LMFDB - Embedded newform 297.2.g.b.98.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [297,2,Mod(98,297)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(297, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("297.98");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.g (of order $6$, degree $2$, not 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:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 15x^{14} + 150x^{12} + 837x^{10} + 3372x^{8} + 8010x^{6} + 13761x^{4} + 13392x^{2} + 8649 $ x^16 + 15x^14 + 150x^12 + 837x^10 + 3372x^8 + 8010x^6 + 13761x^4 + 13392*x^2 + 8649
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			98.5
Root			$0.618600 + 1.07145i$ of defining polynomial
Character	$\chi$	$=$	297.98
Dual form			297.2.g.b.197.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.618600 + 1.07145i) q^{2} +(0.234668 - 0.406456i) q^{4} +(-1.78348 - 1.02969i) q^{5} +(3.59283 - 2.07432i) q^{7} +3.05506 q^{8} +O(q^{10})$	\(q+(0.618600 + 1.07145i) q^{2} +(0.234668 - 0.406456i) q^{4} +(-1.78348 - 1.02969i) q^{5} +(3.59283 - 2.07432i) q^{7} +3.05506 q^{8} -2.54787i q^{10} +(-2.85069 - 1.69515i) q^{11} +(-0.747261 - 0.431431i) q^{13} +(4.44505 + 2.56635i) q^{14} +(1.42053 + 2.46043i) q^{16} +4.25136 q^{17} +5.55362i q^{19} +(-0.837047 + 0.483270i) q^{20} +(0.0528262 - 4.10299i) q^{22} +(2.25042 + 1.29928i) q^{23} +(-0.379477 - 0.657274i) q^{25} -1.06753i q^{26} -1.94710i q^{28} +(1.44670 + 2.50575i) q^{29} +(-2.40400 + 4.16385i) q^{31} +(1.29759 - 2.24748i) q^{32} +(2.62989 + 4.55511i) q^{34} -8.54363 q^{35} -11.7136 q^{37} +(-5.95041 + 3.43547i) q^{38} +(-5.44863 - 3.14577i) q^{40} +(-2.82512 + 4.89325i) q^{41} +(1.96401 - 1.13392i) q^{43} +(-1.35797 + 0.760885i) q^{44} +3.21494i q^{46} +(1.44104 - 0.831985i) q^{47} +(5.10561 - 8.84317i) q^{49} +(0.469489 - 0.813180i) q^{50} +(-0.350716 + 0.202486i) q^{52} -2.28109i q^{53} +(3.33866 + 5.95859i) q^{55} +(10.9763 - 6.33718i) q^{56} +(-1.78985 + 3.10012i) q^{58} +(-5.79946 - 3.34832i) q^{59} +(5.78878 - 3.34215i) q^{61} -5.94845 q^{62} +8.89286 q^{64} +(0.888481 + 1.53889i) q^{65} +(-1.08746 + 1.88354i) q^{67} +(0.997657 - 1.72799i) q^{68} +(-5.28509 - 9.15404i) q^{70} -1.36195i q^{71} +11.1781i q^{73} +(-7.24604 - 12.5505i) q^{74} +(2.25730 + 1.30325i) q^{76} +(-13.7583 - 0.177139i) q^{77} +(-9.22261 + 5.32468i) q^{79} -5.85081i q^{80} -6.99047 q^{82} +(3.10289 + 5.37436i) q^{83} +(-7.58220 - 4.37759i) q^{85} +(2.42988 + 1.40289i) q^{86} +(-8.70905 - 5.17880i) q^{88} +7.44670i q^{89} -3.57971 q^{91} +(1.05620 - 0.609797i) q^{92} +(1.78286 + 1.02933i) q^{94} +(5.71851 - 9.90475i) q^{95} +(5.27494 + 9.13646i) q^{97} +12.6333 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 14 q^{4}+O(q^{10}) $ 16 * q - 14 * q^4	$ 16 q - 14 q^{4} + 12 q^{11} + 6 q^{14} - 2 q^{16} - 36 q^{20} + 6 q^{22} - 12 q^{23} - 12 q^{25} - 4 q^{31} - 28 q^{37} - 66 q^{38} + 30 q^{47} + 10 q^{49} + 20 q^{55} + 120 q^{56} - 6 q^{58} + 36 q^{59} + 40 q^{64} + 8 q^{67} - 72 q^{77} + 12 q^{82} + 72 q^{86} - 6 q^{88} - 12 q^{91} - 18 q^{92} - 4 q^{97}+O(q^{100}) $ 16 * q - 14 * q^4 + 12 * q^11 + 6 * q^14 - 2 * q^16 - 36 * q^20 + 6 * q^22 - 12 * q^23 - 12 * q^25 - 4 * q^31 - 28 * q^37 - 66 * q^38 + 30 * q^47 + 10 * q^49 + 20 * q^55 + 120 * q^56 - 6 * q^58 + 36 * q^59 + 40 * q^64 + 8 * q^67 - 72 * q^77 + 12 * q^82 + 72 * q^86 - 6 * q^88 - 12 * q^91 - 18 * q^92 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	0.618600	+	1.07145i	0.437416	+	0.757627i	0.997489	−	0.0708158i	$-0.0225603\pi$
$2$	0.618600	+	1.07145i	0.437416	+	0.757627i	−0.560073	+	0.828443i	$0.689227\pi$
$3$		0			0
$3$		0			0
$4$	0.234668	−	0.406456i	0.117334	−	0.203228i
$5$	−1.78348	−	1.02969i	−0.797594	−	0.460491i	0.0450349	−	0.998985i	$-0.485660\pi$
$5$	−1.78348	−	1.02969i	−0.797594	−	0.460491i	−0.842629	+	0.538494i	$0.818993\pi$
$6$		0			0
$7$	3.59283	−	2.07432i	1.35796	−	0.784019i	0.368612	−	0.929583i	$-0.379833\pi$
$7$	3.59283	−	2.07432i	1.35796	−	0.784019i	0.989349	+	0.145564i	$0.0464996\pi$
$8$	3.05506			1.08013
$9$		0			0
$10$		−	2.54787i		−	0.805706i
$11$	−2.85069	−	1.69515i	−0.859517	−	0.511108i
$11$	−2.85069	−	1.69515i	−0.859517	−	0.511108i
$12$		0			0
$13$	−0.747261	−	0.431431i	−0.207253	−	0.119658i	0.392781	−	0.919632i	$-0.371513\pi$
$13$	−0.747261	−	0.431431i	−0.207253	−	0.119658i	−0.600034	+	0.799974i	$0.704846\pi$
$14$	4.44505	+	2.56635i	1.18799	+	0.685886i
$15$		0			0
$16$	1.42053	+	2.46043i	0.355132	+	0.615106i
$17$	4.25136			1.03111			0.515553	−	0.856857i	$-0.327586\pi$
$17$	4.25136			1.03111			0.515553	+	0.856857i	$0.327586\pi$
$18$		0			0
$19$			5.55362i			1.27409i	0.770827	+	0.637044i	$0.219843\pi$
$19$			5.55362i			1.27409i	−0.770827	+	0.637044i	$0.780157\pi$
$20$	−0.837047	+	0.483270i	−0.187169	+	0.108062i
$21$		0			0
$22$	0.0528262	−	4.10299i	0.0112626	−	0.874760i
$23$	2.25042	+	1.29928i	0.469244	+	0.270918i	0.715923	−	0.698179i	$-0.246006\pi$
$23$	2.25042	+	1.29928i	0.469244	+	0.270918i	−0.246679	+	0.969097i	$0.579339\pi$
$24$		0			0
$25$	−0.379477	−	0.657274i	−0.0758955	−	0.131455i
$26$		−	1.06753i		−	0.209361i
$27$		0			0
$28$		−	1.94710i		−	0.367968i
$29$	1.44670	+	2.50575i	0.268645	+	0.465306i	0.968512	−	0.248966i	$-0.0800909\pi$
$29$	1.44670	+	2.50575i	0.268645	+	0.465306i	−0.699867	+	0.714273i	$0.746758\pi$
$30$		0			0
$31$	−2.40400	+	4.16385i	−0.431771	+	0.747849i	−0.997026	−	0.0770672i	$-0.975444\pi$
$31$	−2.40400	+	4.16385i	−0.431771	+	0.747849i	0.565255	+	0.824916i	$0.308778\pi$
$32$	1.29759	−	2.24748i	0.229383	−	0.397303i
$33$		0			0
$34$	2.62989	+	4.55511i	0.451023	+	0.781195i
$35$	−8.54363			−1.44414
$36$		0			0
$37$	−11.7136			−1.92571			−0.962853	−	0.270028i	$-0.912967\pi$
$37$	−11.7136			−1.92571			−0.962853	+	0.270028i	$0.912967\pi$
$38$	−5.95041	+	3.43547i	−0.965284	+	0.557307i
$39$		0			0
$40$	−5.44863	−	3.14577i	−0.861504	−	0.497389i
$41$	−2.82512	+	4.89325i	−0.441209	+	0.764197i	−0.997779	−	0.0666039i	$-0.978784\pi$
$41$	−2.82512	+	4.89325i	−0.441209	+	0.764197i	0.556570	+	0.830800i	$0.312117\pi$
$42$		0			0
$43$	1.96401	−	1.13392i	0.299509	−	0.172922i	−0.342713	−	0.939440i	$-0.611346\pi$
$43$	1.96401	−	1.13392i	0.299509	−	0.172922i	0.642222	+	0.766518i	$0.278013\pi$
$44$	−1.35797	+	0.760885i	−0.204722	+	0.114708i
$45$		0			0
$46$			3.21494i			0.474017i
$47$	1.44104	−	0.831985i	0.210197	−	0.121358i	−0.391206	−	0.920303i	$-0.627942\pi$
$47$	1.44104	−	0.831985i	0.210197	−	0.121358i	0.601403	+	0.798946i	$0.294609\pi$
$48$		0			0
$49$	5.10561	−	8.84317i	0.729372	−	1.26331i
$50$	0.469489	−	0.813180i	0.0663958	−	0.115001i
$51$		0			0
$52$	−0.350716	+	0.202486i	−0.0486355	+	0.0280797i
$53$		−	2.28109i		−	0.313331i	−0.987652	−	0.156666i	$-0.949925\pi$
$53$		−	2.28109i		−	0.313331i	0.987652	−	0.156666i	$-0.0500745\pi$
$54$		0			0
$55$	3.33866	+	5.95859i	0.450185	+	0.803457i
$56$	10.9763	−	6.33718i	1.46677	−	0.846841i
$57$		0			0
$58$	−1.78985	+	3.10012i	−0.235019	+	0.407065i
$59$	−5.79946	−	3.34832i	−0.755025	−	0.435914i	0.0724816	−	0.997370i	$-0.476908\pi$
$59$	−5.79946	−	3.34832i	−0.755025	−	0.435914i	−0.827507	+	0.561456i	$0.810241\pi$
$60$		0			0
$61$	5.78878	−	3.34215i	0.741177	−	0.427919i	−0.0813198	−	0.996688i	$-0.525914\pi$
$61$	5.78878	−	3.34215i	0.741177	−	0.427919i	0.822497	+	0.568769i	$0.192580\pi$
$62$	−5.94845			−0.755455
