LMFDB - Embedded newform 693.2.m.a.190.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(64,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("693.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.m (of order $5$, degree $4$, 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:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 231)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			190.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	693.190
Dual form			693.2.m.a.631.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.80902 + 1.31433i) q^{2} +(0.927051 - 2.85317i) q^{4} +(1.30902 + 0.951057i) q^{5} +(0.309017 - 0.951057i) q^{7} +(0.690983 + 2.12663i) q^{8} +O(q^{10})$	\(q+(-1.80902 + 1.31433i) q^{2} +(0.927051 - 2.85317i) q^{4} +(1.30902 + 0.951057i) q^{5} +(0.309017 - 0.951057i) q^{7} +(0.690983 + 2.12663i) q^{8} -3.61803 q^{10} +(-0.809017 - 3.21644i) q^{11} +(1.00000 - 0.726543i) q^{13} +(0.690983 + 2.12663i) q^{14} +(0.809017 + 0.587785i) q^{16} +(-1.50000 - 1.08981i) q^{17} +(-1.19098 - 3.66547i) q^{19} +(3.92705 - 2.85317i) q^{20} +(5.69098 + 4.75528i) q^{22} -6.61803 q^{23} +(-0.736068 - 2.26538i) q^{25} +(-0.854102 + 2.62866i) q^{26} +(-2.42705 - 1.76336i) q^{28} +(1.85410 - 5.70634i) q^{29} +(-6.54508 + 4.75528i) q^{31} -6.70820 q^{32} +4.14590 q^{34} +(1.30902 - 0.951057i) q^{35} +(0.736068 - 2.26538i) q^{37} +(6.97214 + 5.06555i) q^{38} +(-1.11803 + 3.44095i) q^{40} +(-2.97214 - 9.14729i) q^{41} -3.70820 q^{43} +(-9.92705 - 0.673542i) q^{44} +(11.9721 - 8.69827i) q^{46} +(1.38197 + 4.25325i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(4.30902 + 3.13068i) q^{50} +(-1.14590 - 3.52671i) q^{52} +(9.09017 - 6.60440i) q^{53} +(2.00000 - 4.97980i) q^{55} +2.23607 q^{56} +(4.14590 + 12.7598i) q^{58} +(0.381966 - 1.17557i) q^{59} +(5.59017 - 17.2048i) q^{62} +(10.5172 - 7.64121i) q^{64} +2.00000 q^{65} +(-4.50000 + 3.26944i) q^{68} +(-1.11803 + 3.44095i) q^{70} +(10.4721 + 7.60845i) q^{71} +(0.0901699 - 0.277515i) q^{73} +(1.64590 + 5.06555i) q^{74} -11.5623 q^{76} +(-3.30902 - 0.224514i) q^{77} +(8.09017 - 5.87785i) q^{79} +(0.500000 + 1.53884i) q^{80} +(17.3992 + 12.6412i) q^{82} +(6.09017 + 4.42477i) q^{83} +(-0.927051 - 2.85317i) q^{85} +(6.70820 - 4.87380i) q^{86} +(6.28115 - 3.94298i) q^{88} -3.38197 q^{89} +(-0.381966 - 1.17557i) q^{91} +(-6.13525 + 18.8824i) q^{92} +(-8.09017 - 5.87785i) q^{94} +(1.92705 - 5.93085i) q^{95} +(4.85410 - 3.52671i) q^{97} +2.23607 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 5 q^{2} - 3 q^{4} + 3 q^{5} - q^{7} + 5 q^{8}+O(q^{10}) $ 4 * q - 5 * q^2 - 3 * q^4 + 3 * q^5 - q^7 + 5 * q^8	$ 4 q - 5 q^{2} - 3 q^{4} + 3 q^{5} - q^{7} + 5 q^{8} - 10 q^{10} - q^{11} + 4 q^{13} + 5 q^{14} + q^{16} - 6 q^{17} - 7 q^{19} + 9 q^{20} + 25 q^{22} - 22 q^{23} + 6 q^{25} + 10 q^{26} - 3 q^{28} - 6 q^{29} - 15 q^{31} + 30 q^{34} + 3 q^{35} - 6 q^{37} + 10 q^{38} + 6 q^{41} + 12 q^{43} - 33 q^{44} + 30 q^{46} + 10 q^{47} - q^{49} + 15 q^{50} - 18 q^{52} + 14 q^{53} + 8 q^{55} + 30 q^{58} + 