LMFDB - Embedded newform 936.2.m.f.181.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [936,2,Mod(181,936)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(936, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))

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

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

chi := DirichletCharacter("936.181");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.m (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.4521217600.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + x^{6} - 2x^{4} + 4x^{2} + 16 $ x^8 + x^6 - 2x^4 + 4x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 104)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			181.5
Root			$-0.273147 + 1.38758i$ of defining polynomial
Character	$\chi$	$=$	936.181
Dual form			936.2.m.f.181.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.273147 - 1.38758i) q^{2} +(-1.85078 - 0.758030i) q^{4} +3.11473 q^{5} +2.77517i q^{7} +(-1.55737 + 2.36106i) q^{8} +(0.850781 - 4.32196i) q^{10} -2.56844 q^{11} +(0.546295 + 3.56393i) q^{13} +(3.85078 + 0.758030i) q^{14} +(2.85078 + 2.80590i) q^{16} +5.70156 q^{17} +4.75362 q^{19} +(-5.76469 - 2.36106i) q^{20} +(-0.701562 + 3.56393i) q^{22} -4.00000 q^{23} +4.70156 q^{25} +(5.09447 + 0.215447i) q^{26} +(2.10366 - 5.13623i) q^{28} +7.12785i q^{29} -3.60338i q^{31} +(4.67210 - 3.18928i) q^{32} +(1.55737 - 7.91140i) q^{34} +8.64391i q^{35} +4.20732 q^{37} +(1.29844 - 6.59605i) q^{38} +(-4.85078 + 7.35408i) q^{40} +1.51606i q^{43} +(4.75362 + 1.94695i) q^{44} +(-1.09259 + 5.55034i) q^{46} -2.77517i q^{47} -0.701562 q^{49} +(1.28422 - 6.52381i) q^{50} +(1.69049 - 7.01015i) q^{52} +6.06424i q^{53} -8.00000 q^{55} +(-6.55234 - 4.32196i) q^{56} +(9.89049 + 1.94695i) q^{58} +4.75362 q^{59} +(-5.00000 - 0.984255i) q^{62} +(-3.14922 - 7.35408i) q^{64} +(1.70156 + 11.1007i) q^{65} -12.0757 q^{67} +(-10.5523 - 4.32196i) q^{68} +(11.9942 + 2.36106i) q^{70} -6.66908i q^{71} -14.9946i q^{73} +(1.14922 - 5.83802i) q^{74} +(-8.79790 - 3.60338i) q^{76} -7.12785i q^{77} +14.8062 q^{79} +(8.87942 + 8.73961i) q^{80} -9.89049 q^{83} +17.7588 q^{85} +(2.10366 + 0.414108i) q^{86} +(4.00000 - 6.06424i) q^{88} -14.9946i q^{89} +(-9.89049 + 1.51606i) q^{91} +(7.40312 + 3.03212i) q^{92} +(-3.85078 - 0.758030i) q^{94} +14.8062 q^{95} -3.89391i q^{97} +(-0.191630 + 0.973477i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{4} - 6 q^{10} + 18 q^{14} + 10 q^{16} + 20 q^{17} + 20 q^{22} - 32 q^{23} + 12 q^{25} + 14 q^{26} + 36 q^{38} - 26 q^{40} + 20 q^{49} - 4 q^{52} - 64 q^{55} - 14 q^{56} - 40 q^{62} - 38 q^{64}+ \cdots + 16 q^{95}+O(q^{100}) $ 8 * q - 2 * q^4 - 6 * q^10 + 18 * q^14 + 10 * q^16 + 20 * q^17 + 20 * q^22 - 32 * q^23 + 12 * q^25 + 14 * q^26 + 36 * q^38 - 26 * q^40 + 20 * q^49 - 4 * q^52 - 64 * q^55 - 14 * q^56 - 40 * q^62 - 38 * q^64 - 12 * q^65 - 46 * q^68 + 22 * q^74 + 16 * q^79 + 32 * q^88 + 8 * q^92 - 18 * q^94 + 16 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$-1$	$1$	$-1$	$1$

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 $

$2$	0.273147	−	1.38758i	0.193144	−	0.981170i
$2$	0.273147	−	1.38758i	0.193144	−	0.981170i
$3$		0			0
$3$		0			0
$4$	−1.85078	−	0.758030i	−0.925391	−	0.379015i
$5$	3.11473			1.39295			0.696475	−	0.717581i	$-0.254750\pi$
$5$	3.11473			1.39295			0.696475	+	0.717581i	$0.254750\pi$
$6$		0			0
$7$			2.77517i			1.04892i	0.851437	+	0.524458i	$0.175732\pi$
$7$			2.77517i			1.04892i	−0.851437	+	0.524458i	$0.824268\pi$
$8$	−1.55737	+	2.36106i	−0.550612	+	0.834761i
$9$		0			0
$10$	0.850781	−	4.32196i	0.269041	−	1.36672i
$11$	−2.56844			−0.774413			−0.387207	−	0.921993i	$-0.626560\pi$
$11$	−2.56844			−0.774413			−0.387207	+	0.921993i	$0.626560\pi$
$12$		0			0
$13$	0.546295	+	3.56393i	0.151515	+	0.988455i
$13$	0.546295	+	3.56393i	0.151515	+	0.988455i
$14$	3.85078	+	0.758030i	1.02916	+	0.202592i
$15$		0			0
$16$	2.85078	+	2.80590i	0.712695	+	0.701474i
$17$	5.70156			1.38283			0.691416	−	0.722457i	$-0.256987\pi$
$17$	5.70156			1.38283			0.691416	+	0.722457i	$0.256987\pi$
$18$		0			0
$19$	4.75362			1.09055			0.545277	−	0.838256i	$-0.316424\pi$
$19$	4.75362			1.09055			0.545277	+	0.838256i	$0.316424\pi$
$20$	−5.76469	−	2.36106i	−1.28902	−	0.527949i
$21$		0			0
$22$	−0.701562	+	3.56393i	−0.149574	+	0.759831i
$23$	−4.00000			−0.834058			−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000			−0.834058			−0.417029	+	0.908893i	$0.636929\pi$
$24$		0			0
$25$	4.70156			0.940312
$26$	5.09447	+	0.215447i	0.999107	+	0.0422526i
$27$		0			0
$28$	2.10366	−	5.13623i	0.397555	−	0.970656i
$29$			7.12785i			1.32361i	0.749677	+	0.661804i	$0.230209\pi$
$29$			7.12785i			1.32361i	−0.749677	+	0.661804i	$0.769791\pi$
$30$		0			0
$31$		−	3.60338i		−	0.647187i	−0.946196	−	0.323593i	$-0.895109\pi$
$31$		−	3.60338i		−	0.647187i	0.946196	−	0.323593i	$-0.104891\pi$
$32$	4.67210	−	3.18928i	0.825918	−	0.563790i
$33$		0			0
$34$	1.55737	−	7.91140i	0.267086	−	1.35679i
$35$			8.64391i			1.46109i
$36$		0			0
$37$	4.20732			0.691680			0.345840	−	0.938294i	$-0.387594\pi$
$37$	4.20732			0.691680			0.345840	+	0.938294i	$0.387594\pi$
$38$	1.29844	−	6.59605i	0.210634	−	1.07002i
$39$		0			0
$40$	−4.85078	+	7.35408i	−0.766976	+	1.16278i
$41$		0			0		1.00000			$0$
$41$		0			0		−1.00000			$\pi$
$42$		0			0
$43$			1.51606i			0.231197i	0.993296	+	0.115598i	$0.0368786\pi$
$43$			1.51606i			0.231197i	−0.993296	+	0.115598i	$0.963121\pi$
$44$	4.75362	+	1.94695i	0.716635	+	0.293514i
$45$		0			0
$46$	−1.09259	+	5.55034i	−0.161094	+	0.818353i
$47$		−	2.77517i		−	0.404800i	−0.979303	−	0.202400i	$-0.935126\pi$
$47$		−	2.77517i		−	0.404800i	0.979303	−	0.202400i	$-0.0648741\pi$
$48$		0			0
$49$	−0.701562			−0.100223
$50$	1.28422	−	6.52381i	0.181616	−	0.922607i
$51$		0			0
$52$	1.69049	−	7.01015i	0.234429	−	0.972133i
$53$			6.06424i			0.832987i	0.909139	+	0.416494i	$0.136741\pi$
$53$			6.06424i			0.832987i	−0.909139	+	0.416494i	$0.863259\pi$
$54$		0			0
$55$	−8.00000			−1.07872
$56$	−6.55234	−	4.32196i	−0.875594	−	0.577546i
$57$		0			0
$58$	9.89049	+	1.94695i	1.29869	+	0.255647i
$59$	4.75362			0.618868			0.309434	−	0.950921i	$-0.399860\pi$
$59$	4.75362			0.618868			0.309434	+	0.950921i	$0.399860\pi$
$60$		0			0
$61$		0			0		1.00000			$0$
$61$		0			0		−1.00000			$\pi$
$62$	−5.00000	−	0.984255i	−0.635001	−	0.125000i
$63$		0			0
$64$	−3.14922	−	7.35408i	−0.393652	−	0.919259i
$65$	1.70156	+	11.1007i	0.211053	+	1.37687i
$66$		0			0
$67$	−12.0757			−1.47528			−0.737639	−	0.675195i	$-0.764059\pi$
$67$	−12.0757			−1.47528			−0.737639	+	0.675195i	$0.764059\pi$