$63$		0			0
$64$	8.89286			1.11161
$65$	0.888481	+	1.53889i	0.110202	+	0.190876i
$66$		0			0
$67$	−1.08746	+	1.88354i	−0.132855	+	0.230111i	−0.924776	−	0.380512i	$-0.875748\pi$
$67$	−1.08746	+	1.88354i	−0.132855	+	0.230111i	0.791921	+	0.610623i	$0.209081\pi$
$68$	0.997657	−	1.72799i	0.120984	−	0.209550i
$69$		0			0
$70$	−5.28509	−	9.15404i	−0.631689	−	1.09412i
$71$		−	1.36195i		−	0.161634i	−0.996729	−	0.0808168i	$-0.974247\pi$
$71$		−	1.36195i		−	0.161634i	0.996729	−	0.0808168i	$-0.0257529\pi$
$72$		0			0
$73$			11.1781i			1.30830i	0.756367	+	0.654148i	$0.226973\pi$
$73$			11.1781i			1.30830i	−0.756367	+	0.654148i	$0.773027\pi$
$74$	−7.24604	−	12.5505i	−0.842335	−	1.45897i
$75$		0			0
$76$	2.25730	+	1.30325i	0.258930	+	0.149494i
$77$	−13.7583	−	0.177139i	−1.56791	−	0.0201869i
$78$		0			0
$79$	−9.22261	+	5.32468i	−1.03762	+	0.599073i	−0.919160	−	0.393885i	$-0.871131\pi$
$79$	−9.22261	+	5.32468i	−1.03762	+	0.599073i	−0.118465	+	0.992958i	$0.537797\pi$
$80$		−	5.85081i		−	0.654141i
$81$		0			0
$82$	−6.99047			−0.771968
$83$	3.10289	+	5.37436i	0.340586	+	0.589913i	0.984542	−	0.175150i	$-0.0560411\pi$
$83$	3.10289	+	5.37436i	0.340586	+	0.589913i	−0.643955	+	0.765063i	$0.722708\pi$
$84$		0			0
$85$	−7.58220	−	4.37759i	−0.822405	−	0.474816i
$86$	2.42988	+	1.40289i	0.262020	+	0.151277i
$87$		0			0
$88$	−8.70905	−	5.17880i	−0.928388	−	0.552062i
$89$			7.44670i			0.789349i	0.918821	+	0.394674i	$0.129143\pi$
$89$			7.44670i			0.789349i	−0.918821	+	0.394674i	$0.870857\pi$
$90$		0			0
$91$	−3.57971			−0.375255
$92$	1.05620	−	0.609797i	0.110116	−	0.0635757i
$93$		0			0
$94$	1.78286	+	1.02933i	0.183888	+	0.106168i
$95$	5.71851	−	9.90475i	0.586707	−	1.01621i
$96$		0			0
$97$	5.27494	+	9.13646i	0.535589	+	0.927667i	0.999135	+	0.0415940i	$0.0132436\pi$
$97$	5.27494	+	9.13646i	0.535589	+	0.927667i	−0.463546	+	0.886073i	$0.653423\pi$
$98$	12.6333			1.27616
$99$		0			0
$100$	−0.356204			−0.0356204
$101$	−0.517315	−	0.896016i	−0.0514748	−	0.0891569i	0.839140	−	0.543916i	$-0.183059\pi$
$101$	−0.517315	−	0.896016i	−0.0514748	−	0.0891569i	−0.890615	+	0.454759i	$0.849726\pi$
$102$		0			0
$103$	3.91199	−	6.77576i	0.385460	−	0.667636i	−0.606373	−	0.795180i	$-0.707376\pi$
$103$	3.91199	−	6.77576i	0.385460	−	0.667636i	0.991833	+	0.127544i	$0.0407095\pi$
$104$	−2.28293	−	1.31805i	−0.223860	−	0.129245i
$105$		0			0
$106$	2.44406	−	1.41108i	0.237388	−	0.137056i
$107$	−7.88709			−0.762473			−0.381237	−	0.924477i	$-0.624502\pi$
$107$	−7.88709			−0.762473			−0.381237	+	0.924477i	$0.624502\pi$
$108$		0			0
$109$		−	0.542120i		−	0.0519257i	−0.999663	−	0.0259628i	$-0.991735\pi$
$109$		−	0.542120i		−	0.0519257i	0.999663	−	0.0259628i	$-0.00826515\pi$
$110$	−4.31902	+	7.26319i	−0.411803	+	0.692518i
$111$		0			0
$112$	10.2074	+	5.89326i	0.964510	+	0.556860i
$113$	5.40938	+	3.12311i	0.508872	+	0.293797i	0.732370	−	0.680907i	$-0.238414\pi$
$113$	5.40938	+	3.12311i	0.508872	+	0.293797i	−0.223498	+	0.974704i	$0.571748\pi$
$114$		0			0
$115$	−2.67571	−	4.63446i	−0.249511	−	0.432166i
$116$	1.35797			0.126084
$117$		0			0
$118$		−	8.28508i		−	0.762704i
$119$	15.2744	−	8.81869i	1.40020	−	0.808408i
$120$		0			0
$121$	5.25291	+	9.66472i	0.477538	+	0.878611i
$122$	7.16188	+	4.13491i	0.648406	+	0.374358i
$123$		0			0
$124$	1.12828	+	1.95424i	0.101323	+	0.175496i
$125$			11.8599i			1.06078i
$126$		0			0
$127$		−	17.8159i		−	1.58091i	−0.612520	−	0.790455i	$-0.709844\pi$
$127$		−	17.8159i		−	1.58091i	0.612520	−	0.790455i	$-0.290156\pi$
$128$	2.90595	+	5.03326i	0.256852	+	0.444881i
$129$		0			0
$130$	−1.09923	+	1.90392i	−0.0964088	+	0.166985i
$131$	−4.13059	+	7.15440i	−0.360892	+	0.625083i	−0.988108	−	0.153763i	$-0.950861\pi$
$131$	−4.13059	+	7.15440i	−0.360892	+	0.625083i	0.627216	+	0.778845i	$0.284194\pi$
$132$		0			0
$133$	11.5200	+	19.9532i	0.998910	+	1.73016i
$134$	−2.69082			−0.232452
$135$		0			0
$136$	12.9882			1.11373
$137$	−7.32054	+	4.22652i	−0.625436	+	0.361096i	−0.778982	−	0.627046i	$-0.784264\pi$
$137$	−7.32054	+	4.22652i	−0.625436	+	0.361096i	0.153546	+	0.988141i	$0.450931\pi$
$138$		0			0
$139$	−7.02666	−	4.05684i	−0.595993	−	0.344097i	0.171470	−	0.985189i	$-0.445148\pi$
$139$	−7.02666	−	4.05684i	−0.595993	−	0.344097i	−0.767464	+	0.641092i	$0.778482\pi$
$140$	−2.00491	+	3.47261i	−0.169446	+	0.293489i
$141$		0			0
$142$	1.45926	−	0.842502i	0.122458	−	0.0707012i
$143$	1.39887	+	2.49660i	0.116979	+	0.208776i
$144$		0			0
$145$		−	5.95859i		−	0.494834i
$146$	−11.9767	+	6.91477i	−0.991201	+	0.572270i
$147$		0			0
$148$	−2.74880	+	4.76107i	−0.225950	+	0.391357i
$149$	5.01907	−	8.69329i	0.411179	−	0.712182i	−0.583840	−	0.811868i	$-0.698451\pi$
$149$	5.01907	−	8.69329i	0.411179	−	0.712182i	0.995019	+	0.0996863i	$0.0317839\pi$
$150$		0			0
$151$	9.87222	−	5.69973i	0.803390	−	0.463838i	−0.0412650	−	0.999148i	$-0.513139\pi$
$151$	9.87222	−	5.69973i	0.803390	−	0.463838i	0.844655	+	0.535311i	$0.179805\pi$
$152$			16.9667i			1.37618i
$153$		0			0
$154$	−8.32112	−	14.8509i	−0.670535	−	1.19672i
$155$	8.57494	−	4.95075i	0.688756	−	0.397653i
$156$		0			0
$157$	−1.90538	+	3.30021i	−0.152066	+	0.263386i	−0.931987	−	0.362492i	$-0.881926\pi$
$157$	−1.90538	+	3.30021i	−0.152066	+	0.263386i	0.779921	+	0.625878i	$0.215259\pi$
$158$	−11.4102	−	6.58769i	−0.907748	−	0.524089i
$159$		0			0
$160$	−4.62842	+	2.67222i	−0.365909	+	0.211258i
$161$	10.7805			0.849621
$162$		0			0
$163$	5.80321			0.454542			0.227271	−	0.973832i	$-0.427020\pi$
$163$	5.80321			0.454542			0.227271	+	0.973832i	$0.427020\pi$
$164$	1.32593	+	2.29657i	0.103537	+	0.179332i
$165$		0			0
$166$	−3.83889	+	6.64916i	−0.297956	+	0.516075i
$167$	2.80467	−	4.85783i	0.217032	−	0.375910i	−0.736868	−	0.676037i	$-0.763696\pi$
$167$	2.80467	−	4.85783i	0.217032	−	0.375910i	0.953899	+	0.300127i	$0.0970292\pi$
$168$		0			0
$169$	−6.12773	−	10.6135i	−0.471364	−	0.816427i
$170$		−	10.8319i		−	0.830769i
$171$		0			0
$172$		−	1.06438i		−	0.0811581i
$173$	10.4803	+	18.1523i	0.796800	+	1.38010i	0.921690	+	0.387927i	$0.126809\pi$
$173$	10.4803	+	18.1523i	0.796800	+	1.38010i	−0.124891	+	0.992171i	$0.539858\pi$
$174$		0			0
$175$	−2.72679	−	1.57431i	−0.206126	−	0.119007i
$176$	0.121308	−	9.42193i	0.00914393	−	0.710205i
$177$		0			0
$178$	−7.97875	+	4.60653i	−0.598032	+	0.345274i
$179$		−	13.6285i		−	1.01864i	−0.860577	−	0.509321i	$-0.829897\pi$
$179$		−	13.6285i		−	1.01864i	0.860577	−	0.509321i	$-0.170103\pi$
$180$		0			0
$181$	6.84428			0.508731			0.254366	−	0.967108i	$-0.418133\pi$
$181$	6.84428			0.508731			0.254366	+	0.967108i	$0.418133\pi$
$182$	−2.21441	−	3.83547i	−0.164143	−	0.284304i
$183$		0			0
$184$	6.87516	+	3.96938i	0.506844	+	0.292626i
$185$	20.8909	+	12.0614i	1.53593	+	0.886771i
$186$		0			0
$187$	−12.1193	−	7.20671i	−0.886254	−	0.527007i
$188$		−	0.780960i		−	0.0569573i
$189$		0			0
$190$	14.1499			1.02654
$191$	−20.6958	+	11.9487i	−1.49749	+	0.864577i	−0.999996	−	0.00288872i	$-0.999080\pi$
$191$	−20.6958	+	11.9487i	−1.49749	+	0.864577i	−0.497496	+	0.867466i	$0.665747\pi$
$192$		0			0
$193$	13.1143	+	7.57157i	0.943991	+	0.545013i	0.891209	−	0.453593i	$-0.149858\pi$
$193$	13.1143	+	7.57157i	0.943991	+	0.545013i	0.0527816	+	0.998606i	$0.483191\pi$
$194$	−6.52615	+	11.3036i	−0.468551	+	0.811553i
$195$		0			0
$196$	−2.39624	−	4.15041i	−0.171160	−	0.296458i
