
$576$		0			0
$577$	0.814902	+	17.1069i	0.0339248	+	0.712169i	0.950204	+	0.311629i	$0.100875\pi$
$577$	0.814902	+	17.1069i	0.0339248	+	0.712169i	−0.916279	+	0.400540i	$0.868822\pi$
$578$		0			0
$579$	−0.948591	+	0.609623i	−0.0394221	+	0.0253351i
$580$		0			0
$581$	−2.80353	−	19.4990i	−0.116310	−	0.808955i
$582$		0			0
$583$	6.82496	+	5.36720i	0.282661	+	0.222287i
$584$		0			0
$585$	0.557151	−	11.6960i	0.0230354	−	0.483572i
$586$		0			0
$587$	12.2543	−	17.2088i	0.505791	−	0.710283i	−0.480186	−	0.877167i	$-0.659431\pi$
$587$	12.2543	−	17.2088i	0.505791	−	0.710283i	0.985977	+	0.166883i	$0.0533703\pi$
$588$		0			0
$589$	0.709867	+	0.456204i	0.0292496	+	0.0187975i
$590$		0			0
$591$	−1.65161	−	4.77201i	−0.0679381	−	0.196294i
$592$		0			0
$593$	20.6020	−	16.2016i	0.846022	−	0.665319i	−0.0980055	−	0.995186i	$-0.531246\pi$
$593$	20.6020	−	16.2016i	0.846022	−	0.665319i	0.944027	+	0.329867i	$0.107004\pi$
$594$		0			0
$595$	39.7338	+	45.8553i	1.62893	+	1.87988i
$596$		0			0
$597$	7.54295	−	0.720265i	0.308713	−	0.0294785i
$598$		0			0
$599$	26.9034	−	13.8696i	1.09924	−	0.566698i	0.189503	−	0.981880i	$-0.439312\pi$
$599$	26.9034	−	13.8696i	1.09924	−	0.566698i	0.909738	+	0.415182i	$0.136282\pi$
$600$		0			0
$601$	1.43456	+	5.91335i	0.0585171	+	0.241211i	0.993557	−	0.113331i	$-0.0361521\pi$
$601$	1.43456	+	5.91335i	0.0585171	+	0.241211i	−0.935040	+	0.354542i	$0.884637\pi$
$602$		0			0
$603$	−6.15755	+	5.39302i	−0.250755	+	0.219621i
$604$		0			0
$605$	−5.89228	−	24.2883i	−0.239555	−	0.987461i
$606$		0			0
$607$	24.0267	−	12.3866i	0.975212	−	0.502757i	0.104487	−	0.994526i	$-0.466680\pi$
$607$	24.0267	−	12.3866i	0.975212	−	0.502757i	0.870726	+	0.491769i	$0.163650\pi$
$608$		0			0
$609$	−27.4694	+	2.62301i	−1.11312	+	0.106290i
$610$		0			0
$611$	14.7745	+	17.0507i	0.597713	+	0.689798i
$612$		0			0
$613$	27.6716	−	21.7612i	1.11764	−	0.878925i	0.124088	−	0.992271i	$-0.460399\pi$
$613$	27.6716	−	21.7612i	1.11764	−	0.878925i	0.993556	+	0.113346i	$0.0361570\pi$
$614$		0			0
$615$	−10.1642	−	29.3675i	−0.409860	−	1.18421i
$616$		0			0
$617$	−24.1816	−	15.5406i	−0.973515	−	0.625640i	−0.0458085	−	0.998950i	$-0.514586\pi$
$617$	−24.1816	−	15.5406i	−0.973515	−	0.625640i	−0.927707	+	0.373310i	$0.878223\pi$
$618$		0			0
$619$	20.5588	−	28.8708i	0.826328	−	1.16041i	−0.158582	−	0.987346i	$-0.550692\pi$
$619$	20.5588	−	28.8708i	0.826328	−	1.16041i	0.984910	−	0.173069i	$-0.0553683\pi$
$620$		0			0
$621$	−0.302908	+	6.35881i	−0.0121553	+	0.255170i
$622$		0			0
$623$	−62.1352	−	48.8636i	−2.48939	−	1.95768i
$624$		0			0
$625$	3.97034	+	27.6143i	0.158814	+	1.10457i
$626$		0			0
$627$	−0.434187	+	0.279035i	−0.0173398	+	0.0111436i
$628$		0			0
$629$	1.87805	+	39.4252i	0.0748829	+	1.57199i
$630$		0			0
$631$	−0.336453	+	0.972116i	−0.0133940	+	0.0386993i	−0.951500	−	0.307650i	$-0.900458\pi$
$631$	−0.336453	+	0.972116i	−0.0133940	+	0.0386993i	0.938106	+	0.346349i	$0.112579\pi$
$632$		0			0
$633$	6.50972	+	11.2752i	0.258738	+	0.448148i