$68$	−10.5523	−	4.32196i	−1.27966	−	0.524114i
$69$		0			0
$70$	11.9942	+	2.36106i	1.43358	+	0.282201i
$71$		−	6.66908i		−	0.791474i	−0.918364	−	0.395737i	$-0.870489\pi$
$71$		−	6.66908i		−	0.791474i	0.918364	−	0.395737i	$-0.129511\pi$
$72$		0			0
$73$		−	14.9946i		−	1.75498i	−0.479592	−	0.877492i	$-0.659215\pi$
$73$		−	14.9946i		−	1.75498i	0.479592	−	0.877492i	$-0.340785\pi$
$74$	1.14922	−	5.83802i	0.133594	−	0.678655i
$75$		0			0
$76$	−8.79790	−	3.60338i	−1.00919	−	0.413337i
$77$		−	7.12785i		−	0.812294i
$78$		0			0
$79$	14.8062			1.66583			0.832917	−	0.553399i	$-0.186669\pi$
$79$	14.8062			1.66583			0.832917	+	0.553399i	$0.186669\pi$
$80$	8.87942	+	8.73961i	0.992750	+	0.977119i
$81$		0			0
$82$		0			0
$83$	−9.89049			−1.08562			−0.542811	−	0.839855i	$-0.682640\pi$
$83$	−9.89049			−1.08562			−0.542811	+	0.839855i	$0.682640\pi$
$84$		0			0
$85$	17.7588			1.92622
$86$	2.10366	+	0.414108i	0.226844	+	0.0446544i
$87$		0			0
$88$	4.00000	−	6.06424i	0.426401	−	0.646450i
$89$		−	14.9946i		−	1.58942i	−0.606988	−	0.794711i	$-0.707622\pi$
$89$		−	14.9946i		−	1.58942i	0.606988	−	0.794711i	$-0.292378\pi$
$90$		0			0
$91$	−9.89049	+	1.51606i	−1.03681	+	0.158926i
$92$	7.40312	+	3.03212i	0.771829	+	0.316120i
$93$		0			0
$94$	−3.85078	−	0.758030i	−0.397178	−	0.0781848i
$95$	14.8062			1.51909
$96$		0			0
$97$		−	3.89391i		−	0.395366i	−0.980266	−	0.197683i	$-0.936658\pi$
$97$		−	3.89391i		−	0.395366i	0.980266	−	0.197683i	$-0.0633417\pi$
$98$	−0.191630	+	0.973477i	−0.0193575	+	0.0983360i
$99$		0			0
$100$	−8.70156	−	3.56393i	−0.870156	−	0.356393i
$101$		0			0		1.00000			$0$
$101$		0			0		−1.00000			$\pi$
$102$		0			0
$103$	4.00000			0.394132			0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000			0.394132			0.197066	+	0.980390i	$0.436859\pi$
$104$	−9.26543	−	4.26050i	−0.908550	−	0.417777i
$105$		0			0
$106$	8.41464	+	1.65643i	0.817303	+	0.160887i
$107$		−	10.1600i		−	0.982201i	−0.871103	−	0.491101i	$-0.836595\pi$
$107$		−	10.1600i		−	0.982201i	0.871103	−	0.491101i	$-0.163405\pi$
$108$		0			0
$109$	2.02214			0.193686			0.0968431	−	0.995300i	$-0.469125\pi$
$109$	2.02214			0.193686			0.0968431	+	0.995300i	$0.469125\pi$
$110$	−2.18518	+	11.1007i	−0.208349	+	1.05841i
$111$		0			0
$112$	−7.78683	+	7.91140i	−0.735787	+	0.747557i
$113$	−11.4031			−1.07272			−0.536358	−	0.843991i	$-0.680200\pi$
$113$	−11.4031			−1.07272			−0.536358	+	0.843991i	$0.680200\pi$
$114$		0			0
$115$	−12.4589			−1.16180
$116$	5.40312	−	13.1921i	0.501667	−	1.22485i
$117$		0			0
$118$	1.29844	−	6.59605i	0.119531	−	0.607215i
$119$			15.8228i			1.45047i
$120$		0			0
$121$	−4.40312			−0.400284
$122$		0			0
$123$		0			0
$124$	−2.73147	+	6.66908i	−0.245294	+	0.598901i
$125$	−0.929554			−0.0831419
$126$		0			0
$127$	−12.0000			−1.06483			−0.532414	−	0.846484i	$-0.678715\pi$
$127$	−12.0000			−1.06483			−0.532414	+	0.846484i	$0.678715\pi$
$128$	−11.0646	+	2.36106i	−0.977982	+	0.208690i
$129$		0			0
$130$	15.8679	+	0.671059i	1.39171	+	0.0588558i
$131$			18.8039i			1.64290i	0.570279	+	0.821451i	$0.306835\pi$
$131$			18.8039i			1.64290i	−0.570279	+	0.821451i	$0.693165\pi$
$132$		0			0
$133$			13.1921i			1.14390i
$134$	−3.29844	+	16.7560i	−0.284942	+	1.44750i
$135$		0			0
$136$	−8.87942	+	13.4617i	−0.761404	+	1.15433i
$137$			11.1007i			0.948395i	0.880419	+	0.474197i	$0.157262\pi$
$137$			11.1007i			0.948395i	−0.880419	+	0.474197i	$0.842738\pi$
$138$		0			0
$139$			9.70752i			0.823381i	0.911324	+	0.411691i	$0.135062\pi$
$139$			9.70752i			0.823381i	−0.911324	+	0.411691i	$0.864938\pi$
$140$	6.55234	−	15.9980i	0.553774	−	1.35208i
$141$		0			0
$142$	−9.25391	−	1.82164i	−0.776570	−	0.152869i
$143$	−1.40312	−	9.15372i	−0.117335	−	0.765473i
$144$		0			0
$145$			22.2014i			1.84372i
$146$	−20.8062	−	4.09573i	−1.72194	−	0.338965i
$147$		0			0
$148$	−7.78683	−	3.18928i	−0.640074	−	0.262157i
$149$	13.5515			1.11018			0.555092	−	0.831789i	$-0.312683\pi$
$149$	13.5515			1.11018			0.555092	+	0.831789i	$0.312683\pi$
$150$		0			0
$151$			13.8758i			1.12920i	0.825365	+	0.564600i	$0.190970\pi$
$151$			13.8758i			1.12920i	−0.825365	+	0.564600i	$0.809030\pi$
$152$	−7.40312	+	11.2236i	−0.600473	+	0.910353i
$153$		0			0
$154$	−9.89049	−	1.94695i	−0.796999	−	0.156890i
$155$		−	11.2236i		−	0.901500i
$156$		0			0
$157$		−	1.06361i		−	0.0848853i	−0.999099	−	0.0424427i	$-0.986486\pi$
$157$		−	1.06361i		−	0.0848853i	0.999099	−	0.0424427i	$-0.0135140\pi$
$158$	4.04429	−	20.5449i	0.321746	−	1.63447i
$159$		0			0
$160$	14.5523	−	9.93375i	1.15046	−	0.785332i
$161$		−	11.1007i		−	0.874856i
$162$		0			0
$163$	9.89049			0.774683			0.387342	−	0.921936i	$-0.373393\pi$
$163$	9.89049			0.774683			0.387342	+	0.921936i	$0.373393\pi$
$164$		0			0
$165$		0			0
$166$	−2.70156	+	13.7239i	−0.209682	+	1.06518i
$167$			7.49729i			0.580158i	0.957003	+	0.290079i	$0.0936816\pi$
$167$			7.49729i			0.580158i	−0.957003	+	0.290079i	$0.906318\pi$
$168$		0			0
$169$	−12.4031	+	3.89391i	−0.954086	+	0.299531i
$170$	4.85078	−	24.6419i	0.372038	−	1.88995i
$171$		0			0
$172$	1.14922	−	2.80590i	0.0876271	−	0.213947i
$173$			6.06424i			0.461056i	0.973066	+	0.230528i	$0.0740453\pi$
$173$			6.06424i			0.461056i	−0.973066	+	0.230528i	$0.925955\pi$
$174$		0			0
$175$			13.0476i			0.986308i
$176$	−7.32206	−	7.20677i	−0.551921	−	0.543231i
$177$		0			0
$178$	−20.8062	−	4.09573i	−1.55949	−	0.306988i
$179$			12.7396i			0.952205i	0.879390	+	0.476103i	$0.157951\pi$
$179$			12.7396i			0.952205i	−0.879390	+	0.476103i	$0.842049\pi$
$180$		0			0
$181$		−	13.1921i		−	0.980560i	−0.871565	−	0.490280i	$-0.836894\pi$
$181$		−	13.1921i		−	0.980560i	0.871565	−	0.490280i	$-0.163106\pi$
$182$	−0.597901	+	14.1380i	−0.0443194	+	1.04798i
$183$		0			0
$184$	6.22947	−	9.44424i	0.459242	−	0.696239i
$185$	13.1047			0.963476
$186$		0			0
$187$	−14.6441			−1.07088
$188$	−2.10366	+	5.13623i	−0.153425	+	0.374598i
$189$		0			0
$190$	4.04429	−	20.5449i	0.293403	−	1.49049i
$191$	2.80625			0.203053			0.101527	−	0.994833i	$-0.467627\pi$
$191$	2.80625			0.203053			0.101527	+	0.994833i	$0.467627\pi$
$192$		0			0
$193$		−	14.9946i		−	1.07933i	−0.841879	−	0.539667i	$-0.818550\pi$
$193$		−	14.9946i		−	1.07933i	0.841879	−	0.539667i	$-0.181450\pi$
$194$	−5.40312	−	1.06361i	−0.387922	−	0.0763628i
$195$		0			0
$196$	1.29844	+	0.531805i	0.0927456	+	0.0379861i
$197$	−4.20732			−0.299759			−0.149880	−	0.988704i	$-0.547889\pi$
$197$	−4.20732			−0.299759			−0.149880	+	0.988704i	$0.547889\pi$
$198$		0			0
$199$		0			0			−	1.00000i	$-0.5\pi$
$199$		0			0				1.00000i	$0.5\pi$