$197$	−5.74588			−0.409377			−0.204689	−	0.978827i	$-0.565618\pi$
$197$	−5.74588			−0.409377			−0.204689	+	0.978827i	$0.565618\pi$
$198$		0			0
$199$	4.42831			0.313914			0.156957	−	0.987605i	$-0.449832\pi$
$199$	4.42831			0.313914			0.156957	+	0.987605i	$0.449832\pi$
$200$	−1.15933	−	2.00801i	−0.0819768	−	0.141988i
$201$		0			0
$202$	0.640023	−	1.10855i	0.0450318	−	0.0779974i
$203$	10.3955	+	6.00182i	0.729618	+	0.421245i
$204$		0			0
$205$	10.0771	−	5.81799i	0.703812	−	0.406346i
$206$	9.67983			0.674426
$207$		0			0
$208$		−	2.45144i		−	0.169977i
$209$	9.41424	−	15.8317i	0.651196	−	1.09510i
$210$		0			0
$211$	−10.1616	−	5.86680i	−0.699553	−	0.403887i	0.107628	−	0.994191i	$-0.465674\pi$
$211$	−10.1616	−	5.86680i	−0.699553	−	0.403887i	−0.807181	+	0.590304i	$0.799008\pi$
$212$	−0.927162	−	0.535297i	−0.0636777	−	0.0367644i
$213$		0			0
$214$	−4.87895	−	8.45060i	−0.333518	−	0.577671i
$215$	−4.67035			−0.318516
$216$		0			0
$217$			19.9466i			1.35407i
$218$	0.580853	−	0.335355i	0.0393403	−	0.0227131i
$219$		0			0
$220$	3.20538	+	0.0412695i	0.216107	+	0.00278239i
$221$	−3.17688	−	1.83417i	−0.213700	−	0.123380i
$222$		0			0
$223$	−2.31437	−	4.00861i	−0.154982	−	0.268437i	0.778071	−	0.628177i	$-0.216199\pi$
$223$	−2.31437	−	4.00861i	−0.154982	−	0.268437i	−0.933052	+	0.359740i	$0.882865\pi$
$224$		−	10.7664i		−	0.719362i
$225$		0			0
$226$			7.72783i			0.514047i
$227$	−11.3687	−	19.6912i	−0.754570	−	1.30695i	−0.945588	−	0.325367i	$-0.894512\pi$
$227$	−11.3687	−	19.6912i	−0.754570	−	1.30695i	0.191018	−	0.981587i	$-0.438821\pi$
$228$		0			0
$229$	−1.79384	+	3.10702i	−0.118540	+	0.205318i	−0.919189	−	0.393816i	$-0.871155\pi$
$229$	−1.79384	+	3.10702i	−0.118540	+	0.205318i	0.800649	+	0.599133i	$0.204488\pi$
$230$	3.31039	−	5.73376i	0.218280	−	0.378073i
$231$		0			0
$232$	4.41975	+	7.65523i	0.290171	+	0.502590i
$233$	18.6774			1.22360			0.611799	−	0.791013i	$-0.290446\pi$
$233$	18.6774			1.22360			0.611799	+	0.791013i	$0.290446\pi$
$234$		0			0
$235$	−3.42675			−0.223536
$236$	−2.72189	+	1.57148i	−0.177180	+	0.102295i
$237$		0			0
$238$	18.8975	+	10.9105i	1.22494	+	0.707222i
$239$	10.5212	−	18.2232i	0.680557	−	1.17876i	−0.294254	−	0.955727i	$-0.595071\pi$
$239$	10.5212	−	18.2232i	0.680557	−	1.17876i	0.974811	−	0.223033i	$-0.0715956\pi$
$240$		0			0
$241$	0.881555	−	0.508966i	0.0567860	−	0.0327854i	−0.471338	−	0.881953i	$-0.656229\pi$
$241$	0.881555	−	0.508966i	0.0567860	−	0.0327854i	0.528124	+	0.849167i	$0.322896\pi$
$242$	−7.10579	+	11.6068i	−0.456777	+	0.746115i
$243$		0			0
$244$		−	3.13718i		−	0.200837i
$245$	−18.2114	+	10.5144i	−1.16349	+	0.671739i
$246$		0			0
$247$	2.39601	−	4.15001i	0.152454	−	0.264059i
$248$	−7.34436	+	12.7208i	−0.466368	+	0.807772i
$249$		0			0
$250$	−12.7072	+	7.33652i	−0.803676	+	0.464002i
$251$		−	27.8935i		−	1.76062i	−0.474396	−	0.880312i	$-0.657333\pi$
$251$		−	27.8935i		−	1.76062i	0.474396	−	0.880312i	$-0.342667\pi$
$252$		0			0
$253$	−4.21277	−	7.51865i	−0.264855	−	0.472693i
$254$	19.0888	−	11.0209i	1.19774	−	0.691516i
$255$		0			0
$256$	5.29761	−	9.17573i	0.331101	−	0.573483i
$257$	−23.3280	−	13.4684i	−1.45516	−	0.840137i	−0.456393	−	0.889778i	$-0.650859\pi$
$257$	−23.3280	−	13.4684i	−1.45516	−	0.840137i	−0.998767	+	0.0496416i	$0.984192\pi$
$258$		0			0
$259$	−42.0850	+	24.2978i	−2.61503	+	1.50979i
$260$	0.833990			0.0517219
$261$		0			0
$262$	−10.2207			−0.631440
$263$	−9.05134	−	15.6774i	−0.558130	−	0.966709i	−0.997653	−	0.0684777i	$-0.978186\pi$
$263$	−9.05134	−	15.6774i	−0.558130	−	0.966709i	0.439523	−	0.898231i	$-0.355148\pi$
$264$		0			0
$265$	−2.34881	+	4.06826i	−0.144286	+	0.249911i
$266$	−14.2525	+	24.6861i	−0.873879	+	1.51360i
$267$		0			0
$268$	0.510385	+	0.884013i	0.0311767	+	0.0539997i
$269$		−	12.2263i		−	0.745451i	−0.927942	−	0.372726i	$-0.878423\pi$
$269$		−	12.2263i		−	0.745451i	0.927942	−	0.372726i	$-0.121577\pi$
$270$		0			0
$271$		−	14.9816i		−	0.910067i	−0.890474	−	0.455033i	$-0.849627\pi$
$271$		−	14.9816i		−	0.910067i	0.890474	−	0.455033i	$-0.150373\pi$
$272$	6.03918	+	10.4602i	0.366179	+	0.634240i
$273$		0			0
$274$	−9.05698	−	5.22905i	−0.547152	−	0.315898i
$275$	−0.0324060	+	2.51696i	−0.00195416	+	0.151778i
$276$		0			0
$277$	25.7169	−	14.8477i	1.54518	−	0.892110i	0.546682	−	0.837341i	$-0.315891\pi$
$277$	25.7169	−	14.8477i	1.54518	−	0.892110i	0.998499	−	0.0547699i	$-0.0174425\pi$
$278$		−	10.0383i		−	0.602055i
$279$		0			0
$280$	−26.1013			−1.55985
$281$	−1.30747	−	2.26461i	−0.0779973	−	0.135095i	0.824388	−	0.566024i	$-0.191519\pi$
$281$	−1.30747	−	2.26461i	−0.0779973	−	0.135095i	−0.902386	+	0.430929i	$0.858186\pi$
$282$		0			0
$283$	−1.80894	−	1.04439i	−0.107530	−	0.0620827i	0.445270	−	0.895396i	$-0.353108\pi$
$283$	−1.80894	−	1.04439i	−0.107530	−	0.0620827i	−0.552801	+	0.833314i	$0.686441\pi$
$284$	−0.553572	−	0.319605i	−0.0328485	−	0.0189651i
$285$		0			0
$286$	−1.80963	+	3.04321i	−0.107006	+	0.179949i
$287$			23.4408i			1.38367i
$288$		0			0
$289$	1.07409			0.0631815
$290$	6.38432	−	3.68599i	0.374900	−	0.216449i
$291$		0			0
$292$	4.54340	+	2.62313i	0.265882	+	0.153507i
$293$	−15.0707	+	26.1033i	−0.880442	+	1.52497i	−0.0295925	+	0.999562i	$0.509421\pi$
$293$	−15.0707	+	26.1033i	−0.880442	+	1.52497i	−0.850850	+	0.525409i	$0.823912\pi$
$294$		0			0
$295$	6.89546	+	11.9433i	0.401469	+	0.695365i
$296$	−35.7858			−2.08001
$297$		0			0
$298$	12.4192			0.719425
$299$	−1.12110	−	1.94180i	−0.0648348	−	0.112297i
$300$		0			0
$301$	4.70424	−	8.14798i	0.271148	−	0.469642i
$302$	12.2139	+	7.05171i	0.702832	+	0.405780i
$303$		0			0
$304$	−13.6643	+	7.88907i	−0.783700	+	0.452469i
$305$	−13.7655			−0.788212
$306$		0			0
$307$			17.8758i			1.02022i	0.860108	+	0.510112i	$0.170396\pi$
$307$			17.8758i			1.02022i	−0.860108	+	0.510112i	$0.829604\pi$
$308$	−3.30064	+	5.55059i	−0.188071	+	0.316274i
$309$		0			0
$310$	10.6089	+	6.12506i	0.602546	+	0.347880i
$311$	23.5517	+	13.5976i	1.33549	+	0.771047i	0.986135	−	0.165943i	$-0.0530666\pi$
$311$	23.5517	+	13.5976i	1.33549	+	0.771047i	0.349357	+	0.936990i	$0.386400\pi$
$312$		0			0
$313$	−4.40376	−	7.62754i	−0.248915	−	0.431134i	0.714310	−	0.699830i	$-0.246741\pi$
$313$	−4.40376	−	7.62754i	−0.248915	−	0.431134i	−0.963225	+	0.268695i	$0.913407\pi$
$314$	−4.71467			−0.266064
$315$		0			0
$316$			4.99811i			0.281166i
$317$	−9.75760	+	5.63355i	−0.548041	+	0.316412i	−0.748332	−	0.663325i	$-0.769145\pi$
$317$	−9.75760	+	5.63355i	−0.548041	+	0.316412i	0.200290	+	0.979737i	$0.435811\pi$
$318$		0			0
$319$	0.123543	−	9.59550i	0.00691706	−	0.537245i
$320$	−15.8602	−	9.15688i	−0.886611	−	0.511885i
$321$		0			0
$322$	6.66881	+	11.5507i	0.371638	+	0.643696i
$323$			23.6105i			1.31372i
$324$		0			0
$325$			0.654874i			0.0363258i
$326$	3.58987	+	6.21783i	0.198824	+	0.344374i
$327$		0			0
$328$	−8.63091	+	14.9492i	−0.476562	+	0.825430i
$329$	3.45161	−	5.97836i	0.190293	−	0.329598i
$330$		0			0
$331$	−15.5610	−	26.9525i	−0.855312	−	1.48144i	−0.876355	−	0.481665i	$-0.840032\pi$
$331$	−15.5610	−	26.9525i	−0.855312	−	1.48144i	0.0210431	−	0.999779i	$-0.493301\pi$
$332$	2.91259			0.159849
$333$		0			0
$334$	6.93987			0.379733
$335$	3.87893	−	2.23950i	0.211929	−	0.122357i
$336$		0			0
$337$	−30.7641	−	17.7616i	−1.67582	−	0.967538i	−0.964275	−	0.264902i	$-0.914660\pi$
$337$	−30.7641	−	17.7616i	−1.67582	−	0.967538i	−0.711550	−	0.702636i	$-0.752006\pi$