$634$		0			0
$635$	−6.50370	−	2.60369i	−0.258091	−	0.103324i
$636$		0			0
$637$	13.2976	−	54.8136i	0.526871	−	2.17179i
$638$		0			0
$639$	3.27491	−	0.631187i	0.129553	−	0.0249694i
$640$		0			0
$641$	14.9877	−	25.9595i	0.591979	−	1.02534i	−0.401987	−	0.915646i	$-0.631680\pi$
$641$	14.9877	−	25.9595i	0.591979	−	1.02534i	0.993966	−	0.109692i	$-0.0349865\pi$
$642$		0			0
$643$	−1.06910	+	2.34100i	−0.0421611	+	0.0923199i	−0.929541	−	0.368720i	$-0.879796\pi$
$643$	−1.06910	+	2.34100i	−0.0421611	+	0.0923199i	0.887379	+	0.461040i	$0.152523\pi$
$644$		0			0
$645$	22.0115	−	25.4027i	0.866703	−	1.00023i
$646$		0			0
$647$	0.873916	−	0.349863i	0.0343572	−	0.0137545i	−0.354420	−	0.935086i	$-0.615322\pi$
$647$	0.873916	−	0.349863i	0.0343572	−	0.0137545i	0.388777	+	0.921332i	$0.372898\pi$
$648$		0			0
$649$	5.08686	+	7.14349i	0.199677	+	0.280407i
$650$		0			0
$651$	−9.25601	−	8.82559i	−0.362772	−	0.345902i
$652$		0			0
$653$	0.890316	+	0.458990i	0.0348407	+	0.0179617i	0.475559	−	0.879684i	$-0.342246\pi$
$653$	0.890316	+	0.458990i	0.0348407	+	0.0179617i	−0.440718	+	0.897646i	$0.645276\pi$
$654$		0			0
$655$	9.43028	−	2.76898i	0.368471	−	0.108193i
$656$		0			0
$657$	11.9658	+	2.30622i	0.466830	+	0.0899741i
$658$		0			0
$659$	−45.0809	−	4.30471i	−1.75610	−	0.167688i	−0.833264	−	0.552875i	$-0.813531\pi$
$659$	−45.0809	−	4.30471i	−1.75610	−	0.167688i	−0.922839	+	0.385187i	$0.874137\pi$
$660$		0			0
$661$	4.86677	+	1.42901i	0.189295	+	0.0555821i	0.375006	−	0.927022i	$-0.377641\pi$
$661$	4.86677	+	1.42901i	0.189295	+	0.0555821i	−0.185711	+	0.982604i	$0.559459\pi$
$662$		0			0
$663$	11.8259	−	11.2760i	0.459279	−	0.437922i
$664$		0			0
$665$	−1.81797	−	3.98081i	−0.0704980	−	0.154369i
$666$		0			0
$667$	−5.36498	+	37.3143i	−0.207733	+	1.44481i
$668$		0			0
$669$	11.1548			0.431269
$670$		0			0
$671$	14.3828			0.555242
$672$		0			0
$673$	−5.27452	+	36.6851i	−0.203318	+	1.41411i	0.591033	+	0.806648i	$0.298720\pi$
$673$	−5.27452	+	36.6851i	−0.203318	+	1.41411i	−0.794351	+	0.607460i	$0.792189\pi$
$674$		0			0
$675$	1.79907	+	3.93940i	0.0692461	+	0.151628i
$676$		0			0
$677$	7.69839	−	7.34040i	0.295873	−	0.282114i	−0.527572	−	0.849510i	$-0.676898\pi$
$677$	7.69839	−	7.34040i	0.295873	−	0.282114i	0.823445	+	0.567396i	$0.192049\pi$
$678$		0			0
$679$	−34.9114	−	10.2509i	−1.33978	−	0.393394i
$680$		0			0
$681$	−11.3504	−	1.08384i	−0.434950	−	0.0415327i
$682$		0			0
$683$	−0.689882	−	0.132964i	−0.0263976	−	0.00508772i	0.176035	−	0.984384i	$-0.443673\pi$
$683$	−0.689882	−	0.132964i	−0.0263976	−	0.00508772i	−0.202433	+	0.979296i	$0.564885\pi$
$684$		0			0
$685$	38.5001	−	11.3046i	1.47101	−	0.431928i
$686$		0			0
$687$	15.0367	+	7.75194i	0.573684	+	0.295755i
$688$		0			0
$689$	14.3491	+	13.6819i	0.546658	+	0.521237i
$690$		0			0
$691$	−25.8604	−	36.3159i	−0.983777	−	1.38152i	−0.923610	−	0.383332i	$-0.874776\pi$
$691$	−25.8604	−	36.3159i	−0.983777	−	1.38152i	−0.0601661	−	0.998188i	$-0.519163\pi$
$692$		0			0