6 q^{59} + 13 q^{64} + 8 q^{65} - 18 q^{68} + 24 q^{71} - 22 q^{73} + 20 q^{74} - 6 q^{76} - 11 q^{77} + 10 q^{79} + 2 q^{80} + 45 q^{82} + 2 q^{83} + 3 q^{85} + 5 q^{88} - 18 q^{89} - 6 q^{91} + 9 q^{92} - 10 q^{94} + q^{95} + 6 q^{97}+O(q^{100}) $ 4 * q - 5 * q^2 - 3 * q^4 + 3 * q^5 - q^7 + 5 * q^8 - 10 * q^10 - q^11 + 4 * q^13 + 5 * q^14 + q^16 - 6 * q^17 - 7 * q^19 + 9 * q^20 + 25 * q^22 - 22 * q^23 + 6 * q^25 + 10 * q^26 - 3 * q^28 - 6 * q^29 - 15 * q^31 + 30 * q^34 + 3 * q^35 - 6 * q^37 + 10 * q^38 + 6 * q^41 + 12 * q^43 - 33 * q^44 + 30 * q^46 + 10 * q^47 - q^49 + 15 * q^50 - 18 * q^52 + 14 * q^53 + 8 * q^55 + 30 * q^58 + 6 * q^59 + 13 * q^64 + 8 * q^65 - 18 * q^68 + 24 * q^71 - 22 * q^73 + 20 * q^74 - 6 * q^76 - 11 * q^77 + 10 * q^79 + 2 * q^80 + 45 * q^82 + 2 * q^83 + 3 * q^85 + 5 * q^88 - 18 * q^89 - 6 * q^91 + 9 * q^92 - 10 * q^94 + q^95 + 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	−1.80902	+	1.31433i	−1.27917	+	0.929370i	−0.999528	−	0.0307347i	$-0.990215\pi$
$2$	−1.80902	+	1.31433i	−1.27917	+	0.929370i	−0.279641	+	0.960105i	$0.590215\pi$
$3$		0			0
$3$		0			0
$4$	0.927051	−	2.85317i	0.463525	−	1.42658i
$5$	1.30902	+	0.951057i	0.585410	+	0.425325i	0.840670	−	0.541547i	$-0.182161\pi$
$5$	1.30902	+	0.951057i	0.585410	+	0.425325i	−0.255260	+	0.966872i	$0.582161\pi$
$6$		0			0
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$8$	0.690983	+	2.12663i	0.244299	+	0.751876i
$9$		0			0
$10$	−3.61803			−1.14412
$11$	−0.809017	−	3.21644i	−0.243928	−	0.969793i
$11$	−0.809017	−	3.21644i	−0.243928	−	0.969793i
$12$		0			0
$13$	1.00000	−	0.726543i	0.277350	−	0.201507i	−0.440411	−	0.897796i	$-0.645167\pi$
$13$	1.00000	−	0.726543i	0.277350	−	0.201507i	0.717761	+	0.696290i	$0.245167\pi$
$14$	0.690983	+	2.12663i	0.184673	+	0.568365i
$15$		0			0
$16$	0.809017	+	0.587785i	0.202254	+	0.146946i
$17$	−1.50000	−	1.08981i	−0.363803	−	0.264319i	0.390833	−	0.920461i	$-0.372187\pi$
$17$	−1.50000	−	1.08981i	−0.363803	−	0.264319i	−0.754637	+	0.656143i	$0.772187\pi$
$18$		0			0
$19$	−1.19098	−	3.66547i	−0.273230	−	0.840916i	−0.989682	−	0.143280i	$-0.954235\pi$
$19$	−1.19098	−	3.66547i	−0.273230	−	0.840916i	0.716452	−	0.697636i	$-0.245765\pi$
$20$	3.92705	−	2.85317i	0.878115	−	0.637988i
$21$		0			0
$22$	5.69098	+	4.75528i	1.21332	+	1.01383i
$23$	−6.61803			−1.37996			−0.689978	−	0.723831i	$-0.742380\pi$
$23$	−6.61803			−1.37996			−0.689978	+	0.723831i	$0.742380\pi$
$24$		0			0
$25$	−0.736068	−	2.26538i	−0.147214	−	0.453077i
$26$	−0.854102	+	2.62866i	−0.167503	+	0.515522i
$27$		0			0
$28$	−2.42705	−	1.76336i	−0.458670	−	0.333243i
$29$	1.85410	−	5.70634i	0.344298	−	1.05964i	−0.617660	−	0.786445i	$-0.711919\pi$
$29$	1.85410	−	5.70634i	0.344298	−	1.05964i	0.961958	−	0.273196i	$-0.0880806\pi$
$30$		0			0
$31$	−6.54508	+	4.75528i	−1.17553	+	0.854074i	−0.991661	−	0.128876i	$-0.958863\pi$
$31$	−6.54508	+	4.75528i	−1.17553	+	0.854074i	−0.183871	+	0.982950i	$0.558863\pi$
$32$	−6.70820			−1.18585
$33$		0			0
$34$	4.14590			0.711016
$35$	1.30902	−	0.951057i	0.221264	−	0.160758i