$338$	7.58124	−	13.1311i	0.412365	−	0.714237i
$339$		0			0
$340$	−3.55859	+	2.05455i	−0.192992	+	0.111424i
$341$	13.9114	−	7.79471i	0.753346	−	0.422107i
$342$		0			0
$343$		−	13.3222i		−	0.719330i
$344$	6.00018	−	3.46420i	0.323508	−	0.186777i
$345$		0			0
$346$	−12.9662	+	22.4581i	−0.697066	+	1.20735i
$347$	−5.13984	+	8.90247i	−0.275921	+	0.477910i	−0.970367	−	0.241635i	$-0.922316\pi$
$347$	−5.13984	+	8.90247i	−0.275921	+	0.477910i	0.694446	+	0.719545i	$0.255650\pi$
$348$		0			0
$349$	15.7643	−	9.10150i	0.843841	−	0.487192i	−0.0147267	−	0.999892i	$-0.504688\pi$
$349$	15.7643	−	9.10150i	0.843841	−	0.487192i	0.858568	+	0.512699i	$0.171354\pi$
$350$		−	3.89549i		−	0.208222i
$351$		0			0
$352$	−7.50885	+	4.20728i	−0.400223	+	0.224249i
$353$	5.50002	−	3.17544i	0.292737	−	0.169012i	−0.346439	−	0.938073i	$-0.612609\pi$
$353$	5.50002	−	3.17544i	0.292737	−	0.169012i	0.639175	+	0.769061i	$0.279276\pi$
$354$		0			0
$355$	−1.40238	+	2.42900i	−0.0744308	+	0.128918i
$356$	3.02676	+	1.74750i	0.160418	+	0.0926173i
$357$		0			0
$358$	14.6022	−	8.43060i	0.771751	−	0.445571i
$359$	−0.878883			−0.0463857			−0.0231928	−	0.999731i	$-0.507383\pi$
$359$	−0.878883			−0.0463857			−0.0231928	+	0.999731i	$0.507383\pi$
$360$		0			0
$361$	−11.8427			−0.623301
$362$	4.23387	+	7.33329i	0.222527	+	0.385429i
$363$		0			0
$364$	−0.840041	+	1.45499i	−0.0440301	+	0.0762624i
$365$	11.5100	−	19.9358i	0.602459	−	1.04349i
$366$		0			0
$367$	4.57947	+	7.93188i	0.239047	+	0.414041i	0.960441	−	0.278484i	$-0.0898318\pi$
$367$	4.57947	+	7.93188i	0.239047	+	0.414041i	−0.721394	+	0.692524i	$0.756498\pi$
$368$			7.38264i			0.384847i
$369$		0			0
$370$			29.8447i			1.55155i
$371$	−4.73170	−	8.19555i	−0.245658	−	0.425492i
$372$		0			0
$373$	9.13656	+	5.27499i	0.473073	+	0.273129i	0.717525	−	0.696533i	$-0.245275\pi$
$373$	9.13656	+	5.27499i	0.473073	+	0.273129i	−0.244452	+	0.969661i	$0.578608\pi$
$374$	0.224583	−	17.4433i	0.0116129	−	0.901971i
$375$		0			0
$376$	4.40247	−	2.54177i	0.227040	−	0.131082i
$377$		−	2.49660i		−	0.128581i
$378$		0			0
$379$	15.2267			0.782145			0.391072	−	0.920360i	$-0.372104\pi$
$379$	15.2267			0.782145			0.391072	+	0.920360i	$0.372104\pi$
$380$	−2.68390	−	4.64865i	−0.137681	−	0.238470i
$381$		0			0
$382$	−25.6048	−	14.7829i	−1.31006	−	0.756361i
$383$	−23.7003	−	13.6834i	−1.21103	−	0.699187i	−0.248045	−	0.968749i	$-0.579788\pi$
$383$	−23.7003	−	13.6834i	−1.21103	−	0.699187i	−0.962983	+	0.269561i	$0.913121\pi$
$384$		0			0
$385$	24.3553	+	14.4828i	1.24126	+	0.738109i
$386$			18.7351i			0.953591i
$387$		0			0
$388$	4.95143			0.251371
$389$	10.7290	−	6.19442i	0.543984	−	0.314069i	−0.202708	−	0.979239i	$-0.564974\pi$
$389$	10.7290	−	6.19442i	0.543984	−	0.314069i	0.746692	+	0.665170i	$0.231641\pi$
$390$		0			0
$391$	9.56734	+	5.52371i	0.483841	+	0.279346i
$392$	15.5979	−	27.0164i	0.787815	−	1.36454i
$393$		0			0
$394$	−3.55441	−	6.15641i	−0.179068	−	0.310156i
$395$	21.9311			1.10347
$396$		0			0
$397$	12.3514			0.619900			0.309950	−	0.950753i	$-0.399688\pi$
$397$	12.3514			0.619900			0.309950	+	0.950753i	$0.399688\pi$
$398$	2.73935	+	4.74470i	0.137311	+	0.237830i
$399$		0			0
$400$	1.07812	−	1.86735i	0.0539058	−	0.0933676i
$401$	−0.502760	−	0.290268i	−0.0251066	−	0.0144953i	0.487394	−	0.873182i	$-0.337947\pi$
$401$	−0.502760	−	0.290268i	−0.0251066	−	0.0144953i	−0.512501	+	0.858687i	$0.671281\pi$
$402$		0			0
$403$	3.59283	−	2.07432i	0.178971	−	0.103329i
$404$	−0.485588			−0.0241589
$405$		0			0
$406$			14.8509i			0.737038i
$407$	33.3919	+	19.8564i	1.65518	+	0.984243i
$408$		0			0
$409$	−7.43480	−	4.29248i	−0.367627	−	0.212250i	0.304794	−	0.952418i	$-0.401412\pi$
$409$	−7.43480	−	4.29248i	−0.367627	−	0.212250i	−0.672421	+	0.740169i	$0.734746\pi$
$410$	12.4673	+	7.19802i	0.615718	+	0.355485i
$411$		0			0
$412$	−1.83603	−	3.18010i	−0.0904549	−	0.156672i
$413$	−27.7819			−1.36706
$414$		0			0
$415$		−	12.7801i		−	0.627348i
$416$	−1.93927	+	1.11964i	−0.0950805	+	0.0548948i
$417$		0			0
$418$	22.7865	+	0.293377i	1.11452	+	0.0143495i
$419$	2.88622	+	1.66636i	0.141001	+	0.0814070i	0.568841	−	0.822447i	$-0.307392\pi$
$419$	2.88622	+	1.66636i	0.141001	+	0.0814070i	−0.427840	+	0.903855i	$0.640725\pi$
$420$		0			0
$421$	0.811147	+	1.40495i	0.0395329	+	0.0684730i	0.885115	−	0.465373i	$-0.154080\pi$
$421$	0.811147	+	1.40495i	0.0395329	+	0.0684730i	−0.845582	+	0.533846i	$0.820746\pi$
$422$		−	14.5168i		−	0.706667i
$423$		0			0
$424$		−	6.96886i		−	0.338438i
$425$	−1.61330	−	2.79431i	−0.0782563	−	0.135544i
$426$		0			0
$427$	13.8654	−	24.0156i	0.670993	−	1.16219i
$428$	−1.85084	+	3.20575i	−0.0894639	+	0.154956i
$429$		0			0
$430$	−2.88908	−	5.00404i	−0.139324	−	0.241316i
$431$	34.0188			1.63863			0.819313	−	0.573347i	$-0.194355\pi$
$431$	34.0188			1.63863			0.819313	+	0.573347i	$0.194355\pi$
$432$		0			0
$433$	−28.6069			−1.37476			−0.687380	−	0.726298i	$-0.741239\pi$
$433$	−28.6069			−1.37476			−0.687380	+	0.726298i	$0.741239\pi$
$434$	−21.3718	+	12.3390i	−1.02588	+	0.592291i
$435$		0			0
$436$	−0.220348	−	0.127218i	−0.0105527	−	0.00609263i
$437$	−7.21570	+	12.4980i	−0.345174	+	0.597859i
$438$		0			0
$439$	−10.4122	+	6.01151i	−0.496949	+	0.286914i	−0.727453	−	0.686158i	$-0.759296\pi$
$439$	−10.4122	+	6.01151i	−0.496949	+	0.286914i	0.230503	+	0.973071i	$0.425963\pi$
$440$	10.1998	+	18.2039i	0.486257	+	0.867836i
$441$		0			0
$442$		−	4.53847i		−	0.215873i
$443$	−22.2214	+	12.8295i	−1.05577	+	0.609548i	−0.924259	−	0.381766i	$-0.875316\pi$
$443$	−22.2214	+	12.8295i	−1.05577	+	0.609548i	−0.131510	+	0.991315i	$0.541983\pi$
$444$		0			0
$445$	7.66779	−	13.2810i	0.363488	−	0.629580i
$446$	2.86334	−	4.95946i	0.135583	−	0.234837i
$447$		0			0
$448$	31.9505	−	18.4466i	1.50952	−	0.871521i
$449$			19.4014i			0.915608i	0.889053	+	0.457804i	$0.151364\pi$
$449$			19.4014i			0.915608i	−0.889053	+	0.457804i	$0.848636\pi$
$450$		0			0
$451$	16.3483	−	9.16014i	0.769813	−	0.431334i
$452$	2.53881	−	1.46578i	0.119416	−	0.0689447i
$453$		0			0
$454$	14.0654	−	24.3620i	0.660123	−	1.14337i
$455$	6.38432	+	3.68599i	0.299301	+	0.172802i
$456$		0			0
$457$	10.5984	−	6.11897i	0.495770	−	0.286233i	−0.231195	−	0.972907i	$-0.574263\pi$
$457$	10.5984	−	6.11897i	0.495770	−	0.286233i	0.726965	+	0.686674i	$0.240930\pi$
$458$	−4.43867			−0.207406
$459$		0			0
$460$	−2.51161			−0.117104
$461$	16.4063	+	28.4165i	0.764116	+	1.32349i	0.940713	+	0.339205i	$0.110158\pi$
$461$	16.4063	+	28.4165i	0.764116	+	1.32349i	−0.176596	+	0.984283i	$0.556509\pi$
$462$		0			0
$463$	2.52075	−	4.36606i	0.117149	−	0.202908i	−0.801488	−	0.598011i	$-0.795958\pi$
$463$	2.52075	−	4.36606i	0.117149	−	0.202908i	0.918637	+	0.395103i	$0.129291\pi$
$464$	−4.11014	+	7.11898i	−0.190809	+	0.330490i
$465$		0			0
$466$	11.5539	+	20.0119i	0.535222	+	0.927032i
$467$		−	9.20108i		−	0.425775i	−0.977077	−	0.212888i	$-0.931713\pi$
$467$		−	9.20108i		−	0.425775i	0.977077	−	0.212888i	$-0.0682868\pi$
$468$		0			0
$469$			9.02299i			0.416643i
$470$	−2.11979	−	3.67158i	−0.0977785	−	0.169357i
$471$		0			0
$472$	−17.7177	−	10.2293i	−0.815524	−	0.470843i
$473$	−7.52097	−	0.0968329i	−0.345814	−	0.00445238i
$474$		0			0
$475$	3.65025	−	2.10747i	0.167485	−	0.0966975i
$476$		−	8.27784i		−	0.379414i
$477$		0			0
$478$	26.0336			1.19075
$479$	−6.98309	−	12.0951i	−0.319065	−	0.552637i	0.661228	−	0.750185i	$-0.270036\pi$