$693$	7.26215	−	2.90733i	0.275866	−	0.110440i
$694$		0			0
$695$	−30.2824	+	34.9478i	−1.14868	+	1.32564i
$696$		0			0
$697$	18.0153	−	39.4479i	0.682377	−	1.49420i
$698$		0			0
$699$	−9.10828	+	15.7760i	−0.344507	+	0.596703i
$700$		0			0
$701$	−36.3647	+	7.00873i	−1.37348	+	0.264716i	−0.822006	−	0.569478i	$-0.807145\pi$
$701$	−36.3647	+	7.00873i	−1.37348	+	0.264716i	−0.551471	+	0.834194i	$0.685933\pi$
$702$		0			0
$703$	0.671163	−	2.76657i	0.0253134	−	0.104343i
$704$		0			0
$705$	−16.6906	−	6.68189i	−0.628603	−	0.251655i
$706$		0			0
$707$	−26.3937	−	45.7152i	−0.992638	−	1.71930i
$708$		0			0
$709$	0.635938	−	1.83742i	0.0238831	−	0.0690058i	−0.932429	−	0.361353i	$-0.882315\pi$
$709$	0.635938	−	1.83742i	0.0238831	−	0.0690058i	0.956312	+	0.292347i	$0.0944362\pi$
$710$		0			0
$711$	−0.0453370	−	0.951742i	−0.00170027	−	0.0356931i
$712$		0			0
$713$	−14.6984	+	9.44607i	−0.550458	+	0.353758i
$714$		0			0
$715$	2.79741	+	19.4564i	0.104617	+	0.727628i
$716$		0			0
$717$	−9.82958	−	7.73006i	−0.367092	−	0.288685i
$718$		0			0
$719$	1.53319	−	32.1856i	0.0571783	−	1.20032i	−0.769875	−	0.638195i	$-0.779681\pi$
$719$	1.53319	−	32.1856i	0.0571783	−	1.20032i	0.827053	−	0.562124i	$-0.190016\pi$
$720$		0			0
$721$	20.8630	−	29.2979i	0.776977	−	1.09111i
$722$		0			0
$723$	15.7861	+	10.1451i	0.587090	+	0.377300i
$724$		0			0
$725$	8.38789	+	24.2352i	0.311518	+	0.900073i
$726$		0			0
$727$	24.3275	−	19.1314i	0.902257	−	0.709543i	−0.0550905	−	0.998481i	$-0.517545\pi$
$727$	24.3275	−	19.1314i	0.902257	−	0.709543i	0.957348	+	0.288939i	$0.0933023\pi$
$728$		0			0
$729$	−0.654861	−	0.755750i	−0.0242541	−	0.0279907i
$730$		0			0
$731$	46.6932	−	4.45866i	1.72701	−	0.164910i
$732$		0			0
$733$	18.4020	−	9.48689i	0.679694	−	0.350406i	−0.0835625	−	0.996503i	$-0.526630\pi$
$733$	18.4020	−	9.48689i	0.679694	−	0.350406i	0.763256	+	0.646096i	$0.223600\pi$
$734$		0			0
$735$	10.5965	+	43.6792i	0.390856	+	1.61113i
$736$		0			0
$737$	8.43656	−	10.8459i	0.310765	−	0.399514i
$738$		0			0
$739$	−8.74079	−	36.0300i	−0.321535	−	1.32539i	−0.871581	−	0.490252i	$-0.836905\pi$
$739$	−8.74079	−	36.0300i	−0.321535	−	1.32539i	0.550046	−	0.835134i	$-0.314610\pi$
$740$		0			0
$741$	−1.04754	+	0.540043i	−0.0384823	+	0.0198390i
$742$		0			0
$743$	30.6220	−	2.92404i	1.12341	−	0.107273i	0.483227	−	0.875495i	$-0.339464\pi$
$743$	30.6220	−	2.92404i	1.12341	−	0.107273i	0.640183	+	0.768222i	$0.278858\pi$
$744$		0			0
$745$	23.7358	+	27.3926i	0.869612	+	1.00359i
$746$		0			0
$747$	3.32305	−	2.61327i	0.121584	−	0.0956146i
$748$		0			0
$749$	1.46382	+	4.22942i	0.0534867	+	0.154540i
$750$		0			0
$751$	19.0145	+	12.2199i	0.693848	+	0.445909i	0.839452	−	0.543434i	$-0.182876\pi$
$751$	19.0145	+	12.2199i	0.693848	+	0.445909i	−0.145604	+	0.989343i	$0.546513\pi$
$752$		0			0
$753$	7.05911	−	9.91314i	0.257248	−	0.361255i
$754$		0			0
$755$	−1.47555	+	30.9757i	−0.0537009	+	1.12732i
$756$		0			0
$757$	1.47129	+	1.15704i	0.0534751	+	0.0420533i	0.644539	−	0.764572i	$-0.277049\pi$