$200$	−7.32206	+	11.1007i	−0.517748	+	0.784936i
$201$		0			0
$202$		0			0
$203$	−19.7810			−1.38835
$204$		0			0
$205$		0			0
$206$	1.09259	−	5.55034i	0.0761243	−	0.386710i
$207$		0			0
$208$	−8.44263	+	11.6928i	−0.585391	+	0.810751i
$209$	−12.2094			−0.844540
$210$		0			0
$211$		−	18.8039i		−	1.29451i	−0.762272	−	0.647256i	$-0.775916\pi$
$211$		−	18.8039i		−	1.29451i	0.762272	−	0.647256i	$-0.224084\pi$
$212$	4.59688	−	11.2236i	0.315715	−	0.770839i
$213$		0			0
$214$	−14.0978	−	2.77517i	−0.963707	−	0.189707i
$215$			4.72212i			0.322046i
$216$		0			0
$217$	10.0000			0.678844
$218$	0.552343	−	2.80590i	0.0374094	−	0.190039i
$219$		0			0
$220$	14.8062	+	6.06424i	0.998237	+	0.408851i
$221$	3.11473	+	20.3199i	0.209520	+	1.36687i
$222$		0			0
$223$		−	15.5323i		−	1.04012i	−0.854130	−	0.520059i	$-0.825910\pi$
$223$		−	15.5323i		−	1.04012i	0.854130	−	0.520059i	$-0.174090\pi$
$224$	8.85078	+	12.9659i	0.591368	+	0.866318i
$225$		0			0
$226$	−3.11473	+	15.8228i	−0.207189	+	1.05252i
$227$	−6.93880			−0.460544			−0.230272	−	0.973126i	$-0.573962\pi$
$227$	−6.93880			−0.460544			−0.230272	+	0.973126i	$0.573962\pi$
$228$		0			0
$229$	−7.48509			−0.494629			−0.247314	−	0.968935i	$-0.579548\pi$
$229$	−7.48509			−0.494629			−0.247314	+	0.968935i	$0.579548\pi$
$230$	−3.40312	+	17.2878i	−0.224395	+	1.13993i
$231$		0			0
$232$	−16.8293	−	11.1007i	−1.10490	−	0.728795i
$233$	7.10469			0.465443			0.232722	−	0.972543i	$-0.425237\pi$
$233$	7.10469			0.465443			0.232722	+	0.972543i	$0.425237\pi$
$234$		0			0
$235$		−	8.64391i		−	0.563867i
$236$	−8.79790	−	3.60338i	−0.572695	−	0.234560i
$237$		0			0
$238$	21.9555	+	4.32196i	1.42316	+	0.280151i
$239$			12.2194i			0.790408i	0.918593	+	0.395204i	$0.129326\pi$
$239$			12.2194i			0.790408i	−0.918593	+	0.395204i	$0.870674\pi$
$240$		0			0
$241$			7.20677i			0.464229i	0.972688	+	0.232114i	$0.0745644\pi$
$241$			7.20677i			0.464229i	−0.972688	+	0.232114i	$0.925436\pi$
$242$	−1.20270	+	6.10971i	−0.0773126	+	0.392747i
$243$		0			0
$244$		0			0
$245$	−2.18518			−0.139606
$246$		0			0
$247$	2.59688	+	16.9415i	0.165235	+	1.07796i
$248$	8.50781	+	5.61179i	0.540247	+	0.356349i
$249$		0			0
$250$	−0.253905	+	1.28984i	−0.0160584	+	0.0815763i
$251$		−	24.4157i		−	1.54110i	−0.637377	−	0.770552i	$-0.719981\pi$
$251$		−	24.4157i		−	1.54110i	0.637377	−	0.770552i	$-0.280019\pi$
$252$		0			0
$253$	10.2738			0.645905
$254$	−3.27777	+	16.6510i	−0.205665	+	1.04478i
$255$		0			0
$256$	0.253905	+	15.9980i	0.0158691	+	0.999874i
$257$	−6.50781			−0.405946			−0.202973	−	0.979184i	$-0.565060\pi$
$257$	−6.50781			−0.405946			−0.202973	+	0.979184i	$0.565060\pi$
$258$		0			0
$259$			11.6760i			0.725513i
$260$	5.26543	−	21.8348i	0.326548	−	1.35413i
$261$		0			0
$262$	26.0920	+	5.13623i	1.61197	+	0.317317i
$263$	16.0000			0.986602			0.493301	−	0.869859i	$-0.335790\pi$
$263$	16.0000			0.986602			0.493301	+	0.869859i	$0.335790\pi$
$264$		0			0
$265$			18.8885i			1.16031i
$266$	18.3051	+	3.60338i	1.12236	+	0.220938i
$267$		0			0
$268$	22.3494	+	9.15372i	1.36521	+	0.559153i
$269$		−	19.2563i		−	1.17408i	−0.809558	−	0.587040i	$-0.800293\pi$
$269$		−	19.2563i		−	1.17408i	0.809558	−	0.587040i	$-0.199707\pi$
$270$		0			0
$271$		−	27.2140i		−	1.65313i	−0.562839	−	0.826566i	$-0.690291\pi$
$271$		−	27.2140i		−	1.65313i	0.562839	−	0.826566i	$-0.309709\pi$
$272$	16.2539	+	15.9980i	0.985538	+	0.970020i
$273$		0			0
$274$	15.4031	+	3.03212i	0.930537	+	0.183177i
$275$	−12.0757			−0.728190
$276$		0			0
$277$			12.1285i			0.728730i	0.931256	+	0.364365i	$0.118714\pi$
$277$			12.1285i			0.728730i	−0.931256	+	0.364365i	$0.881286\pi$
$278$	13.4700	+	2.65158i	0.807877	+	0.159031i
$279$		0			0
$280$	−20.4088	−	13.4617i	−1.21966	−	0.804493i
$281$			7.20677i			0.429920i	0.976623	+	0.214960i	$0.0689621\pi$
$281$			7.20677i			0.429920i	−0.976623	+	0.214960i	$0.931038\pi$
$282$		0			0
$283$		−	4.09573i		−	0.243466i	−0.992563	−	0.121733i	$-0.961155\pi$
$283$		−	4.09573i		−	0.243466i	0.992563	−	0.121733i	$-0.0388451\pi$
$284$	−5.05536	+	12.3430i	−0.299980	+	0.732422i
$285$		0			0
$286$	−13.0848	−	0.553362i	−0.773722	−	0.0327210i
$287$		0			0
$288$		0			0
$289$	15.5078			0.912224
$290$	30.8062	+	6.06424i	1.80901	+	0.356104i
$291$		0			0
$292$	−11.3663	+	27.7517i	−0.665165	+	1.62404i
$293$	29.4513			1.72056			0.860280	−	0.509821i	$-0.170288\pi$
$293$	29.4513			1.72056			0.860280	+	0.509821i	$0.170288\pi$
$294$		0			0
$295$	14.8062			0.862053
$296$	−6.55234	+	9.93375i	−0.380847	+	0.577387i
$297$		0			0
$298$	3.70156	−	18.8039i	0.214426	−	1.08928i
$299$	−2.18518	−	14.2557i	−0.126372	−	0.824428i
$300$		0			0
$301$	−4.20732			−0.242506
$302$	19.2539	+	3.79015i	1.10794	+	0.218099i
$303$		0			0
$304$	13.5515	+	13.3382i	0.777233	+	0.764995i
$305$		0			0
$306$		0			0
$307$	−29.6715			−1.69344			−0.846720	−	0.532038i	$-0.821426\pi$
$307$	−29.6715			−1.69344			−0.846720	+	0.532038i	$0.821426\pi$
$308$	−5.40312	+	13.1921i	−0.307872	+	0.751689i
$309$		0			0
$310$	−15.5737	−	3.06569i	−0.884525	−	0.174120i
$311$	−12.0000			−0.680458			−0.340229	−	0.940343i	$-0.610505\pi$
$311$	−12.0000			−0.680458			−0.340229	+	0.940343i	$0.610505\pi$
$312$		0			0
$313$	−24.5078			−1.38526			−0.692632	−	0.721291i	$-0.743549\pi$
$313$	−24.5078			−1.38526			−0.692632	+	0.721291i	$0.743549\pi$
$314$	−1.47585	−	0.290522i	−0.0832870	−	0.0163951i
$315$		0			0
$316$	−27.4031	−	11.2236i	−1.54155	−	0.631376i
$317$	−25.2439			−1.41784			−0.708920	−	0.705289i	$-0.750817\pi$
$317$	−25.2439			−1.41784			−0.708920	+	0.705289i	$0.750817\pi$
$318$		0			0
$319$		−	18.3074i		−	1.02502i
$320$	−9.80898	−	22.9060i	−0.548338	−	1.28048i
$321$		0			0
$322$	−15.4031	−	3.03212i	−0.858383	−	0.168973i
$323$	27.1030			1.50805
$324$		0			0
$325$	2.56844	+	16.7560i	0.142471	+	0.929456i
$326$	2.70156	−	13.7239i	0.149626	−	0.760096i
$327$		0			0
$328$		0			0
$329$	7.70156			0.424601
$330$		0			0
$331$	−5.52014			−0.303414			−0.151707	−	0.988425i	$-0.548477\pi$
$331$	−5.52014			−0.303414			−0.151707	+	0.988425i	$0.548477\pi$
$332$	18.3051	+	7.49729i	1.00463	+	0.411467i
$333$		0			0
$334$	10.4031	+	2.04787i	0.569234	+	0.112054i
$335$	−37.6125			−2.05499
$336$		0			0
$337$	14.2984			0.778886			0.389443	−	0.921051i	$-0.372668\pi$
$337$	14.2984			0.778886			0.389443	+	0.921051i	$0.372668\pi$
$338$	2.01524	+	18.2740i	0.109615	+	0.993974i
$339$		0			0
$340$	−32.8677	−	13.4617i	−1.78250	−	0.730065i
$341$			9.25507i			0.501190i
$342$		0			0
$343$			17.4792i			0.943790i
$344$	−3.57951	−	2.36106i	−0.192994	−	0.127300i
$345$		0			0
$346$	8.41464	+	1.65643i	0.452374	+	0.0890503i