$479$	−6.98309	−	12.0951i	−0.319065	−	0.552637i	−0.980293	+	0.197548i	$0.936702\pi$
$480$		0			0
$481$	8.75312	+	5.05362i	0.399108	+	0.230425i
$482$	1.09066	+	0.629693i	0.0496782	+	0.0286817i
$483$		0			0
$484$	5.16097	+	0.132918i	0.234590	+	0.00604171i
$485$		−	21.7262i		−	0.986536i
$486$		0			0
$487$	−28.9483			−1.31177			−0.655886	−	0.754860i	$-0.727705\pi$
$487$	−28.9483			−1.31177			−0.655886	+	0.754860i	$0.727705\pi$
$488$	17.6851	−	10.2105i	0.800566	−	0.462207i
$489$		0			0
$490$	−22.5312	−	13.0084i	−1.01786	−	0.587660i
$491$	9.63961	−	16.6963i	0.435029	−	0.753493i	−0.562269	−	0.826955i	$-0.690071\pi$
$491$	9.63961	−	16.6963i	0.435029	−	0.753493i	0.997298	+	0.0734617i	$0.0234047\pi$
$492$		0			0
$493$	6.15043	+	10.6529i	0.277001	+	0.479781i
$494$	5.92868			0.266744
$495$		0			0
$496$	−13.6598			−0.613342
$497$	−2.82512	−	4.89325i	−0.126724	−	0.219492i
$498$		0			0
$499$	−16.9288	+	29.3216i	−0.757838	+	1.31261i	0.186112	+	0.982528i	$0.440411\pi$
$499$	−16.9288	+	29.3216i	−0.757838	+	1.31261i	−0.943951	+	0.330086i	$0.892922\pi$
$500$	4.82052	+	2.78313i	0.215580	+	0.124465i
$501$		0			0
$502$	29.8864	−	17.2549i	1.33390	−	0.770126i
$503$	4.01382			0.178967			0.0894836	−	0.995988i	$-0.471478\pi$
$503$	4.01382			0.178967			0.0894836	+	0.995988i	$0.471478\pi$
$504$		0			0
$505$			2.13070i			0.0948148i
$506$	5.44981	−	9.16480i	0.242274	−	0.407425i
$507$		0			0
$508$	−7.24140	−	4.18082i	−0.321285	−	0.185494i
$509$	−3.23995	−	1.87059i	−0.143608	−	0.0829123i	0.426474	−	0.904500i	$-0.359755\pi$
$509$	−3.23995	−	1.87059i	−0.143608	−	0.0829123i	−0.570083	+	0.821587i	$0.693089\pi$
$510$		0			0
$511$	23.1869	+	40.1609i	1.02573	+	1.77662i
$512$	24.7322			1.09302
$513$		0			0
$514$		−	33.3263i		−	1.46996i
$515$	−13.9539	+	8.05627i	−0.614881	+	0.355002i
$516$		0			0
$517$	−5.51831	−	0.0710486i	−0.242695	−	0.00312471i
$518$	−52.0675	−	30.0612i	−2.28772	−	1.32081i
$519$		0			0
$520$	2.71436	+	4.70142i	0.119033	+	0.206171i
$521$			13.3122i			0.583216i	0.956538	+	0.291608i	$0.0941903\pi$
$521$			13.3122i			0.583216i	−0.956538	+	0.291608i	$0.905810\pi$
$522$		0			0
$523$			19.7745i			0.864678i	0.901711	+	0.432339i	$0.142312\pi$
$523$			19.7745i			0.864678i	−0.901711	+	0.432339i	$0.857688\pi$
$524$	1.93863	+	3.35781i	0.0846895	+	0.146687i
$525$		0			0
$526$	11.1983	−	19.3961i	0.488270	−	0.845709i
$527$	−10.2203	+	17.7020i	−0.445202	+	0.771112i
$528$		0			0
$529$	−8.12375	−	14.0707i	−0.353207	−	0.611772i
$530$	−5.81190			−0.252453
$531$		0			0
$532$	10.8135			0.468823
$533$	4.22220	−	2.43769i	0.182884	−	0.105588i
$534$		0			0
$535$	14.0664	+	8.12125i	0.608145	+	0.351112i
$536$	−3.32227	+	5.75434i	−0.143500	+	0.248550i
$537$		0			0
$538$	13.0998	−	7.56320i	0.564774	−	0.326073i
$539$	−29.5450	+	16.5544i	−1.27260	+	0.713048i
$540$		0			0
$541$			23.4225i			1.00701i	0.863992	+	0.503506i	$0.167957\pi$
$541$			23.4225i			1.00701i	−0.863992	+	0.503506i	$0.832043\pi$
$542$	16.0520	−	9.26761i	0.689492	−	0.398078i
$543$		0			0
$544$	5.51651	−	9.55487i	0.236518	−	0.409662i
$545$	−0.558215	+	0.966857i	−0.0239113	+	0.0414156i
$546$		0			0
$547$	−17.2285	+	9.94686i	−0.736636	+	0.425297i	−0.820845	−	0.571151i	$-0.806497\pi$
$547$	−17.2285	+	9.94686i	−0.736636	+	0.425297i	0.0842088	+	0.996448i	$0.473164\pi$
$548$			3.96730i			0.169475i
$549$		0			0
$550$	−2.71683	+	1.52227i	−0.115846	+	0.0649098i
$551$	−13.9160	+	8.03440i	−0.592841	+	0.342277i
$552$		0			0
$553$	−22.0902	+	38.2613i	−0.939369	+	1.62704i
$554$	31.8170	+	18.3696i	1.35177	+	0.780447i
$555$		0			0
$556$	−3.29786	+	1.90402i	−0.139860	+	0.0807484i
$557$	6.10079			0.258499			0.129249	−	0.991612i	$-0.458743\pi$
$557$	6.10079			0.258499			0.129249	+	0.991612i	$0.458743\pi$
$558$		0			0
$559$	−1.95684			−0.0827655
$560$	−12.1365	−	21.0210i	−0.512859	−	0.888297i
$561$		0			0
$562$	1.61761	−	2.80177i	0.0682346	−	0.118186i
$563$	0.00492939	−	0.00853795i	0.000207749	−	0.000359832i	−0.865922	−	0.500180i	$-0.833267\pi$
$563$	0.00492939	−	0.00853795i	0.000207749	−	0.000359832i	0.866129	+	0.499820i	$0.166601\pi$
$564$		0			0
$565$	−6.43167	−	11.1400i	−0.270582	−	0.468662i
$566$		−	2.58424i		−	0.108624i
$567$		0			0
$568$		−	4.16084i		−	0.174585i
$569$	−3.45428	−	5.98299i	−0.144811	−	0.250820i	0.784491	−	0.620140i	$-0.212924\pi$
$569$	−3.45428	−	5.98299i	−0.144811	−	0.250820i	−0.929302	+	0.369320i	$0.879591\pi$
$570$		0			0
$571$	16.6286	+	9.60053i	0.695886	+	0.401770i	0.805813	−	0.592170i	$-0.201729\pi$
$571$	16.6286	+	9.60053i	0.695886	+	0.401770i	−0.109927	+	0.993940i	$0.535062\pi$
$572$	1.34303	+	0.0172916i	0.0561548	+	0.000722997i
$573$		0			0
$574$	−25.1156	+	14.5005i	−1.04830	+	0.605238i
$575$		−	1.97219i		−	0.0822459i
$576$		0			0
$577$	25.0209			1.04163			0.520816	−	0.853669i	$-0.325628\pi$
$577$	25.0209			1.04163			0.520816	+	0.853669i	$0.325628\pi$
$578$	0.664430	+	1.15083i	0.0276366	+	0.0478681i
$579$		0			0
$580$	−2.42191	−	1.39829i	−0.100564	−	0.0580608i
$581$	22.2963	+	12.8728i	0.925006	+	0.534052i
$582$		0			0
$583$	−3.86679	+	6.50268i	−0.160146	+	0.269314i
$584$			34.1497i			1.41313i
$585$		0			0
$586$	−37.2911			−1.54048
$587$	37.0963	−	21.4176i	1.53113	−	0.883998i	0.531820	−	0.846858i	$-0.321508\pi$
$587$	37.0963	−	21.4176i	1.53113	−	0.883998i	0.999310	−	0.0371404i	$-0.0118249\pi$
$588$		0			0
$589$	−23.1244	−	13.3509i	−0.952826	−	0.550114i
$590$	−8.53107	+	14.7762i	−0.351218	+	0.608328i
$591$		0			0
$592$	−16.6395	−	28.8205i	−0.683879	−	1.18451i
$593$	−21.7398			−0.892745			−0.446373	−	0.894847i	$-0.647284\pi$
$593$	−21.7398			−0.892745			−0.446373	+	0.894847i	$0.647284\pi$
$594$		0			0
$595$	−36.3221			−1.48906
$596$	−2.35563	−	4.08007i	−0.0964902	−	0.167126i
$597$		0			0
$598$	1.38702	−	2.40240i	0.0567196	−	0.0982413i
$599$	9.32083	+	5.38138i	0.380839	+	0.219877i	0.678183	−	0.734893i	$-0.262768\pi$
$599$	9.32083	+	5.38138i	0.380839	+	0.219877i	−0.297344	+	0.954770i	$0.596101\pi$
$600$		0			0
$601$	−22.6605	+	13.0831i	−0.924343	+	0.533670i	−0.885018	−	0.465557i	$-0.845854\pi$
$601$	−22.6605	+	13.0831i	−0.924343	+	0.533670i	−0.0393250	+	0.999226i	$0.512521\pi$
$602$	11.6402			0.474418
$603$		0			0
$604$		−	5.35017i		−	0.217695i
$605$	0.583225	−	22.6457i	0.0237115	−	0.920677i
$606$		0			0
$607$	16.9909	+	9.80971i	0.689640	+	0.398164i	0.803477	−	0.595335i	$-0.202981\pi$
$607$	16.9909	+	9.80971i	0.689640	+	0.398164i	−0.113837	+	0.993499i	$0.536314\pi$
$608$	12.4817	+	7.20630i	0.506199	+	0.292254i
$609$		0			0
$610$	−8.51536	−	14.7490i	−0.344777	−	0.597171i
$611$	−1.43578			−0.0580854
$612$		0			0
$613$			33.5233i			1.35399i	0.735987	+	0.676996i	$0.236718\pi$
$613$			33.5233i			1.35399i	−0.735987	+	0.676996i	$0.763282\pi$
$614$	−19.1530	+	11.0580i	−0.772950	+	0.446263i
$615$		0			0
$616$	−42.0326	−	0.541172i	−1.69354	−	0.0218044i
$617$	−16.5667	−	9.56478i	−0.666950	−	0.385064i	0.127970	−	0.991778i	$-0.459154\pi$
$617$	−16.5667	−	9.56478i	−0.666950	−	0.385064i	−0.794920	+	0.606714i	$0.792487\pi$
$618$		0			0
$619$	−16.6869	−	28.9026i	−0.670704	−	1.16169i	−0.977705	−	0.209984i	$-0.932659\pi$
$619$	−16.6869	−	28.9026i	−0.670704	−	1.16169i	0.307001	−	0.951709i	$-0.400675\pi$
$620$		−	4.64712i		−	0.186633i
$621$		0			0
$622$			33.6458i			1.34907i
$623$	15.4468	+	26.7547i	0.618865	+	1.07190i
$624$		0			0
$625$	10.3146	−	17.8654i	0.412584	−	0.714617i