$757$	1.47129	+	1.15704i	0.0534751	+	0.0420533i	−0.591064	+	0.806625i	$0.701292\pi$
$758$		0			0
$759$	−1.52087	−	10.5779i	−0.0552041	−	0.383953i
$760$		0			0
$761$	−27.1944	+	17.4768i	−0.985798	+	0.633534i	−0.931021	−	0.364965i	$-0.881081\pi$
$761$	−27.1944	+	17.4768i	−0.985798	+	0.633534i	−0.0547766	+	0.998499i	$0.517445\pi$
$762$		0			0
$763$	3.78968	+	79.5552i	0.137196	+	2.88009i
$764$		0			0
$765$	−4.25872	+	12.3048i	−0.153974	+	0.444879i
$766$		0			0
$767$	10.0126	+	17.3423i	0.361534	+	0.626196i
$768$		0			0
$769$	−44.7218	−	17.9039i	−1.61271	−	0.645632i	−0.622173	−	0.782880i	$-0.713750\pi$
$769$	−44.7218	−	17.9039i	−1.61271	−	0.645632i	−0.990537	+	0.137248i	$0.956174\pi$
$770$		0			0
$771$	3.31989	−	13.6848i	0.119563	−	0.492846i
$772$		0			0
$773$	40.3369	−	7.77430i	1.45082	−	0.279622i	0.597859	−	0.801601i	$-0.296018\pi$
$773$	40.3369	−	7.77430i	1.45082	−	0.279622i	0.852958	+	0.521979i	$0.174806\pi$
$774$		0			0
$775$	−5.94304	+	10.2936i	−0.213480	+	0.369759i
$776$		0			0
$777$	−17.9241	+	39.2483i	−0.643023	+	1.40802i
$778$		0			0
$779$	−2.04834	+	2.36391i	−0.0733893	+	0.0846957i
$780$		0			0
$781$	−5.19773	+	2.08086i	−0.185989	+	0.0744589i
$782$		0			0
$783$	−3.43495	−	4.82371i	−0.122755	−	0.172385i
$784$		0			0
$785$	41.1740	+	39.2593i	1.46956	+	1.40122i
$786$		0			0
$787$	9.20617	+	4.74611i	0.328164	+	0.169181i	0.614433	−	0.788969i	$-0.289385\pi$
$787$	9.20617	+	4.74611i	0.328164	+	0.169181i	−0.286269	+	0.958149i	$0.592415\pi$
$788$		0			0
$789$	−4.18403	+	1.22854i	−0.148955	+	0.0437373i
$790$		0			0
$791$	−20.0003	−	3.85475i	−0.711130	−	0.137059i
$792$		0			0
$793$	32.6942	+	3.12192i	1.16101	+	0.110863i
$794$		0			0
$795$	−15.1591	−	4.45112i	−0.537639	−	0.157865i
$796$		0			0
$797$	−22.1042	+	21.0763i	−0.782971	+	0.746562i	−0.971891	−	0.235431i	$-0.924350\pi$
$797$	−22.1042	+	21.0763i	−0.782971	+	0.746562i	0.188920	+	0.981993i	$0.439501\pi$
$798$		0			0
$799$	−10.4221	−	22.8213i	−0.368708	−	0.807359i
$800$		0			0
$801$	2.41415	−	16.7908i	0.0852999	−	0.593274i
$802$		0			0
$803$	−20.4567			−0.721902
$804$		0			0
$805$	90.6145			3.19374
$806$		0			0
$807$	1.56160	−	10.8612i	0.0549710	−	0.382331i
$808$		0			0
$809$	2.68853	+	5.88706i	0.0945237	+	0.206978i	0.950988	−	0.309229i	$-0.100071\pi$
$809$	2.68853	+	5.88706i	0.0945237	+	0.206978i	−0.856464	+	0.516207i	$0.827344\pi$
$810$		0			0
$811$	−29.5804	+	28.2048i	−1.03871	+	0.990406i	−0.999961	−	0.00884326i	$-0.997185\pi$
$811$	−29.5804	+	28.2048i	−1.03871	+	0.990406i	−0.0387468	+	0.999249i	$0.512337\pi$
$812$		0			0
$813$	−16.8487	−	4.94722i	−0.590910	−	0.173507i
$814$		0			0
$815$	22.3891	+	2.13790i	0.784255	+	0.0748872i
$816$		0			0
$817$	−3.32199	−	0.640261i	−0.116222	−	0.0223999i
$818$		0			0
$819$	17.1390	−	5.03246i	0.598885	−	0.175848i
$820$		0			0
$821$	−36.6891	−	18.9145i	−1.28046	−	0.660122i	−0.322375	−	0.946612i	$-0.604481\pi$
$821$	−36.6891	−	18.9145i	−1.28046	−	0.660122i	−0.958083	+	0.286490i	$0.907511\pi$