$347$			6.67540i			0.358354i	0.983817	+	0.179177i	$0.0573435\pi$
$347$			6.67540i			0.358354i	−0.983817	+	0.179177i	$0.942656\pi$
$348$		0			0
$349$	3.44080			0.184182			0.0920910	−	0.995751i	$-0.470645\pi$
$349$	3.44080			0.184182			0.0920910	+	0.995751i	$0.470645\pi$
$350$	18.1047	+	3.56393i	0.967736	+	0.190500i
$351$		0			0
$352$	−12.0000	+	8.19146i	−0.639602	+	0.436606i
$353$		−	33.3020i		−	1.77249i	−0.463219	−	0.886244i	$-0.653306\pi$
$353$		−	33.3020i		−	1.77249i	0.463219	−	0.886244i	$-0.346694\pi$
$354$		0			0
$355$		−	20.7724i		−	1.10248i
$356$	−11.3663	+	27.7517i	−0.602415	+	1.47084i
$357$		0			0
$358$	17.6773	+	3.47980i	0.934276	+	0.183913i
$359$		−	18.5980i		−	0.981563i	−0.871283	−	0.490782i	$-0.836711\pi$
$359$		−	18.5980i		−	0.981563i	0.871283	−	0.490782i	$-0.163289\pi$
$360$		0			0
$361$	3.59688			0.189309
$362$	−18.3051	−	3.60338i	−0.962097	−	0.189390i
$363$		0			0
$364$	19.4544	+	4.69140i	1.01969	+	0.245896i
$365$		−	46.7041i		−	2.44461i
$366$		0			0
$367$	8.00000			0.417597			0.208798	−	0.977959i	$-0.433045\pi$
$367$	8.00000			0.417597			0.208798	+	0.977959i	$0.433045\pi$
$368$	−11.4031	−	11.2236i	−0.594429	−	0.585070i
$369$		0			0
$370$	3.57951	−	18.1839i	0.186090	−	0.945334i
$371$	−16.8293			−0.873733
$372$		0			0
$373$		−	19.2563i		−	0.997055i	−0.866874	−	0.498527i	$-0.833874\pi$
$373$		−	19.2563i		−	0.997055i	0.866874	−	0.498527i	$-0.166126\pi$
$374$	−4.00000	+	20.3199i	−0.206835	+	1.05072i
$375$		0			0
$376$	6.55234	+	4.32196i	0.337911	+	0.222888i
$377$	−25.4031	+	3.89391i	−1.30833	+	0.200546i
$378$		0			0
$379$	4.75362			0.244177			0.122088	−	0.992519i	$-0.461041\pi$
$379$	4.75362			0.244177			0.122088	+	0.992519i	$0.461041\pi$
$380$	−27.4031	−	11.2236i	−1.40575	−	0.575758i
$381$		0			0
$382$	0.766519	−	3.89391i	0.0392185	−	0.199230i
$383$			1.11874i			0.0571648i	0.999591	+	0.0285824i	$0.00909930\pi$
$383$			1.11874i			0.0571648i	−0.999591	+	0.0285824i	$0.990901\pi$
$384$		0			0
$385$		−	22.2014i		−	1.13149i
$386$	−20.8062	−	4.09573i	−1.05901	−	0.208467i
$387$		0			0
$388$	−2.95170	+	7.20677i	−0.149850	+	0.365868i
$389$		−	15.3193i		−	0.776720i	−0.921508	−	0.388360i	$-0.873042\pi$
$389$		−	15.3193i		−	0.776720i	0.921508	−	0.388360i	$-0.126958\pi$
$390$		0			0
$391$	−22.8062			−1.15336
$392$	1.09259	−	1.65643i	0.0551841	−	0.0836624i
$393$		0			0
$394$	−1.14922	+	5.83802i	−0.0578968	+	0.294115i
$395$	46.1175			2.32042
$396$		0			0
$397$	6.22947			0.312648			0.156324	−	0.987706i	$-0.450036\pi$
$397$	6.22947			0.312648			0.156324	+	0.987706i	$0.450036\pi$
$398$		0			0
$399$		0			0
$400$	13.4031	+	13.1921i	0.670156	+	0.659605i
$401$			7.20677i			0.359889i	0.983677	+	0.179944i	$0.0575918\pi$
$401$			7.20677i			0.359889i	−0.983677	+	0.179944i	$0.942408\pi$
$402$		0			0
$403$	12.8422	−	1.96851i	0.639715	−	0.0980585i
$404$		0			0
$405$		0			0
$406$	−5.40312	+	27.4478i	−0.268153	+	1.36221i
$407$	−10.8062			−0.535646
$408$		0			0
$409$		−	33.3020i		−	1.64668i	−0.567549	−	0.823340i	$-0.692108\pi$
$409$		−	33.3020i		−	1.64668i	0.567549	−	0.823340i	$-0.307892\pi$
$410$		0			0
$411$		0			0
$412$	−7.40312	−	3.03212i	−0.364726	−	0.149382i
$413$			13.1921i			0.649140i
$414$		0			0
$415$	−30.8062			−1.51222
$416$	13.9187	+	14.9087i	0.682420	+	0.730961i
$417$		0			0
$418$	−3.33496	+	16.9415i	−0.163118	+	0.828638i
$419$		−	13.6445i		−	0.666579i	−0.942824	−	0.333290i	$-0.891841\pi$
$419$		−	13.6445i		−	0.666579i	0.942824	−	0.333290i	$-0.108159\pi$
$420$		0			0
$421$	36.4472			1.77633			0.888165	−	0.459525i	$-0.151980\pi$
$421$	36.4472			1.77633			0.888165	+	0.459525i	$0.151980\pi$
$422$	−26.0920	−	5.13623i	−1.27014	−	0.250028i
$423$		0			0
$424$	−14.3180	−	9.44424i	−0.695346	−	0.458653i
$425$	26.8062			1.30029
$426$		0			0
$427$		0			0
$428$	−7.70156	+	18.8039i	−0.372269	+	0.908920i
$429$		0			0
$430$	6.55234	+	1.28984i	0.315982	+	0.0622014i
$431$			0.537693i			0.0258998i	0.999916	+	0.0129499i	$0.00412219\pi$
$431$			0.537693i			0.0258998i	−0.999916	+	0.0129499i	$0.995878\pi$
$432$		0			0
$433$	2.50781			0.120518			0.0602588	−	0.998183i	$-0.480807\pi$
$433$	2.50781			0.120518			0.0602588	+	0.998183i	$0.480807\pi$
$434$	2.73147	−	13.8758i	0.131115	−	0.666062i
$435$		0			0
$436$	−3.74255	−	1.53285i	−0.179235	−	0.0734100i
$437$	−19.0145			−0.909585
$438$		0			0
$439$	−14.8062			−0.706664			−0.353332	−	0.935498i	$-0.614951\pi$
$439$	−14.8062			−0.706664			−0.353332	+	0.935498i	$0.614951\pi$
$440$	12.4589	−	18.8885i	0.593956	−	0.900473i
$441$		0			0
$442$	29.0464	+	1.22838i	1.38160	+	0.0584282i
$443$		−	1.51606i		−	0.0720302i	−0.999351	−	0.0360151i	$-0.988534\pi$
$443$		−	1.51606i		−	0.0720302i	0.999351	−	0.0360151i	$-0.0114664\pi$
$444$		0			0
$445$		−	46.7041i		−	2.21399i
$446$	−21.5523	−	4.24260i	−1.02053	−	0.200893i
$447$		0			0
$448$	20.4088	−	8.73961i	0.964225	−	0.412908i
$449$			11.6817i			0.551294i	0.961259	+	0.275647i	$0.0888922\pi$
$449$			11.6817i			0.551294i	−0.961259	+	0.275647i	$0.911108\pi$
$450$		0			0
$451$		0			0
$452$	21.1047	+	8.64391i	0.992681	+	0.406575i
$453$		0			0
$454$	−1.89531	+	9.62817i	−0.0889515	+	0.451872i
$455$	−30.8062	+	4.72212i	−1.44422	+	0.221377i
$456$		0			0
$457$			3.31286i			0.154969i	0.996994	+	0.0774846i	$0.0246889\pi$
$457$			3.31286i			0.154969i	−0.996994	+	0.0774846i	$0.975311\pi$
$458$	−2.04453	+	10.3862i	−0.0955347	+	0.485315i
$459$		0			0
$460$	23.0588	+	9.44424i	1.07512	+	0.440340i
$461$	8.25161			0.384316			0.192158	−	0.981364i	$-0.438451\pi$
$461$	8.25161			0.384316			0.192158	+	0.981364i	$0.438451\pi$
$462$		0			0
$463$		−	11.3912i		−	0.529394i	−0.964332	−	0.264697i	$-0.914728\pi$
$463$		−	11.3912i		−	0.529394i	0.964332	−	0.264697i	$-0.0852719\pi$
$464$	−20.0000	+	20.3199i	−0.928477	+	0.943330i
$465$		0			0
$466$	1.94063	−	9.85835i	0.0898978	−	0.456679i
$467$			16.2242i			0.750767i	0.926870	+	0.375383i	$0.122489\pi$
$467$			16.2242i			0.750767i	−0.926870	+	0.375383i	$0.877511\pi$
$468$		0			0
$469$		−	33.5120i		−	1.54744i
$470$	−11.9942	−	2.36106i	−0.553249	−	0.108908i
$471$		0			0
$472$	−7.40312	+	11.2236i	−0.340756	+	0.516607i
$473$		−	3.89391i		−	0.179042i
$474$		0			0
$475$	22.3494			1.02546
$476$	11.9942	−	29.2845i	0.549751	−	1.34225i
$477$		0			0
$478$	16.9555	+	3.33770i	0.775525	+	0.152663i
$479$		−	28.8704i		−	1.31912i	−0.751650	−	0.659562i	$-0.770742\pi$
$479$		−	28.8704i		−	1.31912i	0.751650	−	0.659562i	$-0.229258\pi$
$480$		0			0
$481$	2.29844	+	14.9946i	0.104800	+	0.683694i
$482$	10.0000	+	1.96851i	0.455488	+	0.0896632i
$483$		0			0
$484$	8.14922	+	3.33770i	0.370419	+	0.151714i
$485$		−	12.1285i		−	0.550726i