$626$	5.44834	−	9.43680i	0.217759	−	0.377170i
$627$		0			0
$628$	0.894261	+	1.54890i	0.0356849	+	0.0618080i
$629$	−49.7988			−1.98561
$630$		0			0
$631$	14.2718			0.568152			0.284076	−	0.958802i	$-0.408313\pi$
$631$	14.2718			0.568152			0.284076	+	0.958802i	$0.408313\pi$
$632$	−28.1757	+	16.2672i	−1.12077	+	0.647075i
$633$		0			0
$634$	−12.0721	−	6.96983i	−0.479445	−	0.276807i
$635$	−18.3449	+	31.7743i	−0.727995	+	1.26092i
$636$		0			0
$637$	−7.63044	+	4.40544i	−0.302329	+	0.174550i
$638$	10.3575	−	5.80341i	0.410057	−	0.229759i
$639$		0			0
$640$		−	11.9689i		−	0.473113i
$641$	−23.8511	+	13.7704i	−0.942062	+	0.543900i	−0.890606	−	0.454776i	$-0.849719\pi$
$641$	−23.8511	+	13.7704i	−0.942062	+	0.543900i	−0.0514559	+	0.998675i	$0.516386\pi$
$642$		0			0
$643$	−20.3147	+	35.1861i	−0.801133	+	1.38760i	0.117738	+	0.993045i	$0.462436\pi$
$643$	−20.3147	+	35.1861i	−0.801133	+	1.38760i	−0.918871	+	0.394558i	$0.870898\pi$
$644$	2.52983	−	4.38179i	0.0996892	−	0.172667i
$645$		0			0
$646$	−25.2974	+	14.6054i	−0.995311	+	0.574643i
$647$		−	37.7946i		−	1.48586i	−0.669371	−	0.742929i	$-0.733436\pi$
$647$		−	37.7946i		−	1.48586i	0.669371	−	0.742929i	$-0.266564\pi$
$648$		0			0
$649$	10.8566	+	19.3760i	0.426158	+	0.760575i
$650$	−0.701662	+	0.405105i	−0.0275215	+	0.0158895i
$651$		0			0
$652$	1.36182	−	2.35875i	0.0533332	−	0.0923758i
$653$	33.5277	+	19.3573i	1.31204	+	0.757508i	0.982434	−	0.186610i	$-0.0597501\pi$
$653$	33.5277	+	19.3573i	1.31204	+	0.757508i	0.329608	+	0.944118i	$0.393083\pi$
$654$		0			0
$655$	14.7336	−	8.50646i	0.575690	−	0.332375i
$656$	−16.0526			−0.626750
$657$		0			0
$658$	8.54066			0.332950
$659$	−15.8461	−	27.4462i	−0.617275	−	1.06915i	−0.989981	−	0.141202i	$-0.954903\pi$
$659$	−15.8461	−	27.4462i	−0.617275	−	1.06915i	0.372706	−	0.927949i	$-0.378430\pi$
$660$		0			0
$661$	13.4387	−	23.2766i	0.522706	−	0.905353i	−0.476945	−	0.878933i	$-0.658256\pi$
$661$	13.4387	−	23.2766i	0.522706	−	0.905353i	0.999651	−	0.0264199i	$-0.00841069\pi$
$662$	19.2521	−	33.3457i	0.748255	−	1.29602i
$663$		0			0
$664$	9.47952	+	16.4190i	0.367877	+	0.637181i
$665$		−	47.4481i		−	1.83996i
$666$		0			0
$667$			7.51865i			0.291123i
$668$	−1.31633	−	2.27995i	−0.0509303	−	0.0882138i
$669$		0			0
$670$	4.79902	+	2.77071i	0.185402	+	0.107042i
$671$	−22.1675	−	0.285408i	−0.855767	−	0.0110181i
$672$		0			0
$673$	−14.7738	+	8.52968i	−0.569490	+	0.328795i	−0.756946	−	0.653478i	$-0.773309\pi$
$673$	−14.7738	+	8.52968i	−0.569490	+	0.328795i	0.187456	+	0.982273i	$0.439976\pi$
$674$		−	43.9494i		−	1.69287i
$675$		0			0
$676$	−5.75192			−0.221228
$677$	1.45562	+	2.52120i	0.0559439	+	0.0968978i	0.892641	−	0.450768i	$-0.148850\pi$
$677$	1.45562	+	2.52120i	0.0559439	+	0.0968978i	−0.836697	+	0.547666i	$0.815517\pi$
$678$		0			0
$679$	37.9039	+	21.8838i	1.45462	+	0.839824i
$680$	−23.1641	−	13.3738i	−0.888303	−	0.512862i
$681$		0			0
$682$	16.9572	+	10.0835i	0.649326	+	0.386119i
$683$		−	20.5133i		−	0.784918i	−0.919770	−	0.392459i	$-0.871625\pi$
$683$		−	20.5133i		−	0.784918i	0.919770	−	0.392459i	$-0.128375\pi$
$684$		0			0
$685$	17.4080			0.665126
$686$	14.2740	−	8.24110i	0.544984	−	0.314647i
$687$		0			0
$688$	5.57986	+	3.22154i	0.212730	+	0.122820i
$689$	−0.984132	+	1.70457i	−0.0374925	+	0.0649388i
$690$		0			0
$691$	−4.32135	−	7.48480i	−0.164392	−	0.284735i	0.772047	−	0.635565i	$-0.219233\pi$
$691$	−4.32135	−	7.48480i	−0.164392	−	0.284735i	−0.936439	+	0.350830i	$0.885900\pi$
$692$	9.83751			0.373966
$693$		0			0
$694$	−12.7180			−0.482770
$695$	8.35458	+	14.4706i	0.316907	+	0.548900i
$696$		0			0
$697$	−12.0106	+	20.8030i	−0.454934	+	0.787968i
$698$	19.5035	+	11.2604i	0.738220	+	0.426212i
$699$		0			0
$700$	−1.27978	+	0.738881i	−0.0483711	+	0.0279271i
$701$	30.3341			1.14570			0.572852	−	0.819659i	$-0.305837\pi$
$701$	30.3341			1.14570			0.572852	+	0.819659i	$0.305837\pi$
$702$		0			0
$703$		−	65.0530i		−	2.45352i
$704$	−25.3508	−	15.0747i	−0.955445	−	0.568151i
$705$		0			0
$706$	6.80463	+	3.92866i	0.256096	+	0.147857i
$707$	−3.71725	−	2.14615i	−0.139802	−	0.0807144i
$708$		0			0
$709$	−0.842981	−	1.46009i	−0.0316588	−	0.0548347i	0.849762	−	0.527167i	$-0.176746\pi$
$709$	−0.842981	−	1.46009i	−0.0316588	−	0.0548347i	−0.881421	+	0.472332i	$0.843412\pi$
$710$	−3.47006			−0.130229
$711$		0			0
$712$			22.7501i			0.852597i
$713$	−10.8200	+	6.24693i	−0.405212	+	0.233949i
$714$		0			0
$715$	0.0758731	−	5.89303i	0.00283749	−	0.220387i
$716$	−5.53939	−	3.19817i	−0.207017	−	0.119521i
$717$		0			0
$718$	−0.543677	−	0.941677i	−0.0202899	−	0.0351431i
$719$			17.8522i			0.665775i	0.942967	+	0.332887i	$0.108023\pi$
$719$			17.8522i			0.665775i	−0.942967	+	0.332887i	$0.891977\pi$
$720$		0			0
$721$		−	32.4589i		−	1.20883i
$722$	−7.32591	−	12.6888i	−0.272642	−	0.472230i
$723$		0			0
$724$	1.60613	−	2.78190i	0.0596914	−	0.103388i
$725$	1.09798	−	1.90175i	0.0407778	−	0.0706293i
$726$		0			0
$727$	−13.8248	−	23.9453i	−0.512734	−	0.888081i	−0.999891	−	0.0147668i	$-0.995299\pi$
$727$	−13.8248	−	23.9453i	−0.512734	−	0.888081i	0.487157	−	0.873314i	$-0.338034\pi$
$728$	−10.9362			−0.405324
$729$		0			0
$730$	28.4803			1.05410
$731$	8.34972	−	4.82072i	0.308826	−	0.178301i
$732$		0			0
$733$	11.6445	+	6.72297i	0.430100	+	0.248318i	0.699389	−	0.714741i	$-0.253455\pi$
$733$	11.6445	+	6.72297i	0.430100	+	0.248318i	−0.269289	+	0.963059i	$0.586789\pi$
$734$	−5.66573	+	9.81332i	−0.209126	+	0.362216i
$735$		0			0
$736$	5.84022	−	3.37185i	0.215273	−	0.124288i
$737$	6.29292	−	3.52599i	0.231803	−	0.129881i
$738$		0			0
$739$			2.47408i			0.0910107i	0.998964	+	0.0455053i	$0.0144898\pi$
$739$			2.47408i			0.0910107i	−0.998964	+	0.0455053i	$0.985510\pi$
$740$	9.80485	−	5.66083i	0.360433	−	0.208096i
$741$		0			0
$742$	5.85407	−	10.1395i	0.214910	−	0.372234i
$743$	4.53380	−	7.85278i	0.166329	−	0.288090i	−0.770797	−	0.637080i	$-0.780142\pi$
$743$	4.53380	−	7.85278i	0.166329	−	0.288090i	0.937126	+	0.348990i	$0.113475\pi$
$744$		0			0
$745$	−17.9028	+	10.3362i	−0.655907	+	0.378688i
$746$			13.0524i			0.477884i
$747$		0			0
$748$	−5.77322	+	3.23480i	−0.211090	+	0.118276i
$749$	−28.3369	+	16.3603i	−1.03541	+	0.597794i
$750$		0			0
$751$	6.98349	−	12.0958i	0.254831	−	0.441381i	−0.710018	−	0.704183i	$-0.751313\pi$
$751$	6.98349	−	12.0958i	0.254831	−	0.441381i	0.964850	+	0.262802i	$0.0846467\pi$
$752$	4.09408	+	2.36372i	0.149296	+	0.0861958i
$753$		0			0
$754$	2.67497	−	1.54440i	0.0974168	−	0.0562436i
$755$	−23.4758			−0.854373
$756$		0			0
$757$	−7.49099			−0.272265			−0.136132	−	0.990691i	$-0.543467\pi$
$757$	−7.49099			−0.272265			−0.136132	+	0.990691i	$0.543467\pi$
$758$	9.41926	+	16.3146i	0.342123	+	0.592574i
$759$		0			0
$760$	17.4704	−	30.2596i	0.633718	−	1.09763i
$761$	−8.01546	+	13.8832i	−0.290560	+	0.503265i	−0.973942	−	0.226796i	$-0.927175\pi$
$761$	−8.01546	+	13.8832i	−0.290560	+	0.503265i	0.683382	+	0.730061i	$0.260508\pi$
$762$		0			0
$763$	−1.12453	−	1.94774i	−0.0407107	−	0.0705130i
$764$			11.2159i			0.405776i
$765$		0			0
$766$		−	33.8581i		−	1.22334i
$767$	2.88914	+	5.00414i	0.104321	+	0.180689i
$768$		0			0
$769$	7.49374	+	4.32651i	0.270231	+	0.156018i	0.628993	−	0.777411i	$-0.283468\pi$
$769$	7.49374	+	4.32651i	0.270231	+	0.156018i	−0.358762	+	0.933429i	$0.616801\pi$
$770$	−0.451328	+	35.0544i	−0.0162647	+	1.26327i