$822$		0			0
$823$	−0.524307	−	0.499926i	−0.0182762	−	0.0174263i	0.680886	−	0.732390i	$-0.261595\pi$
$823$	−0.524307	−	0.499926i	−0.0182762	−	0.0174263i	−0.699162	+	0.714963i	$0.746443\pi$
$824$		0			0
$825$	−4.21706	−	5.92203i	−0.146819	−	0.206179i
$826$		0			0
$827$	20.5827	−	8.24006i	0.715730	−	0.286535i	0.0149256	−	0.999889i	$-0.495249\pi$
$827$	20.5827	−	8.24006i	0.715730	−	0.286535i	0.700804	+	0.713354i	$0.252825\pi$
$828$		0			0
$829$	4.53356	−	5.23201i	0.157457	−	0.181715i	−0.671540	−	0.740969i	$-0.734367\pi$
$829$	4.53356	−	5.23201i	0.157457	−	0.181715i	0.828997	+	0.559254i	$0.188912\pi$
$830$		0			0
$831$	3.72553	−	8.15776i	0.129237	−	0.282990i
$832$		0			0
$833$	−31.3607	+	54.3183i	−1.08658	+	1.88202i
$834$		0			0
$835$	74.3713	−	14.3339i	2.57373	−	0.496045i
$836$		0			0
$837$	0.647056	−	2.66720i	0.0223655	−	0.0921920i
$838$		0			0
$839$	43.1967	+	17.2934i	1.49132	+	0.597033i	0.967065	−	0.254530i	$-0.0819209\pi$
$839$	43.1967	+	17.2934i	1.49132	+	0.597033i	0.524252	+	0.851563i	$0.324345\pi$
$840$		0			0
$841$	−3.03356	−	5.25427i	−0.104605	−	0.181182i
$842$		0			0
$843$	−2.11138	+	6.10043i	−0.0727198	+	0.210110i
$844$		0			0
$845$	0.246238	+	5.16917i	0.00847085	+	0.177825i
$846$		0			0
$847$	32.0741	−	20.6128i	1.10208	−	0.708264i
$848$		0			0
$849$	1.87960	+	13.0729i	0.0645077	+	0.448661i
$850$		0			0
$851$	46.3345	+	36.4378i	1.58832	+	1.24907i
$852$		0			0
$853$	−2.06202	+	43.2870i	−0.0706021	+	1.48212i	0.634450	+	0.772964i	$0.281227\pi$
$853$	−2.06202	+	43.2870i	−0.0706021	+	1.48212i	−0.705052	+	0.709156i	$0.749076\pi$
$854$		0			0
$855$	0.544760	−	0.765009i	0.0186304	−	0.0261627i
$856$		0			0
$857$	−36.7090	−	23.5914i	−1.25395	−	0.805867i	−0.266509	−	0.963832i	$-0.585870\pi$
$857$	−36.7090	−	23.5914i	−1.25395	−	0.805867i	−0.987445	+	0.157965i	$0.949507\pi$
$858$		0			0
$859$	−10.3571	−	29.9249i	−0.353380	−	1.02103i	−0.971928	−	0.235278i	$-0.924400\pi$
$859$	−10.3571	−	29.9249i	−0.353380	−	1.02103i	0.618548	−	0.785747i	$-0.287721\pi$
$860$		0			0
$861$	37.2648	−	29.3054i	1.26998	−	0.998725i
$862$		0			0
$863$	−7.71682	−	8.90569i	−0.262684	−	0.303153i	0.609051	−	0.793131i	$-0.291550\pi$
$863$	−7.71682	−	8.90569i	−0.262684	−	0.303153i	−0.871735	+	0.489978i	$0.837005\pi$
$864$		0			0
$865$	−64.6183	+	6.17030i	−2.19709	+	0.209797i
$866$		0			0
$867$	−1.04028	+	0.536303i	−0.0353299	+	0.0182138i
$868$		0			0
$869$	0.377097	+	1.55442i	0.0127922	+	0.0527300i
$870$		0			0
$871$	21.5317	−	22.8231i	0.729574	−	0.773331i
$872$		0			0
$873$	−1.84087	−	7.58817i	−0.0623040	−	0.256821i
$874$		0			0
$875$	−8.46699	+	4.36504i	−0.286236	+	0.147565i
$876$		0			0
$877$	0.120995	−	0.0115536i	0.00408572	−	0.000390139i	−0.0930130	−	0.995665i	$-0.529650\pi$
$877$	0.120995	−	0.0115536i	0.00408572	−	0.000390139i	0.0970987	+	0.995275i	$0.469044\pi$
$878$		0			0
$879$	−11.3534	−	13.1025i	−0.382941	−	0.441938i
$880$		0			0
$881$	20.7539	−	16.3210i	0.699215	−	0.549869i	−0.204045	−	0.978961i	$-0.565409\pi$