$486$		0			0
$487$			26.3858i			1.19565i	0.801625	+	0.597827i	$0.203969\pi$
$487$			26.3858i			1.19565i	−0.801625	+	0.597827i	$0.796031\pi$
$488$		0			0
$489$		0			0
$490$	−0.596876	+	3.03212i	−0.0269641	+	0.136977i
$491$		−	3.64328i		−	0.164419i	−0.996615	−	0.0822095i	$-0.973802\pi$
$491$		−	3.64328i		−	0.164419i	0.996615	−	0.0822095i	$-0.0261977\pi$
$492$		0			0
$493$			40.6399i			1.83033i
$494$	24.2171	+	1.02415i	1.08958	+	0.0460787i
$495$		0			0
$496$	10.1107	−	10.2725i	0.453985	−	0.461247i
$497$	18.5078			0.830189
$498$		0			0
$499$	31.8567			1.42610			0.713050	−	0.701113i	$-0.247313\pi$
$499$	31.8567			1.42610			0.713050	+	0.701113i	$0.247313\pi$
$500$	1.72040	+	0.704630i	0.0769387	+	0.0315120i
$501$		0			0
$502$	−33.8788	−	6.66908i	−1.51209	−	0.297655i
$503$	25.6125			1.14200			0.571002	−	0.820948i	$-0.306555\pi$
$503$	25.6125			1.14200			0.571002	+	0.820948i	$0.306555\pi$
$504$		0			0
$505$		0			0
$506$	2.80625	−	14.2557i	0.124753	−	0.633743i
$507$		0			0
$508$	22.2094	+	9.09636i	0.985382	+	0.403586i
$509$	23.0588			1.02206			0.511031	−	0.859562i	$-0.329264\pi$
$509$	23.0588			1.02206			0.511031	+	0.859562i	$0.329264\pi$
$510$		0			0
$511$	41.6125			1.84083
$512$	22.2679	+	4.01749i	0.984112	+	0.177550i
$513$		0			0
$514$	−1.77759	+	9.03014i	−0.0784062	+	0.398302i
$515$	12.4589			0.549006
$516$		0			0
$517$			7.12785i			0.313482i
$518$	16.2015	+	3.18928i	0.711852	+	0.140129i
$519$		0			0
$520$	−28.8593	−	13.2703i	−1.26557	−	0.581942i
$521$	−13.1047			−0.574127			−0.287063	−	0.957912i	$-0.592679\pi$
$521$	−13.1047			−0.574127			−0.287063	+	0.957912i	$0.592679\pi$
$522$		0			0
$523$		−	4.09573i		−	0.179094i	−0.995983	−	0.0895469i	$-0.971458\pi$
$523$		−	4.09573i		−	0.179094i	0.995983	−	0.0895469i	$-0.0285419\pi$
$524$	14.2539	−	34.8019i	0.622685	−	1.52033i
$525$		0			0
$526$	4.37036	−	22.2014i	0.190557	−	0.968025i
$527$		−	20.5449i		−	0.894951i
$528$		0			0
$529$	−7.00000			−0.304348
$530$	26.2094	+	5.15934i	1.13846	+	0.224107i
$531$		0			0
$532$	10.0000	−	24.4157i	0.433555	−	1.05855i
$533$		0			0
$534$		0			0
$535$		−	31.6456i		−	1.36816i
$536$	18.8062	−	28.5114i	0.812306	−	1.23150i
$537$		0			0
$538$	−26.7198	−	5.25982i	−1.15197	−	0.226767i
$539$	1.80192			0.0776141
$540$		0			0
$541$	−8.25161			−0.354764			−0.177382	−	0.984142i	$-0.556763\pi$
$541$	−8.25161			−0.354764			−0.177382	+	0.984142i	$0.556763\pi$
$542$	−37.7617	−	7.43343i	−1.62200	−	0.319293i
$543$		0			0
$544$	26.6383	−	18.1839i	1.14211	−	0.779627i
$545$	6.29844			0.269795
$546$		0			0
$547$			42.1559i			1.80246i	0.433343	+	0.901229i	$0.357334\pi$
$547$			42.1559i			1.80246i	−0.433343	+	0.901229i	$0.642666\pi$
$548$	8.41464	−	20.5449i	0.359456	−	0.877635i
$549$		0			0
$550$	−3.29844	+	16.7560i	−0.140646	+	0.714479i
$551$			33.8831i			1.44347i
$552$		0			0
$553$			41.0898i			1.74732i
$554$	16.8293	+	3.31286i	0.715008	+	0.140750i
$555$		0			0
$556$	7.35859	−	17.9665i	0.312074	−	0.761949i
$557$	−12.2959			−0.520994			−0.260497	−	0.965475i	$-0.583886\pi$
$557$	−12.2959			−0.520994			−0.260497	+	0.965475i	$0.583886\pi$
$558$		0			0
$559$	−5.40312	+	0.828216i	−0.228528	+	0.0350298i
$560$	−24.2539	+	24.6419i	−1.02491	+	1.04131i
$561$		0			0
$562$	10.0000	+	1.96851i	0.421825	+	0.0830366i
$563$		−	27.9002i		−	1.17585i	−0.808914	−	0.587927i	$-0.799944\pi$
$563$		−	27.9002i		−	1.17585i	0.808914	−	0.587927i	$-0.200056\pi$
$564$		0			0
$565$	−35.5177			−1.49424
$566$	−5.68317	−	1.11874i	−0.238882	−	0.0470241i
$567$		0			0
$568$	15.7461	+	10.3862i	0.660691	+	0.435795i
$569$	−18.5078			−0.775888			−0.387944	−	0.921683i	$-0.626815\pi$
$569$	−18.5078			−0.775888			−0.387944	+	0.921683i	$0.626815\pi$
$570$		0			0
$571$		−	18.8039i		−	0.786918i	−0.919342	−	0.393459i	$-0.871278\pi$
$571$		−	18.8039i		−	0.786918i	0.919342	−	0.393459i	$-0.128722\pi$
$572$	−4.34192	+	18.0051i	−0.181545	+	0.752833i
$573$		0			0
$574$		0			0
$575$	−18.8062			−0.784275
$576$		0			0
$577$		−	25.5142i		−	1.06217i	−0.847318	−	0.531085i	$-0.821784\pi$
$577$		−	25.5142i		−	1.06217i	0.847318	−	0.531085i	$-0.178216\pi$
$578$	4.23592	−	21.5184i	0.176191	−	0.895047i
$579$		0			0
$580$	16.8293	−	41.0898i	0.698798	−	1.70616i
$581$		−	27.4478i		−	1.13873i
$582$		0			0
$583$		−	15.5756i		−	0.645077i
$584$	35.4031	+	23.3521i	1.46499	+	0.966315i
$585$		0			0
$586$	8.04453	−	40.8661i	0.332317	−	1.68816i
$587$	−15.0274			−0.620246			−0.310123	−	0.950696i	$-0.600370\pi$
$587$	−15.0274			−0.620246			−0.310123	+	0.950696i	$0.600370\pi$
$588$		0			0
$589$		−	17.1291i		−	0.705793i
$590$	4.04429	−	20.5449i	0.166501	−	0.845821i
$591$		0			0
$592$	11.9942	+	11.8053i	0.492957	+	0.485195i
$593$			7.78781i			0.319807i	0.987133	+	0.159904i	$0.0511183\pi$
$593$			7.78781i			0.319807i	−0.987133	+	0.159904i	$0.948882\pi$
$594$		0			0
$595$			49.2838i			2.02044i
$596$	−25.0809	−	10.2725i	−1.02735	−	0.420776i
$597$		0			0
$598$	−20.3779	−	0.861787i	−0.833313	−	0.0352411i
$599$	20.0000			0.817178			0.408589	−	0.912719i	$-0.366021\pi$
$599$	20.0000			0.817178			0.408589	+	0.912719i	$0.366021\pi$
$600$		0			0
$601$	−6.89531			−0.281266			−0.140633	−	0.990062i	$-0.544914\pi$
$601$	−6.89531			−0.281266			−0.140633	+	0.990062i	$0.544914\pi$
$602$	−1.14922	+	5.83802i	−0.0468387	+	0.237940i
$603$		0			0
$604$	10.5183	−	25.6811i	0.427984	−	1.04495i
$605$	−13.7146			−0.557576
$606$		0			0
$607$	−12.0000			−0.487065			−0.243532	−	0.969893i	$-0.578306\pi$
$607$	−12.0000			−0.487065			−0.243532	+	0.969893i	$0.578306\pi$
$608$	22.2094	−	15.1606i	0.900709	−	0.614844i
$609$		0			0
$610$		0			0
$611$	9.89049	−	1.51606i	0.400127	−	0.0613332i
$612$		0			0
$613$	−34.0990			−1.37725			−0.688623	−	0.725119i	$-0.741785\pi$
$613$	−34.0990			−1.37725			−0.688623	+	0.725119i	$0.741785\pi$
$614$	−8.10469	+	41.1717i	−0.327079	+	1.66155i
$615$		0			0
$616$	16.8293	+	11.1007i	0.678071	+	0.447259i
$617$		−	10.5196i		−	0.423504i	−0.977323	−	0.211752i	$-0.932083\pi$
$617$		−	10.5196i		−	0.423504i	0.977323	−	0.211752i	$-0.0679170\pi$
$618$		0			0
$619$	31.8567			1.28043			0.640214	−	0.768197i	$-0.278846\pi$
$619$	31.8567			1.28043			0.640214	+	0.768197i	$0.278846\pi$
$620$	−8.50781	+	20.7724i	−0.341682	+	0.834239i
$621$		0			0
$622$	−3.27777	+	16.6510i	−0.131427	+	0.667645i
$623$	41.6125			1.66717
$624$		0			0
$625$	−26.4031			−1.05612
$626$	−6.69424	+	34.0067i	−0.267556	+	1.35918i
$627$		0			0
$628$	−0.806248	+	1.96851i	−0.0321728	+	0.0785521i
$629$	23.9883			0.956477
$630$		0			0
$631$		−	0.537693i		−	0.0214052i	−0.999943	−	0.0107026i	$-0.996593\pi$
$631$		−	0.537693i		−	0.0214052i	0.999943	−	0.0107026i	$-0.00340681\pi$