$771$		0			0
$772$	6.15502	−	3.55360i	0.221524	−	0.127897i
$773$			9.20292i			0.331006i	0.986209	+	0.165503i	$0.0529248\pi$
$773$			9.20292i			0.331006i	−0.986209	+	0.165503i	$0.947075\pi$
$774$		0			0
$775$	3.64905			0.131078
$776$	16.1153	+	27.9125i	0.578504	+	1.00200i
$777$		0			0
$778$	13.2740	+	7.66374i	0.475895	+	0.274758i
$779$	−27.1752	−	15.6896i	−0.973654	−	0.562139i
$780$		0			0
$781$	−2.30871	+	3.88250i	−0.0826122	+	0.138927i
$782$			13.6679i			0.488762i
$783$		0			0
$784$	29.0106			1.03609
$785$	6.79639	−	3.92390i	0.242574	−	0.140050i
$786$		0			0
$787$	34.9642	+	20.1866i	1.24634	+	0.719575i	0.970378	−	0.241593i	$-0.0776699\pi$
$787$	34.9642	+	20.1866i	1.24634	+	0.719575i	0.275963	+	0.961168i	$0.411003\pi$
$788$	−1.34837	+	2.33545i	−0.0480338	+	0.0831970i
$789$		0			0
$790$	13.5666	+	23.4980i	0.482677	+	0.836020i
$791$	25.9133			0.921371
$792$		0			0
$793$	−5.76764			−0.204815
$794$	7.64059	+	13.2339i	0.271154	+	0.469653i
$795$		0			0
$796$	1.03918	−	1.79991i	0.0368328	−	0.0637962i
$797$	0.574131	+	0.331475i	0.0203368	+	0.0117414i	0.510134	−	0.860095i	$-0.329596\pi$
$797$	0.574131	+	0.331475i	0.0203368	+	0.0117414i	−0.489797	+	0.871836i	$0.662929\pi$
$798$		0			0
$799$	6.12639	−	3.53707i	0.216736	−	0.125133i
$800$	−1.96962			−0.0696365
$801$		0			0
$802$		−	0.718241i		−	0.0253620i
$803$	18.9486	−	31.8653i	0.668680	−	1.12450i
$804$		0			0
$805$	−19.2267	−	11.1006i	−0.677653	−	0.391243i
$806$	4.44505	+	2.56635i	0.156570	+	0.0903958i
$807$		0			0
$808$	−1.58043	−	2.73739i	−0.0555993	−	0.0963009i
$809$	52.6473			1.85098			0.925490	−	0.378772i	$-0.123653\pi$
$809$	52.6473			1.85098			0.925490	+	0.378772i	$0.123653\pi$
$810$		0			0
$811$		−	23.1946i		−	0.814474i	−0.913323	−	0.407237i	$-0.866492\pi$
$811$		−	23.1946i		−	0.814474i	0.913323	−	0.407237i	$-0.133508\pi$
$812$	4.87895	−	2.81687i	0.171218	−	0.0988526i
$813$		0			0
$814$	−0.618786	+	48.0608i	−0.0216884	+	1.68453i
$815$	−10.3499	−	5.97551i	−0.362540	−	0.209313i
$816$		0			0
$817$	6.29738	+	10.9074i	0.220317	+	0.381601i
$818$		−	10.6213i		−	0.371366i
$819$		0			0
$820$		−	5.46117i		−	0.190712i
$821$	−4.61093	−	7.98637i	−0.160923	−	0.278726i	0.774277	−	0.632847i	$-0.218114\pi$
$821$	−4.61093	−	7.98637i	−0.160923	−	0.278726i	−0.935200	+	0.354120i	$0.884780\pi$
$822$		0			0
$823$	−2.85199	+	4.93978i	−0.0994140	+	0.172190i	−0.911442	−	0.411428i	$-0.865030\pi$
$823$	−2.85199	+	4.93978i	−0.0994140	+	0.172190i	0.812028	+	0.583618i	$0.198363\pi$
$824$	11.9514	−	20.7004i	0.416346	−	0.721132i
$825$		0			0
$826$	−17.1859	−	29.7669i	−0.597974	−	1.03572i
$827$	−35.5680			−1.23682			−0.618411	−	0.785855i	$-0.712223\pi$
$827$	−35.5680			−1.23682			−0.618411	+	0.785855i	$0.712223\pi$
$828$		0			0
$829$	−9.38140			−0.325830			−0.162915	−	0.986640i	$-0.552090\pi$
$829$	−9.38140			−0.325830			−0.162915	+	0.986640i	$0.552090\pi$
$830$	13.6931	−	7.90574i	0.475296	−	0.274412i
$831$		0			0
$832$	−6.64528	−	3.83666i	−0.230384	−	0.133012i
$833$	21.7058	−	37.5955i	0.752061	−	1.30261i
$834$		0			0
$835$	−10.0041	+	5.77587i	−0.346206	+	0.199882i
$836$	−4.22567	−	7.54165i	−0.146148	−	0.260834i
$837$		0			0
$838$			4.12324i			0.142435i
$839$	−30.1200	+	17.3898i	−1.03986	+	0.600363i	−0.919793	−	0.392403i	$-0.871644\pi$
$839$	−30.1200	+	17.3898i	−1.03986	+	0.600363i	−0.120066	+	0.992766i	$0.538311\pi$
$840$		0			0
$841$	10.3141	−	17.8646i	0.355660	−	0.616021i
$842$	−1.00355	+	1.73820i	−0.0345847	+	0.0599024i
$843$		0			0
$844$	−4.76919	+	2.75349i	−0.164162	+	0.0947791i
$845$			25.2387i			0.868236i
$846$		0			0
$847$	38.9205	+	23.8275i	1.33733	+	0.818721i
$848$	5.61244	−	3.24035i	0.192732	−	0.111274i
$849$		0			0
$850$	1.99597	−	3.45712i	0.0684612	−	0.118578i
$851$	−26.3605	−	15.2192i	−0.903626	−	0.521709i
$852$		0			0
$853$	5.85013	−	3.37757i	0.200305	−	0.115646i	−0.396493	−	0.918038i	$-0.629773\pi$
$853$	5.85013	−	3.37757i	0.200305	−	0.115646i	0.596798	+	0.802392i	$0.296440\pi$
$854$	34.3085			1.17401
$855$		0			0
$856$	−24.0955			−0.823569
$857$	5.87551	+	10.1767i	0.200704	+	0.347629i	0.948755	−	0.316012i	$-0.102344\pi$
$857$	5.87551	+	10.1767i	0.200704	+	0.347629i	−0.748052	+	0.663640i	$0.769011\pi$
$858$		0			0
$859$	−26.5699	+	46.0204i	−0.906552	+	1.57019i	−0.0877320	+	0.996144i	$0.527962\pi$
$859$	−26.5699	+	46.0204i	−0.906552	+	1.57019i	−0.818820	+	0.574050i	$0.805371\pi$
$860$	−1.09598	+	1.89829i	−0.0373726	+	0.0647313i
$861$		0			0
$862$	21.0440	+	36.4493i	0.716762	+	1.24147i
$863$			46.1145i			1.56976i	0.619651	+	0.784878i	$0.287274\pi$
$863$			46.1145i			1.56976i	−0.619651	+	0.784878i	$0.712726\pi$
$864$		0			0
$865$		−	43.1657i		−	1.46768i
$866$	−17.6962	−	30.6508i	−0.601342	−	1.04156i
$867$		0			0
$868$	8.10743	+	4.68083i	0.275184	+	0.158878i
$869$	35.3170	+	0.454708i	1.19805	+	0.0154249i
$870$		0			0
$871$	1.62524	−	0.938332i	0.0550691	−	0.0317942i
$872$		−	1.65621i		−	0.0560863i
$873$		0			0
$874$	−17.8545			−0.603939
$875$	24.6012	+	42.6105i	0.831672	+	1.44050i
$876$		0			0
$877$	−40.8587	−	23.5898i	−1.37970	−	0.796570i	−0.387577	−	0.921837i	$-0.626688\pi$
$877$	−40.8587	−	23.5898i	−1.37970	−	0.796570i	−0.992123	+	0.125267i	$0.960021\pi$
$878$	−12.8820	−	7.43745i	−0.434748	−	0.251002i
$879$		0			0
$880$	−9.91802	+	16.6789i	−0.334336	+	0.562245i
$881$			17.0910i			0.575812i	0.957659	+	0.287906i	$0.0929590\pi$
$881$			17.0910i			0.575812i	−0.957659	+	0.287906i	$0.907041\pi$
$882$		0			0
$883$	9.98172			0.335912			0.167956	−	0.985795i	$-0.446283\pi$
$883$	9.98172			0.335912			0.167956	+	0.985795i	$0.446283\pi$
$884$	−1.49102	+	0.860841i	−0.0501484	+	0.0289532i
$885$		0			0
$886$	−27.4923	−	15.8727i	−0.923621	−	0.533253i
$887$	9.31066	−	16.1265i	0.312621	−	0.541476i	−0.666308	−	0.745677i	$-0.732126\pi$
$887$	9.31066	−	16.1265i	0.312621	−	0.541476i	0.978929	+	0.204201i	$0.0654596\pi$
$888$		0			0
$889$	−36.9560	−	64.0096i	−1.23946	−	2.14681i
$890$	18.9732			0.635983
$891$		0			0
$892$	−2.17243			−0.0727385
$893$	4.62053	+	8.00300i	0.154620	+	0.267810i
$894$		0			0
$895$	−14.0331	+	24.3061i	−0.469076	+	0.812463i
$896$	20.8812	+	12.0557i	0.697591	+	0.402754i
$897$		0			0
$898$	−20.7875	+	12.0017i	−0.693689	+	0.400502i
$899$	−13.9114			−0.463972
$900$		0			0
$901$		−	9.69773i		−	0.323078i
$902$	19.9277	+	11.8499i	0.663520	+	0.394559i
$903$		0			0
$904$	16.5260	+	9.54130i	0.549647	+	0.317339i
$905$	−12.2066	−	7.04749i	−0.405761	−	0.234266i
$906$		0			0
$907$	18.9894	+	32.8906i	0.630532	+	1.09211i	0.987443	+	0.157975i	$0.0504966\pi$
$907$	18.9894	+	32.8906i	0.630532	+	1.09211i	−0.356911	+	0.934138i	$0.616170\pi$
$908$	−10.6715			−0.354146
$909$		0			0
$910$			9.12061i			0.302345i
$911$	−13.6814	+	7.89896i	−0.453285	+	0.261704i	−0.709217	−	0.704991i	$-0.750951\pi$
$911$	−13.6814	+	7.89896i	−0.453285	+	0.261704i	0.255931	+	0.966695i	$0.417618\pi$
$912$		0			0
$913$	0.264975	−	20.5805i	0.00876941	−	0.681116i
$914$	13.1123	+	7.57039i	0.433716	+	0.250406i
$915$		0			0
$916$	0.841911	+	1.45823i	0.0278175	+	0.0481813i
$917$			34.2727i			1.13178i
$918$		0			0
$919$		−	45.4869i		−	1.50047i	−0.661169	−	0.750237i	$-0.729939\pi$
$919$		−	45.4869i		−	1.50047i	0.661169	−	0.750237i	$-0.270061\pi$
$920$	−8.17446	−	14.1586i	−0.269504	−	0.466794i
$921$		0			0
$922$	−20.2978	+	35.1569i	−0.668474	+	1.15783i
$923$	−0.587587	+	1.01773i	−0.0193407	+	0.0334990i