$881$	20.7539	−	16.3210i	0.699215	−	0.549869i	0.903261	+	0.429093i	$0.141167\pi$
$882$		0			0
$883$	16.8318	+	48.6323i	0.566436	+	1.63661i	0.755875	+	0.654716i	$0.227212\pi$
$883$	16.8318	+	48.6323i	0.566436	+	1.63661i	−0.189440	+	0.981892i	$0.560667\pi$
$884$		0			0
$885$	−13.4243	−	8.62725i	−0.451251	−	0.290002i
$886$		0			0
$887$	26.0879	−	36.6353i	0.875945	−	1.23009i	−0.0961171	−	0.995370i	$-0.530642\pi$
$887$	26.0879	−	36.6353i	0.875945	−	1.23009i	0.972062	−	0.234723i	$-0.0754183\pi$
$888$		0			0
$889$	0.508504	−	10.6748i	0.0170547	−	0.358022i
$890$		0			0
$891$	1.31955	+	1.03771i	0.0442066	+	0.0347645i
$892$		0			0
$893$	0.257524	+	1.79112i	0.00861772	+	0.0599376i
$894$		0			0
$895$	−55.2049	+	35.4781i	−1.84530	+	1.18590i
$896$		0			0
$897$	−1.16113	−	24.3752i	−0.0387691	−	0.813865i
$898$		0			0
$899$	5.31572	−	15.3588i	0.177289	−	0.512243i
$900$		0			0
$901$	−11.0237	−	19.0935i	−0.367251	−	0.636098i
$902$		0			0
$903$	47.6029	+	19.0573i	1.58413	+	0.634188i
$904$		0			0
$905$	−18.5758	+	76.5705i	−0.617481	+	2.54529i
$906$		0			0
$907$	42.4664	−	8.18473i	1.41007	−	0.271769i	0.573312	−	0.819337i	$-0.305658\pi$
$907$	42.4664	−	8.18473i	1.41007	−	0.271769i	0.836761	+	0.547568i	$0.184446\pi$
$908$		0			0
$909$	5.66408	−	9.81048i	0.187866	−	0.325393i
$910$		0			0
$911$	9.09206	−	19.9088i	0.301233	−	0.659609i	−0.697121	−	0.716953i	$-0.745536\pi$
$911$	9.09206	−	19.9088i	0.301233	−	0.659609i	0.998354	+	0.0573444i	$0.0182633\pi$
$912$		0			0
$913$	−4.64737	+	5.36336i	−0.153806	+	0.177501i
$914$		0			0
$915$	−24.2968	+	9.72696i	−0.803226	+	0.321563i
$916$		0			0
$917$	8.69692	+	12.2131i	0.287198	+	0.403313i
$918$		0			0
$919$	13.3344	+	12.7143i	0.439861	+	0.419406i	0.877375	−	0.479805i	$-0.159293\pi$
$919$	13.3344	+	12.7143i	0.439861	+	0.419406i	−0.437514	+	0.899211i	$0.644141\pi$
$920$		0			0
$921$	1.08745	+	0.560619i	0.0358326	+	0.0184730i
$922$		0			0
$923$	−12.2669	+	3.60187i	−0.403769	+	0.118557i
$924$		0			0
$925$	39.3757	+	7.58905i	1.29467	+	0.249526i
$926$		0			0
$927$	7.68357	+	0.733692i	0.252362	+	0.0240976i
$928$		0			0
$929$	−38.7758	−	11.3856i	−1.27219	−	0.373549i	−0.425173	−	0.905112i	$-0.639787\pi$
$929$	−38.7758	−	11.3856i	−1.27219	−	0.373549i	−0.847019	+	0.531563i	$0.821605\pi$
$930$		0			0
$931$	3.27408	−	3.12182i	0.107303	−	0.102314i
$932$		0			0
$933$	7.32664	+	16.0431i	0.239864	+	0.525228i
$934$		0			0
$935$	3.11075	−	21.6357i	0.101732	−	0.707565i
$936$		0			0
$937$	−38.4196			−1.25511			−0.627556	−	0.778571i	$-0.715945\pi$
$937$	−38.4196			−1.25511			−0.627556	+	0.778571i	$0.715945\pi$
$938$		0			0
$939$	14.6236			0.477223
$940$		0			0
$941$	7.06561	−	49.1424i	0.230332	−	1.60200i	−0.466339	−	0.884606i	$-0.654427\pi$
$941$	7.06561	−	49.1424i	0.230332	−	1.60200i	0.696672	−	0.717390i	$-0.254664\pi$
$942$		0			0
$943$	−26.9046	−	58.9129i	−0.876134	−	1.91847i
$944$		0			0
$945$	−10.3017	+	9.82264i	−0.335114	+	0.319531i
$946$		0			0
$947$	37.5065	+	11.0129i	1.21880	+	0.357871i	0.827012	−	0.562185i	$-0.190039\pi$