$632$	−23.0588	+	34.9585i	−0.917228	+	1.39057i
$633$		0			0
$634$	−6.89531	+	35.0281i	−0.273848	+	1.39114i
$635$	−37.3768			−1.48325
$636$		0			0
$637$	−0.383260	−	2.50031i	−0.0151853	−	0.0990661i
$638$	−25.4031	−	5.00063i	−1.00572	−	0.197977i
$639$		0			0
$640$	−34.4633	+	7.35408i	−1.36228	+	0.290695i
$641$	−24.5969			−0.971518			−0.485759	−	0.874093i	$-0.661457\pi$
$641$	−24.5969			−0.971518			−0.485759	+	0.874093i	$0.661457\pi$
$642$		0			0
$643$	36.9935			1.45888			0.729441	−	0.684043i	$-0.239780\pi$
$643$	36.9935			1.45888			0.729441	+	0.684043i	$0.239780\pi$
$644$	−8.41464	+	20.5449i	−0.331583	+	0.809583i
$645$		0			0
$646$	7.40312	−	37.6078i	0.291272	−	1.47966i
$647$	17.1938			0.675956			0.337978	−	0.941154i	$-0.390257\pi$
$647$	17.1938			0.675956			0.337978	+	0.941154i	$0.390257\pi$
$648$		0			0
$649$	−12.2094			−0.479260
$650$	23.9519	+	1.01294i	0.939473	+	0.0397306i
$651$		0			0
$652$	−18.3051	−	7.49729i	−0.716885	−	0.293617i
$653$			19.2563i			0.753558i	0.926303	+	0.376779i	$0.122968\pi$
$653$			19.2563i			0.753558i	−0.926303	+	0.376779i	$0.877032\pi$
$654$		0			0
$655$			58.5691i			2.28848i
$656$		0			0
$657$		0			0
$658$	2.10366	−	10.6866i	0.0820093	−	0.416606i
$659$		−	8.03275i		−	0.312912i	−0.987685	−	0.156456i	$-0.949993\pi$
$659$		−	8.03275i		−	0.312912i	0.987685	−	0.156456i	$-0.0500069\pi$
$660$		0			0
$661$	1.85911			0.0723109			0.0361555	−	0.999346i	$-0.488489\pi$
$661$	1.85911			0.0723109			0.0361555	+	0.999346i	$0.488489\pi$
$662$	−1.50781	+	7.65966i	−0.0586027	+	0.297701i
$663$		0			0
$664$	15.4031	−	23.3521i	0.597757	−	0.906236i
$665$			41.0898i			1.59340i
$666$		0			0
$667$		−	28.5114i		−	1.10397i
$668$	5.68317	−	13.8758i	0.219889	−	0.536873i
$669$		0			0
$670$	−10.2738	+	52.1905i	−0.396910	+	2.01630i
$671$		0			0
$672$		0			0
$673$	−0.0890652			−0.00343321			−0.00171660	−	0.999999i	$-0.500546\pi$
$673$	−0.0890652			−0.00343321			−0.00171660	+	0.999999i	$0.500546\pi$
$674$	3.90558	−	19.8403i	0.150437	−	0.764219i
$675$		0			0
$676$	25.9072	+	2.19517i	0.996429	+	0.0844297i
$677$			18.1927i			0.699203i	0.936898	+	0.349602i	$0.113683\pi$
$677$			18.1927i			0.699203i	−0.936898	+	0.349602i	$0.886317\pi$
$678$		0			0
$679$	10.8062			0.414706
$680$	−27.6570	+	41.9297i	−1.06060	+	1.60793i
$681$		0			0
$682$	12.8422	+	2.52800i	0.491753	+	0.0968020i
$683$	15.7939			0.604336			0.302168	−	0.953255i	$-0.402290\pi$
$683$	15.7939			0.604336			0.302168	+	0.953255i	$0.402290\pi$
$684$		0			0
$685$			34.5756i			1.32107i
$686$	24.2539	+	4.77440i	0.926018	+	0.182288i
$687$		0			0
$688$	−4.25391	+	4.32196i	−0.162179	+	0.164773i
$689$	−21.6125	+	3.31286i	−0.823371	+	0.126210i
$690$		0			0
$691$	2.56844			0.0977080			0.0488540	−	0.998806i	$-0.484443\pi$
$691$	2.56844			0.0977080			0.0488540	+	0.998806i	$0.484443\pi$
$692$	4.59688	−	11.2236i	0.174747	−	0.426657i
$693$		0			0
$694$	9.26268	+	1.82337i	0.351607	+	0.0692141i
$695$			30.2363i			1.14693i
$696$		0			0
$697$		0			0
$698$	0.939846	−	4.77440i	0.0355737	−	0.180714i
$699$		0			0
$700$	9.89049	−	24.1483i	0.373826	−	0.912720i
$701$		−	13.1921i		−	0.498258i	−0.968470	−	0.249129i	$-0.919856\pi$
$701$		−	13.1921i		−	0.498258i	0.968470	−	0.249129i	$-0.0801444\pi$
$702$		0			0
$703$	20.0000			0.754314
$704$	8.08857	+	18.8885i	0.304850	+	0.711887i
$705$		0			0
$706$	−46.2094	−	9.09636i	−1.73911	−	0.342346i
$707$		0			0
$708$		0			0
$709$	−39.2359			−1.47354			−0.736768	−	0.676146i	$-0.763649\pi$
$709$	−39.2359			−1.47354			−0.736768	+	0.676146i	$0.763649\pi$
$710$	−28.8234	−	5.67392i	−1.08172	−	0.212939i
$711$		0			0
$712$	35.4031	+	23.3521i	1.32679	+	0.875155i
$713$			14.4135i			0.539791i
$714$		0			0
$715$	−4.37036	−	28.5114i	−0.163442	−	1.06627i
$716$	9.65703	−	23.5783i	0.360900	−	0.881162i
$717$		0			0
$718$	−25.8062	−	5.07999i	−0.963081	−	0.189583i
$719$	5.19375			0.193694			0.0968471	−	0.995299i	$-0.469124\pi$
$719$	5.19375			0.193694			0.0968471	+	0.995299i	$0.469124\pi$
$720$		0			0
$721$			11.1007i			0.413411i
$722$	0.982477	−	4.99097i	0.0365640	−	0.185745i
$723$		0			0
$724$	−10.0000	+	24.4157i	−0.371647	+	0.907401i
$725$			33.5120i			1.24461i
$726$		0			0
$727$	42.8062			1.58760			0.793798	−	0.608182i	$-0.208101\pi$
$727$	42.8062			1.58760			0.793798	+	0.608182i	$0.208101\pi$
$728$	11.8236	−	25.7131i	0.438212	−	0.952992i
$729$		0			0
$730$	−64.8059	−	12.7571i	−2.39857	−	0.472162i
$731$			8.64391i			0.319707i
$732$		0			0
$733$	−19.9440			−0.736649			−0.368325	−	0.929697i	$-0.620069\pi$
$733$	−19.9440			−0.736649			−0.368325	+	0.929697i	$0.620069\pi$
$734$	2.18518	−	11.1007i	0.0806564	−	0.409733i
$735$		0			0
$736$	−18.6884	+	12.7571i	−0.688864	+	0.470233i
$737$	31.0156			1.14248
$738$		0			0
$739$	−6.17228			−0.227051			−0.113525	−	0.993535i	$-0.536214\pi$
$739$	−6.17228			−0.227051			−0.113525	+	0.993535i	$0.536214\pi$
$740$	−24.2539	−	9.93375i	−0.891591	−	0.365172i
$741$		0			0
$742$	−4.59688	+	23.3521i	−0.168757	+	0.857281i
$743$		−	39.9711i		−	1.46640i	−0.680014	−	0.733199i	$-0.738026\pi$
$743$		−	39.9711i		−	1.46640i	0.680014	−	0.733199i	$-0.261974\pi$
$744$		0			0
$745$	42.2094			1.54643
$746$	−26.7198	−	5.25982i	−0.978281	−	0.192576i
$747$		0			0
$748$	27.1030	+	11.1007i	0.990985	+	0.405881i
$749$	28.1956			1.03025
$750$		0			0
$751$	−32.4187			−1.18298			−0.591488	−	0.806313i	$-0.701459\pi$
$751$	−32.4187			−1.18298			−0.591488	+	0.806313i	$0.701459\pi$
$752$	7.78683	−	7.91140i	0.283957	−	0.288499i
$753$		0			0
$754$	−1.53567	+	36.3126i	−0.0559259	+	1.32243i
$755$			43.2196i			1.57292i
$756$		0			0
$757$			34.5756i			1.25667i	0.777942	+	0.628337i	$0.216264\pi$
$757$			34.5756i			1.25667i	−0.777942	+	0.628337i	$0.783736\pi$
$758$	1.29844	−	6.59605i	0.0471614	−	0.239579i
$759$		0			0
$760$	−23.0588	+	34.9585i	−0.836429	+	1.26808i
$761$		−	26.6763i		−	0.967015i	−0.875340	−	0.483508i	$-0.839363\pi$
$761$		−	26.6763i		−	0.967015i	0.875340	−	0.483508i	$-0.160637\pi$
$762$		0			0
$763$			5.61179i			0.203160i
$764$	−5.19375	−	2.12722i	−0.187903	−	0.0769601i
$765$		0			0
$766$	1.55234	+	0.305580i	0.0560884	+	0.0110411i
$767$	2.59688	+	16.9415i	0.0937677	+	0.611723i
$768$		0			0
$769$		−	26.0953i		−	0.941019i	−0.882395	−	0.470510i	$-0.844070\pi$
$769$		−	26.0953i		−	0.941019i	0.882395	−	0.470510i	$-0.155930\pi$
$770$	−30.8062	−	6.06424i	−1.11018	−	0.218540i
$771$		0			0
$772$	−11.3663	+	27.7517i	−0.409084	+	0.998805i
$773$	−42.3506			−1.52325			−0.761623	−	0.648020i	$-0.775597\pi$
$773$	−42.3506			−1.52325			−0.761623	+	0.648020i	$0.775597\pi$
$774$		0			0