$924$		0			0
$925$	4.44505	+	7.69905i	0.146152	+	0.253143i
$926$	6.23734			0.204972
$927$		0			0
$928$	7.50885			0.246490
$929$	46.6177	−	26.9147i	1.52948	−	0.883044i	0.530093	−	0.847940i	$-0.322157\pi$
$929$	46.6177	−	26.9147i	1.52948	−	0.883044i	0.999384	−	0.0351041i	$-0.0111763\pi$
$930$		0			0
$931$	49.1116	+	28.3546i	1.60957	+	0.929285i
$932$	4.38298	−	7.59155i	0.143569	−	0.248670i
$933$		0			0
$934$	9.85847	−	5.69179i	0.322579	−	0.186241i
$935$	14.1939	+	25.3321i	0.464189	+	0.828450i
$936$		0			0
$937$			12.3751i			0.404276i	0.979357	+	0.202138i	$0.0647890\pi$
$937$			12.3751i			0.404276i	−0.979357	+	0.202138i	$0.935211\pi$
$938$	−9.66766	+	5.58163i	−0.315660	+	0.182247i
$939$		0			0
$940$	−0.804146	+	1.39282i	−0.0262284	+	0.0454289i
$941$	14.1440	−	24.4982i	0.461082	−	0.798618i	−0.537933	−	0.842988i	$-0.680795\pi$
$941$	14.1440	−	24.4982i	0.461082	−	0.798618i	0.999015	+	0.0443696i	$0.0141279\pi$
$942$		0			0
$943$	−12.7154	+	7.34123i	−0.414070	+	0.239063i
$944$		−	19.0255i		−	0.619228i
$945$		0			0
$946$	−4.54872	−	8.11822i	−0.147892	−	0.263946i
$947$	12.5955	−	7.27199i	0.409297	−	0.236308i	−0.281190	−	0.959652i	$-0.590729\pi$
$947$	12.5955	−	7.27199i	0.409297	−	0.236308i	0.690488	+	0.723344i	$0.257396\pi$
$948$		0			0
$949$	4.82258	−	8.35295i	0.156547	−	0.271148i
$950$	4.51609	+	2.60737i	0.146521	+	0.0845942i
$951$		0			0
$952$	46.6643	−	26.9416i	1.51240	−	0.873184i
$953$	7.80664			0.252882			0.126441	−	0.991974i	$-0.459645\pi$
$953$	7.80664			0.252882			0.126441	+	0.991974i	$0.459645\pi$
$954$		0			0
$955$	49.2138			1.59252
$956$	−4.93795	−	8.55278i	−0.159705	−	0.276617i
$957$		0			0
$958$	8.63948	−	14.9640i	0.279129	−	0.483465i
$959$	−17.5343	+	30.3703i	−0.566212	+	0.980708i
$960$		0			0
$961$	3.94159	+	6.82703i	0.127148	+	0.220227i
$962$			12.5047i			0.403167i
$963$		0			0
$964$		−	0.477751i		−	0.0153873i
$965$	−15.5927	−	27.0074i	−0.501948	−	0.869399i
$966$		0			0
$967$	3.52549	+	2.03544i	0.113372	+	0.0654554i	0.555614	−	0.831441i	$-0.312483\pi$
$967$	3.52549	+	2.03544i	0.113372	+	0.0654554i	−0.442242	+	0.896896i	$0.645817\pi$
$968$	16.0480	+	29.5263i	0.515802	+	0.949012i
$969$		0			0
$970$	23.2785	−	13.4398i	0.747427	−	0.431527i
$971$			23.6225i			0.758084i	0.925380	+	0.379042i	$0.123746\pi$
$971$			23.6225i			0.758084i	−0.925380	+	0.379042i	$0.876254\pi$
$972$		0			0
$973$	−33.6608			−1.07911
$974$	−17.9074	−	31.0166i	−0.573791	−	0.993835i
$975$		0			0
$976$	16.4462	+	9.49524i	0.526431	+	0.303935i
$977$	27.2616	+	15.7395i	0.872175	+	0.503550i	0.868070	−	0.496441i	$-0.165360\pi$
$977$	27.2616	+	15.7395i	0.872175	+	0.503550i	0.00410429	+	0.999992i	$0.498694\pi$
$978$		0			0
$979$	12.6233	−	21.2283i	0.403442	−	0.678458i
$980$			9.86954i			0.315271i
$981$		0			0
$982$	23.8523			0.761156
$983$	−28.3373	+	16.3606i	−0.903821	+	0.521821i	−0.878438	−	0.477857i	$-0.841414\pi$
$983$	−28.3373	+	16.3606i	−0.903821	+	0.521821i	−0.0253828	+	0.999678i	$0.508080\pi$
$984$		0			0
$985$	10.2476	+	5.91648i	0.326517	+	0.188515i
$986$	−7.60932	+	13.1797i	−0.242330	+	0.419728i
$987$		0			0
$988$	−1.12453	−	1.94774i	−0.0357761	−	0.0619660i
$989$	5.89313			0.187390
$990$		0			0
$991$	34.5499			1.09751			0.548757	−	0.835982i	$-0.315101\pi$
$991$	34.5499			1.09751			0.548757	+	0.835982i	$0.315101\pi$
$992$	6.23879	+	10.8059i	0.198082	+	0.343087i
$993$		0			0
$994$	3.49524	−	6.05393i	0.110862	−	0.192019i
$995$	−7.89778	−	4.55978i	−0.250376	−	0.144555i
$996$		0			0
$997$	−22.3641	+	12.9119i	−0.708277	+	0.408924i	−0.810423	−	0.585846i	$-0.800763\pi$
$997$	−22.3641	+	12.9119i	−0.708277	+	0.408924i	0.102146	+	0.994769i	$0.467429\pi$
$998$	−41.8887			−1.32596
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.g.b.98.5		16
3.2	odd	2		99.2.g.b.32.4	✓	16
9.2	odd	6	inner	297.2.g.b.197.4		16
9.4	even	3		891.2.d.b.890.8		16
9.5	odd	6		891.2.d.b.890.9		16
9.7	even	3		99.2.g.b.65.5	yes	16
11.10	odd	2	inner	297.2.g.b.98.4		16
33.32	even	2		99.2.g.b.32.5	yes	16
99.32	even	6		891.2.d.b.890.7		16
99.43	odd	6		99.2.g.b.65.4	yes	16
99.65	even	6	inner	297.2.g.b.197.5		16
99.76	odd	6		891.2.d.b.890.10		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.g.b.32.4	✓	16	3.2	odd	2
99.2.g.b.32.5	yes	16	33.32	even	2
99.2.g.b.65.4	yes	16	99.43	odd	6
99.2.g.b.65.5	yes	16	9.7	even	3
297.2.g.b.98.4		16	11.10	odd	2	inner
297.2.g.b.98.5		16	1.1	even	1	trivial
297.2.g.b.197.4		16	9.2	odd	6	inner
297.2.g.b.197.5		16	99.65	even	6	inner
891.2.d.b.890.7		16	99.32	even	6
891.2.d.b.890.8		16	9.4	even	3
891.2.d.b.890.9		16	9.5	odd	6
891.2.d.b.890.10		16	99.76	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.g (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.618600 + 1.07145i) q^{2} +(0.234668 - 0.406456i) q^{4} +(-1.78348 - 1.02969i) q^{5} +(3.59283 - 2.07432i) q^{7} +3.05506 q^{8} +O(q^{10})\)	\(q+(0.618600 + 1.07145i) q^{2} +(0.234668 - 0.406456i) q^{4} +(-1.78348 - 1.02969i) q^{5} +(3.59283 - 2.07432i) q^{7} +3.05506 q^{8} -2.54787i q^{10} +(-2.85069 - 1.69515i) q^{11} +(-0.747261 - 0.431431i) q^{13} +(4.44505 + 2.56635i) q^{14} +(1.42053 + 2.46043i) q^{16} +4.25136 q^{17} +5.55362i q^{19} +(-0.837047 + 0.483270i) q^{20} +(0.0528262 - 4.10299i) q^{22} +(2.25042 + 1.29928i) q^{23} +(-0.379477 - 0.657274i) q^{25} -1.06753i q^{26} -1.94710i q^{28} +(1.44670 + 2.50575i) q^{29} +(-2.40400 + 4.16385i) q^{31} +(1.29759 - 2.24748i) q^{32} +(2.62989 + 4.55511i) q^{34} -8.54363 q^{35} -11.7136 q^{37} +(-5.95041 + 3.43547i) q^{38} +(-5.44863 - 3.14577i) q^{40} +(-2.82512 + 4.89325i) q^{41} +(1.96401 - 1.13392i) q^{43} +(-1.35797 + 0.760885i) q^{44} +3.21494i q^{46} +(1.44104 - 0.831985i) q^{47} +(5.10561 - 8.84317i) q^{49} +(0.469489 - 0.813180i) q^{50} +(-0.350716 + 0.202486i) q^{52} -2.28109i q^{53} +(3.33866 + 5.95859i) q^{55} +(10.9763 - 6.33718i) q^{56} +(-1.78985 + 3.10012i) q^{58} +(-5.79946 - 3.34832i) q^{59} +(5.78878 - 3.34215i) q^{61} -5.94845 q^{62} +8.89286 q^{64} +(0.888481 + 1.53889i) q^{65} +(-1.08746 + 1.88354i) q^{67} +(0.997657 - 1.72799i) q^{68} +(-5.28509 - 9.15404i) q^{70} -1.36195i q^{71} +11.1781i q^{73} +(-7.24604 - 12.5505i) q^{74} +(2.25730 + 1.30325i) q^{76} +(-13.7583 - 0.177139i) q^{77} +(-9.22261 + 5.32468i) q^{79} -5.85081i q^{80} -6.99047 q^{82} +(3.10289 + 5.37436i) q^{83} +(-7.58220 - 4.37759i) q^{85} +(2.42988 + 1.40289i) q^{86} +(-8.70905 - 5.17880i) q^{88} +7.44670i q^{89} -3.57971 q^{91} +(1.05620 - 0.609797i) q^{92} +(1.78286 + 1.02933i) q^{94} +(5.71851 - 9.90475i) q^{95} +(5.27494 + 9.13646i) q^{97} +12.6333 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 14 q^{4}+O(q^{10}) \) 16 * q - 14 * q^4	\( 16 q - 14 q^{4} + 12 q^{11} + 6 q^{14} - 2 q^{16} - 36 q^{20} + 6 q^{22} - 12 q^{23} - 12 q^{25} - 4 q^{31} - 28 q^{37} - 66 q^{38} + 30 q^{47} + 10 q^{49} + 20 q^{55} + 120 q^{56} - 6 q^{58} + 36 q^{59} + 40 q^{64} + 8 q^{67} - 72 q^{77} + 12 q^{82} + 72 q^{86} - 6 q^{88} - 12 q^{91} - 18 q^{92} - 4 q^{97}+O(q^{100}) \) 16 * q - 14 * q^4 + 12 * q^11 + 6 * q^14 - 2 * q^16 - 36 * q^20 + 6 * q^22 - 12 * q^23 - 12 * q^25 - 4 * q^31 - 28 * q^37 - 66 * q^38 + 30 * q^47 + 10 * q^49 + 20 * q^55 + 120 * q^56 - 6 * q^58 + 36 * q^59 + 40 * q^64 + 8 * q^67 - 72 * q^77 + 12 * q^82 + 72 * q^86 - 6 * q^88 - 12 * q^91 - 18 * q^92 - 4 * q^97

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