$947$	37.5065	+	11.0129i	1.21880	+	0.357871i	0.391787	+	0.920056i	$0.371857\pi$
$948$		0			0
$949$	−46.5011	−	4.44032i	−1.50949	−	0.144139i
$950$		0			0
$951$	−3.79020	−	0.730501i	−0.122906	−	0.0236881i
$952$		0			0
$953$	31.5351	−	9.25954i	1.02152	−	0.299946i	0.272263	−	0.962223i	$-0.412228\pi$
$953$	31.5351	−	9.25954i	1.02152	−	0.299946i	0.749259	+	0.662277i	$0.230410\pi$
$954$		0			0
$955$	−17.0463	−	8.78798i	−0.551606	−	0.284372i
$956$		0			0
$957$	7.19454	+	6.85998i	0.232567	+	0.221752i
$958$		0			0
$959$	35.5061	+	49.8613i	1.14655	+	1.61011i
$960$		0			0
$961$	−21.7863	+	8.72193i	−0.702785	+	0.281353i
$962$		0			0
$963$	−0.628966	+	0.725865i	−0.0202681	+	0.0233907i
$964$		0			0
$965$	−1.43085	+	3.13312i	−0.0460606	+	0.100859i
$966$		0			0
$967$	18.8547	−	32.6574i	0.606327	−	1.05019i	−0.385513	−	0.922702i	$-0.625975\pi$
$967$	18.8547	−	32.6574i	0.606327	−	1.05019i	0.991840	−	0.127487i	$-0.0406912\pi$
$968$		0			0
$969$	1.28688	−	0.248026i	0.0413405	−	0.00796774i
$970$		0			0
$971$	−7.54384	+	31.0961i	−0.242093	+	0.997922i	0.712893	+	0.701273i	$0.247384\pi$
$971$	−7.54384	+	31.0961i	−0.242093	+	0.997922i	−0.954986	+	0.296649i	$0.904131\pi$
$972$		0			0
$973$	−65.4898	−	26.2182i	−2.09951	−	0.840516i
$974$		0			0
$975$	−8.30055	−	14.3770i	−0.265830	−	0.460432i
$976$		0			0
$977$	14.5378	−	42.0041i	0.465104	−	1.34383i	−0.431945	−	0.901900i	$-0.642172\pi$
$977$	14.5378	−	42.0041i	0.465104	−	1.34383i	0.897049	−	0.441931i	$-0.145706\pi$
$978$		0			0
$979$	1.35497	+	28.4444i	0.0433052	+	0.909087i
$980$		0			0
$981$	−14.3786	+	9.24057i	−0.459074	+	0.295029i
$982$		0			0
$983$	−4.06245	−	28.2550i	−0.129572	−	0.901194i	−0.946097	−	0.323883i	$-0.895011\pi$
$983$	−4.06245	−	28.2550i	−0.129572	−	0.901194i	0.816525	−	0.577310i	$-0.195898\pi$
$984$		0			0
$985$	−12.1249	−	9.53516i	−0.386333	−	0.303815i
$986$		0			0
$987$	1.30498	−	27.3950i	0.0415381	−	0.871991i
$988$		0			0
$989$	40.6332	−	57.0614i	1.29206	−	1.81445i
$990$		0			0
$991$	−15.9590	−	10.2562i	−0.506954	−	0.325800i	0.262038	−	0.965057i	$-0.415605\pi$
$991$	−15.9590	−	10.2562i	−0.506954	−	0.325800i	−0.768992	+	0.639258i	$0.779242\pi$
$992$		0			0
$993$	−2.36543	−	6.83446i	−0.0750646	−	0.216885i
$994$		0			0
$995$	18.1938	−	14.3077i	0.576782	−	0.453586i
$996$		0			0
$997$	−38.1530	−	44.0310i	−1.20832	−	1.39447i	−0.895737	−	0.444583i	$-0.853352\pi$
$997$	−38.1530	−	44.0310i	−1.20832	−	1.39447i	−0.312581	−	0.949891i	$-0.601194\pi$
$998$		0			0
$999$	−9.21750	+	0.880164i	−0.291629	+	0.0278472i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.y.a.157.5	✓	100
67.35	even	33	inner	804.2.y.a.169.5	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.y.a.157.5	✓	100	1.1	even	1	trivial