$775$		−	16.9415i		−	0.608558i
$776$	9.19375	+	6.06424i	0.330036	+	0.217694i
$777$		0			0
$778$	−21.2568	−	4.18443i	−0.762095	−	0.150019i
$779$		0			0
$780$		0			0
$781$			17.1291i			0.612928i
$782$	−6.22947	+	31.6456i	−0.222765	+	1.13164i
$783$		0			0
$784$	−2.00000	−	1.96851i	−0.0714286	−	0.0703039i
$785$		−	3.31286i		−	0.118241i
$786$		0			0
$787$	−40.5974			−1.44714			−0.723570	−	0.690251i	$-0.757500\pi$
$787$	−40.5974			−1.44714			−0.723570	+	0.690251i	$0.757500\pi$
$788$	7.78683	+	3.18928i	0.277394	+	0.113613i
$789$		0			0
$790$	12.5969	−	63.9919i	0.448177	−	2.27673i
$791$		−	31.6456i		−	1.12519i
$792$		0			0
$793$		0			0
$794$	1.70156	−	8.64391i	0.0603862	−	0.306761i
$795$		0			0
$796$		0			0
$797$			53.8320i			1.90683i	0.301668	+	0.953413i	$0.402457\pi$
$797$			53.8320i			1.90683i	−0.301668	+	0.953413i	$0.597543\pi$
$798$		0			0
$799$		−	15.8228i		−	0.559770i
$800$	21.9662	−	14.9946i	0.776621	−	0.530139i
$801$		0			0
$802$	10.0000	+	1.96851i	0.353112	+	0.0695105i
$803$			38.5127i			1.35908i
$804$		0			0
$805$		−	34.5756i		−	1.21863i
$806$	0.776337	−	18.3573i	0.0273453	−	0.646609i
$807$		0			0
$808$		0			0
$809$	8.50781			0.299119			0.149559	−	0.988753i	$-0.452214\pi$
$809$	8.50781			0.299119			0.149559	+	0.988753i	$0.452214\pi$
$810$		0			0
$811$	31.0901			1.09172			0.545861	−	0.837876i	$-0.316203\pi$
$811$	31.0901			1.09172			0.545861	+	0.837876i	$0.316203\pi$
$812$	36.6103	+	14.9946i	1.28477	+	0.526207i
$813$		0			0
$814$	−2.95170	+	14.9946i	−0.103457	+	0.525560i
$815$	30.8062			1.07910
$816$		0			0
$817$			7.20677i			0.252133i
$818$	−46.2094	−	9.09636i	−1.61567	−	0.318047i
$819$		0			0
$820$		0			0
$821$	−17.4328			−0.608408			−0.304204	−	0.952607i	$-0.598390\pi$
$821$	−17.4328			−0.608408			−0.304204	+	0.952607i	$0.598390\pi$
$822$		0			0
$823$	−25.6125			−0.892796			−0.446398	−	0.894835i	$-0.647293\pi$
$823$	−25.6125			−0.892796			−0.446398	+	0.894835i	$0.647293\pi$
$824$	−6.22947	+	9.44424i	−0.217014	+	0.329006i
$825$		0			0
$826$	18.3051	+	3.60338i	0.636917	+	0.125378i
$827$	48.6860			1.69298			0.846488	−	0.532408i	$-0.178713\pi$
$827$	48.6860			1.69298			0.846488	+	0.532408i	$0.178713\pi$
$828$		0			0
$829$		−	16.3829i		−	0.569002i	−0.958676	−	0.284501i	$-0.908172\pi$
$829$		−	16.3829i		−	0.569002i	0.958676	−	0.284501i	$-0.0918280\pi$
$830$	−8.41464	+	42.7463i	−0.292077	+	1.48374i
$831$		0			0
$832$	24.4890	−	15.2411i	0.849002	−	0.528389i
$833$	−4.00000			−0.138592
$834$		0			0
$835$			23.3521i			0.808131i
$836$	22.5969	+	9.25507i	0.781529	+	0.320093i
$837$		0			0
$838$	−18.9330	−	3.72697i	−0.654028	−	0.128746i
$839$		−	18.5980i		−	0.642073i	−0.947067	−	0.321037i	$-0.895969\pi$
$839$		−	18.5980i		−	0.642073i	0.947067	−	0.321037i	$-0.104031\pi$
$840$		0			0
$841$	−21.8062			−0.751940
$842$	9.95547	−	50.5736i	0.343088	−	1.74288i
$843$		0			0
$844$	−14.2539	+	34.8019i	−0.490640	+	1.19793i
$845$	−38.6324	+	12.1285i	−1.32900	+	0.417232i
$846$		0			0
$847$		−	12.2194i		−	0.419864i
$848$	−17.0156	+	17.2878i	−0.584319	+	0.593666i
$849$		0			0
$850$	7.32206	−	37.1959i	0.251144	−	1.27581i
$851$	−16.8293			−0.576901
$852$		0			0
$853$	−28.0326			−0.959818			−0.479909	−	0.877318i	$-0.659330\pi$
$853$	−28.0326			−0.959818			−0.479909	+	0.877318i	$0.659330\pi$
$854$		0			0
$855$		0			0
$856$	23.9883	+	15.8228i	0.819904	+	0.540812i
$857$	−12.8062			−0.437453			−0.218727	−	0.975786i	$-0.570190\pi$
$857$	−12.8062			−0.437453			−0.218727	+	0.975786i	$0.570190\pi$
$858$		0			0
$859$		−	18.3514i		−	0.626143i	−0.949730	−	0.313071i	$-0.898642\pi$
$859$		−	18.3514i		−	0.626143i	0.949730	−	0.313071i	$-0.101358\pi$
$860$	3.57951	−	8.73961i	0.122060	−	0.298018i
$861$		0			0
$862$	0.746095	+	0.146869i	0.0254121	+	0.00500239i
$863$			22.7390i			0.774046i	0.922070	+	0.387023i	$0.126497\pi$
$863$			22.7390i			0.774046i	−0.922070	+	0.387023i	$0.873503\pi$
$864$		0			0
$865$			18.8885i			0.642228i
$866$	0.685002	−	3.47980i	0.0232773	−	0.118248i
$867$		0			0
$868$	−18.5078	−	7.58030i	−0.628196	−	0.257292i
$869$	−38.0289			−1.29004
$870$		0			0
$871$	−6.59688	−	43.0368i	−0.223527	−	1.45825i
$872$	−3.14922	+	4.77440i	−0.106646	+	0.161682i
$873$		0			0
$874$	−5.19375	+	26.3842i	−0.175681	+	0.892458i
$875$		−	2.57967i		−	0.0872088i
$876$		0			0
$877$	−43.3288			−1.46311			−0.731556	−	0.681782i	$-0.761205\pi$
$877$	−43.3288			−1.46311			−0.731556	+	0.681782i	$0.761205\pi$
$878$	−4.04429	+	20.5449i	−0.136488	+	0.693357i
$879$		0			0
$880$	−22.8062	−	22.4472i	−0.768798	−	0.756694i
$881$	−35.7016			−1.20282			−0.601408	−	0.798942i	$-0.705393\pi$
$881$	−35.7016			−1.20282			−0.601408	+	0.798942i	$0.705393\pi$
$882$		0			0
$883$			23.9632i			0.806427i	0.915106	+	0.403213i	$0.132107\pi$
$883$			23.9632i			0.806427i	−0.915106	+	0.403213i	$0.867893\pi$
$884$	9.63844	−	39.9688i	0.324176	−	1.34430i
$885$		0			0
$886$	−2.10366	−	0.414108i	−0.0706739	−	0.0139122i
$887$	51.2250			1.71997			0.859983	−	0.510322i	$-0.170474\pi$
$887$	51.2250			1.71997			0.859983	+	0.510322i	$0.170474\pi$
$888$		0			0
$889$		−	33.3020i		−	1.11691i
$890$	−64.8059	−	12.7571i	−2.17230	−	0.427619i
$891$		0			0
$892$	−11.7739	+	28.7468i	−0.394220	+	0.962515i
$893$		−	13.1921i		−	0.441456i
$894$		0			0
$895$			39.6806i			1.32638i
$896$	−6.55234	−	30.7061i	−0.218898	−	1.02582i
$897$		0			0
$898$	16.2094	+	3.19083i	0.540914	+	0.106479i
$899$	25.6844			0.856622
$900$		0			0
$901$			34.5756i			1.15188i
$902$		0			0
$903$		0			0
$904$	17.7588	−	26.9235i	0.590650	−	0.895461i
$905$		−	41.0898i		−	1.36587i
$906$		0			0
$907$		−	55.5067i		−	1.84307i	−0.388294	−	0.921536i	$-0.626935\pi$
$907$		−	55.5067i		−	1.84307i	0.388294	−	0.921536i	$-0.373065\pi$
$908$	12.8422	+	5.25982i	0.426183	+	0.174553i
$909$		0			0
$910$	−1.86230	+	44.0361i	−0.0617347	+	1.45978i
$911$	−32.0000			−1.06021			−0.530104	−	0.847933i	$-0.677847\pi$
$911$	−32.0000			−1.06021			−0.530104	+	0.847933i	$0.677847\pi$
$912$		0			0
$913$	25.4031			0.840721
$914$	4.59688	+	0.904899i	0.152051	+	0.0299314i
$915$		0			0
$916$	13.8533	+	5.67392i	0.457725	+	0.187472i
$917$	−52.1839			−1.72327
$918$		0			0
$919$	40.0000			1.31948			0.659739	−	0.751495i	$-0.270667\pi$
$919$	40.0000			1.31948			0.659739	+	0.751495i	$0.270667\pi$
$920$	19.4031	−	29.4163i	0.639702	−	0.969827i
$921$		0			0
$922$	2.25391	−	11.4498i	0.0742284	−	0.377079i
$923$	23.7681	−	3.64328i	0.782336	−	0.119920i
$924$		0			0
$925$	19.7810			0.650395
$926$	−15.8062	−	3.11148i	−0.519426	−	0.102249i
$927$		0			0
$928$	22.7327	+	33.3020i	0.746237	+	1.09319i
$929$			11.6817i			0.383265i	0.981467	+	0.191632i	$0.0613781\pi$