804.2.y.a.169.5	yes	100	67.35	even	33	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.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.142315 + 0.989821i) q^{3} +(1.26894 + 2.77859i) q^{5} +(-3.37248 + 3.21566i) q^{7} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})\)	\(q+(-0.142315 + 0.989821i) q^{3} +(1.26894 + 2.77859i) q^{5} +(-3.37248 + 3.21566i) q^{7} +(-0.959493 - 0.281733i) q^{9} +(1.67110 + 0.159571i) q^{11} +(3.76402 + 0.725456i) q^{13} +(-2.93090 + 0.860589i) q^{15} +(-3.78882 - 1.95327i) q^{17} +(0.222513 + 0.212166i) q^{19} +(-2.70297 - 3.79579i) q^{21} +(-5.91001 + 2.36601i) q^{23} +(-2.83605 + 3.27297i) q^{25} +(0.415415 - 0.909632i) q^{27} +(2.96087 - 5.12839i) q^{29} +(2.69497 - 0.519413i) q^{31} +(-0.395770 + 1.63138i) q^{33} +(-13.2145 - 5.29027i) q^{35} +(-4.62971 - 8.01890i) q^{37} +(-1.25375 + 3.62247i) q^{39} +(0.484081 + 10.1621i) q^{41} +(-9.25698 + 5.94910i) q^{43} +(-0.434719 - 3.02354i) q^{45} +(4.62641 + 3.63825i) q^{47} +(0.700125 - 14.6974i) q^{49} +(2.47259 - 3.47227i) q^{51} +(4.35112 + 2.79629i) q^{53} +(1.67715 + 4.84580i) q^{55} +(-0.241673 + 0.190054i) q^{57} +(3.42100 + 3.94805i) q^{59} +(8.52901 - 0.814422i) q^{61} +(4.14183 - 2.13526i) q^{63} +(2.76057 + 11.3792i) q^{65} +(4.38873 - 6.90934i) q^{67} +(-1.50085 - 6.18657i) q^{69} +(-2.96443 + 1.52827i) q^{71} +(-12.1308 + 1.15835i) q^{73} +(-2.83605 - 3.27297i) q^{75} +(-6.14889 + 4.83554i) q^{77} +(0.311637 + 0.900416i) q^{79} +(0.841254 + 0.540641i) q^{81} +(-2.45220 + 3.44363i) q^{83} +(0.619559 - 13.0061i) q^{85} +(4.65481 + 3.66058i) q^{87} +(2.41415 + 16.7908i) q^{89} +(-15.0269 + 9.65722i) q^{91} +(0.130592 + 2.74146i) q^{93} +(-0.307166 + 0.887497i) q^{95} +(3.90414 + 6.76216i) q^{97} +(-1.55846 - 0.623911i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 10 q^{3} + 2 q^{5} - 3 q^{7} - 10 q^{9}+O(q^{10}) \) 100 * q - 10 * q^3 + 2 * q^5 - 3 * q^7 - 10 * q^9	\( 100 q - 10 q^{3} + 2 q^{5} - 3 q^{7} - 10 q^{9} - 13 q^{11} - 3 q^{13} - 9 q^{15} - 44 q^{17} - 16 q^{19} - 3 q^{21} - 16 q^{23} + 28 q^{25} - 10 q^{27} - 7 q^{29} + 20 q^{31} - 2 q^{33} - 19 q^{35} - 22 q^{37} - 3 q^{39} - 14 q^{41} - 27 q^{43} + 2 q^{45} + 4 q^{47} - 92 q^{49} + 22 q^{51} + 8 q^{53} - 13 q^{55} + 17 q^{57} + 22 q^{59} + 17 q^{61} - 3 q^{63} + 56 q^{65} - 14 q^{67} + 17 q^{69} - q^{71} + 26 q^{73} + 28 q^{75} + 112 q^{77} + 69 q^{79} - 10 q^{81} + 15 q^{83} + 69 q^{85} + 4 q^{87} + 73 q^{89} - 40 q^{91} - 13 q^{93} + 59 q^{95} + 29 q^{97} - 2 q^{99}+O(q^{100}) \) 100 * q - 10 * q^3 + 2 * q^5 - 3 * q^7 - 10 * q^9 - 13 * q^11 - 3 * q^13 - 9 * q^15 - 44 * q^17 - 16 * q^19 - 3 * q^21 - 16 * q^23 + 28 * q^25 - 10 * q^27 - 7 * q^29 + 20 * q^31 - 2 * q^33 - 19 * q^35 - 22 * q^37 - 3 * q^39 - 14 * q^41 - 27 * q^43 + 2 * q^45 + 4 * q^47 - 92 * q^49 + 22 * q^51 + 8 * q^53 - 13 * q^55 + 17 * q^57 + 22 * q^59 + 17 * q^61 - 3 * q^63 + 56 * q^65 - 14 * q^67 + 17 * q^69 - q^71 + 26 * q^73 + 28 * q^75 + 112 * q^77 + 69 * q^79 - 10 * q^81 + 15 * q^83 + 69 * q^85 + 4 * q^87 + 73 * q^89 - 40 * q^91 - 13 * q^93 + 59 * q^95 + 29 * q^97 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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