$929$			11.6817i			0.383265i	−0.981467	+	0.191632i	$0.938622\pi$
$930$		0			0
$931$	−3.33496			−0.109299
$932$	−13.1492	−	5.38557i	−0.430717	−	0.176410i
$933$		0			0
$934$	22.5125	+	4.43160i	0.736630	+	0.145006i
$935$	−45.6125			−1.49169
$936$		0			0
$937$	12.8062			0.418362			0.209181	−	0.977877i	$-0.432920\pi$
$937$	12.8062			0.418362			0.209181	+	0.977877i	$0.432920\pi$
$938$	−46.5008	−	9.15372i	−1.51830	−	0.298880i
$939$		0			0
$940$	−6.55234	+	15.9980i	−0.213714	+	0.521797i
$941$	25.8474			0.842602			0.421301	−	0.906921i	$-0.361574\pi$
$941$	25.8474			0.842602			0.421301	+	0.906921i	$0.361574\pi$
$942$		0			0
$943$		0			0
$944$	13.5515	+	13.3382i	0.441064	+	0.434120i
$945$		0			0
$946$	−5.40312	−	1.06361i	−0.175671	−	0.0345810i
$947$	12.0757			0.392407			0.196203	−	0.980563i	$-0.437139\pi$
$947$	12.0757			0.392407			0.196203	+	0.980563i	$0.437139\pi$
$948$		0			0
$949$	53.4396	−	8.19146i	1.73472	−	0.265906i
$950$	6.10469	−	31.0117i	0.198062	−	1.00615i
$951$		0			0
$952$	−37.3586	−	24.6419i	−1.21080	−	0.798648i
$953$	51.5234			1.66901			0.834504	−	0.551002i	$-0.185754\pi$
$953$	51.5234			1.66901			0.834504	+	0.551002i	$0.185754\pi$
$954$		0			0
$955$	8.74071			0.282843
$956$	9.26268	−	22.6155i	0.299577	−	0.731436i
$957$		0			0
$958$	−40.0602	−	7.88588i	−1.29428	−	0.254781i
$959$	−30.8062			−0.994786
$960$		0			0
$961$	18.0156			0.581149
$962$	21.4341	+	0.906454i	0.691062	+	0.0292252i
$963$		0			0
$964$	5.46295	−	13.3382i	0.175950	−	0.429593i
$965$		−	46.7041i		−	1.50346i
$966$		0			0
$967$			51.0718i			1.64236i	0.570671	+	0.821179i	$0.306683\pi$
$967$			51.0718i			1.64236i	−0.570671	+	0.821179i	$0.693317\pi$
$968$	6.85728	−	10.3960i	0.220401	−	0.334142i
$969$		0			0
$970$	−16.8293	−	3.31286i	−0.540356	−	0.106370i
$971$		−	30.0275i		−	0.963627i	−0.876274	−	0.481814i	$-0.839978\pi$
$971$		−	30.0275i		−	0.963627i	0.876274	−	0.481814i	$-0.160022\pi$
$972$		0			0
$973$	−26.9400			−0.863657
$974$	36.6125	+	7.20721i	1.17314	+	0.230934i
$975$		0			0
$976$		0			0
$977$			18.3074i			0.585707i	0.956157	+	0.292854i	$0.0946048\pi$
$977$			18.3074i			0.585707i	−0.956157	+	0.292854i	$0.905395\pi$
$978$		0			0
$979$			38.5127i			1.23087i
$980$	4.04429	+	1.65643i	0.129190	+	0.0529127i
$981$		0			0
$982$	−5.05536	−	0.995152i	−0.161323	−	0.0317566i
$983$			29.9458i			0.955123i	0.878598	+	0.477562i	$0.158479\pi$
$983$			29.9458i			0.955123i	−0.878598	+	0.477562i	$0.841521\pi$
$984$		0			0
$985$	−13.1047			−0.417550
$986$	56.3913	+	11.1007i	1.79586	+	0.353518i
$987$		0			0
$988$	8.03594	−	33.3236i	0.255657	−	1.06016i
$989$		−	6.06424i		−	0.192832i
$990$		0			0
$991$	41.6125			1.32186			0.660932	−	0.750446i	$-0.270161\pi$
$991$	41.6125			1.32186			0.660932	+	0.750446i	$0.270161\pi$
$992$	−11.4922	−	16.8354i	−0.364877	−	0.534524i
$993$		0			0
$994$	5.05536	−	25.6811i	0.160346	−	0.814557i
$995$		0			0
$996$		0			0
$997$		−	40.6399i		−	1.28708i	−0.765413	−	0.643539i	$-0.777465\pi$
$997$		−	40.6399i		−	1.28708i	0.765413	−	0.643539i	$-0.222535\pi$
$998$	8.70156	−	44.2038i	0.275443	−	1.39925i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.m.f.181.5		8
3.2	odd	2		104.2.e.c.77.4	yes	8
4.3	odd	2		3744.2.m.g.1585.7		8
8.3	odd	2		3744.2.m.g.1585.1		8
8.5	even	2	inner	936.2.m.f.181.3		8
12.11	even	2		416.2.e.c.337.3		8
13.12	even	2	inner	936.2.m.f.181.4		8
24.5	odd	2		104.2.e.c.77.6	yes	8
24.11	even	2		416.2.e.c.337.6		8
39.38	odd	2		104.2.e.c.77.5	yes	8
52.51	odd	2		3744.2.m.g.1585.2		8
104.51	odd	2		3744.2.m.g.1585.8		8
104.77	even	2	inner	936.2.m.f.181.6		8
156.155	even	2		416.2.e.c.337.4		8
312.77	odd	2		104.2.e.c.77.3	✓	8
312.155	even	2		416.2.e.c.337.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.e.c.77.3	✓	8	312.77	odd	2
104.2.e.c.77.4	yes	8	3.2	odd	2
104.2.e.c.77.5	yes	8	39.38	odd	2
104.2.e.c.77.6	yes	8	24.5	odd	2
416.2.e.c.337.3		8	12.11	even	2
416.2.e.c.337.4		8	156.155	even	2
416.2.e.c.337.5		8	312.155	even	2
416.2.e.c.337.6		8	24.11	even	2
936.2.m.f.181.3		8	8.5	even	2	inner
936.2.m.f.181.4		8	13.12	even	2	inner
936.2.m.f.181.5		8	1.1	even	1	trivial
936.2.m.f.181.6		8	104.77	even	2	inner
3744.2.m.g.1585.1		8	8.3	odd	2
3744.2.m.g.1585.2		8	52.51	odd	2
3744.2.m.g.1585.7		8	4.3	odd	2
3744.2.m.g.1585.8		8	104.51	odd	2

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:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.m (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.273147 - 1.38758i) q^{2} +(-1.85078 - 0.758030i) q^{4} +3.11473 q^{5} +2.77517i q^{7} +(-1.55737 + 2.36106i) q^{8} +(0.850781 - 4.32196i) q^{10} -2.56844 q^{11} +(0.546295 + 3.56393i) q^{13} +(3.85078 + 0.758030i) q^{14} +(2.85078 + 2.80590i) q^{16} +5.70156 q^{17} +4.75362 q^{19} +(-5.76469 - 2.36106i) q^{20} +(-0.701562 + 3.56393i) q^{22} -4.00000 q^{23} +4.70156 q^{25} +(5.09447 + 0.215447i) q^{26} +(2.10366 - 5.13623i) q^{28} +7.12785i q^{29} -3.60338i q^{31} +(4.67210 - 3.18928i) q^{32} +(1.55737 - 7.91140i) q^{34} +8.64391i q^{35} +4.20732 q^{37} +(1.29844 - 6.59605i) q^{38} +(-4.85078 + 7.35408i) q^{40} +1.51606i q^{43} +(4.75362 + 1.94695i) q^{44} +(-1.09259 + 5.55034i) q^{46} -2.77517i q^{47} -0.701562 q^{49} +(1.28422 - 6.52381i) q^{50} +(1.69049 - 7.01015i) q^{52} +6.06424i q^{53} -8.00000 q^{55} +(-6.55234 - 4.32196i) q^{56} +(9.89049 + 1.94695i) q^{58} +4.75362 q^{59} +(-5.00000 - 0.984255i) q^{62} +(-3.14922 - 7.35408i) q^{64} +(1.70156 + 11.1007i) q^{65} -12.0757 q^{67} +(-10.5523 - 4.32196i) q^{68} +(11.9942 + 2.36106i) q^{70} -6.66908i q^{71} -14.9946i q^{73} +(1.14922 - 5.83802i) q^{74} +(-8.79790 - 3.60338i) q^{76} -7.12785i q^{77} +14.8062 q^{79} +(8.87942 + 8.73961i) q^{80} -9.89049 q^{83} +17.7588 q^{85} +(2.10366 + 0.414108i) q^{86} +(4.00000 - 6.06424i) q^{88} -14.9946i q^{89} +(-9.89049 + 1.51606i) q^{91} +(7.40312 + 3.03212i) q^{92} +(-3.85078 - 0.758030i) q^{94} +14.8062 q^{95} -3.89391i q^{97} +(-0.191630 + 0.973477i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{4} - 6 q^{10} + 18 q^{14} + 10 q^{16} + 20 q^{17} + 20 q^{22} - 32 q^{23} + 12 q^{25} + 14 q^{26} + 36 q^{38} - 26 q^{40} + 20 q^{49} - 4 q^{52} - 64 q^{55} - 14 q^{56} - 40 q^{62} - 38 q^{64}+ \cdots + 16 q^{95}+O(q^{100}) \) 8 * q - 2 * q^4 - 6 * q^10 + 18 * q^14 + 10 * q^16 + 20 * q^17 + 20 * q^22 - 32 * q^23 + 12 * q^25 + 14 * q^26 + 36 * q^38 - 26 * q^40 + 20 * q^49 - 4 * q^52 - 64 * q^55 - 14 * q^56 - 40 * q^62 - 38 * q^64 - 12 * q^65 - 46 * q^68 + 22 * q^74 + 16 * q^79 + 32 * q^88 + 8 * q^92 - 18 * q^94 + 16 * q^95

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