$36$		0			0
$37$	0.736068	−	2.26538i	0.121009	−	0.372427i	−0.872144	−	0.489249i	$-0.837271\pi$
$37$	0.736068	−	2.26538i	0.121009	−	0.372427i	0.993153	+	0.116822i	$0.0372708\pi$
$38$	6.97214	+	5.06555i	1.13103	+	0.821741i
$39$		0			0
$40$	−1.11803	+	3.44095i	−0.176777	+	0.544063i
$41$	−2.97214	−	9.14729i	−0.464170	−	1.42857i	−0.860024	−	0.510254i	$-0.829551\pi$
$41$	−2.97214	−	9.14729i	−0.464170	−	1.42857i	0.395854	−	0.918313i	$-0.370449\pi$
$42$		0			0
$43$	−3.70820			−0.565496			−0.282748	−	0.959194i	$-0.591246\pi$
$43$	−3.70820			−0.565496			−0.282748	+	0.959194i	$0.591246\pi$
$44$	−9.92705	−	0.673542i	−1.49656	−	0.101540i
$45$		0			0
$46$	11.9721	−	8.69827i	1.76520	−	1.28249i
$47$	1.38197	+	4.25325i	0.201580	+	0.620401i	0.999836	+	0.0180826i	$0.00575618\pi$
$47$	1.38197	+	4.25325i	0.201580	+	0.620401i	−0.798256	+	0.602318i	$0.794244\pi$
$48$		0			0
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	4.30902	+	3.13068i	0.609387	+	0.442746i
$51$		0			0
$52$	−1.14590	−	3.52671i	−0.158907	−	0.489067i
$53$	9.09017	−	6.60440i	1.24863	−	0.907183i	0.250489	−	0.968119i	$-0.419409\pi$
$53$	9.09017	−	6.60440i	1.24863	−	0.907183i	0.998142	+	0.0609360i	$0.0194085\pi$
$54$		0			0
$55$	2.00000	−	4.97980i	0.269680	−	0.671476i
$56$	2.23607			0.298807
$57$		0			0
$58$	4.14590	+	12.7598i	0.544383	+	1.67544i
$59$	0.381966	−	1.17557i	0.0497277	−	0.153046i	−0.923109	−	0.384538i	$-0.874361\pi$
$59$	0.381966	−	1.17557i	0.0497277	−	0.153046i	0.972837	+	0.231492i	$0.0743607\pi$
$60$		0			0
$61$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$61$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$62$	5.59017	−	17.2048i	0.709952	−	2.18501i
$63$		0			0
$64$	10.5172	−	7.64121i	1.31465	−	0.955151i
$65$	2.00000			0.248069
$66$		0			0
$67$		0			0			−	1.00000i	$-0.5\pi$
$67$		0			0				1.00000i	$0.5\pi$
$68$	−4.50000	+	3.26944i	−0.545705	+	0.396478i
$69$		0			0
$70$	−1.11803	+	3.44095i	−0.133631	+	0.411273i
$71$	10.4721	+	7.60845i	1.24281	+	0.902957i	0.997783	−	0.0665580i	$-0.0212017\pi$
$71$	10.4721	+	7.60845i	1.24281	+	0.902957i	0.245031	+	0.969515i	$0.421202\pi$
$72$		0			0
$73$	0.0901699	−	0.277515i	0.0105536	−	0.0324806i	−0.945641	−	0.325212i	$-0.894564\pi$
$73$	0.0901699	−	0.277515i	0.0105536	−	0.0324806i	0.956195	+	0.292732i	$0.0945643\pi$
$74$	1.64590	+	5.06555i	0.191332	+	0.588859i
$75$		0			0
$76$	−11.5623			−1.32629
$77$	−3.30902	−	0.224514i	−0.377097	−	0.0255857i
$78$		0			0
$79$	8.09017	−	5.87785i	0.910215	−	0.661310i	−0.0308541	−	0.999524i	$-0.509823\pi$
$79$	8.09017	−	5.87785i	0.910215	−	0.661310i	0.941069	+	0.338214i	$0.109823\pi$
$80$	0.500000	+	1.53884i	0.0559017	+	0.172048i
$81$		0			0
$82$	17.3992	+	12.6412i	1.92142	+	1.39599i
$83$	6.09017	+	4.42477i	0.668483	+	0.485681i	0.869517	−	0.493903i	$-0.164430\pi$
$83$	6.09017	+	4.42477i	0.668483	+	0.485681i	−0.201034	+	0.979584i	$0.564430\pi$
$84$		0			0
$85$	−0.927051	−	2.85317i	−0.100553	−	0.309470i
$86$	6.70820	−	4.87380i	0.723364	−	0.525555i
$87$		0			0
$88$	6.28115	−	3.94298i	0.669573	−	0.420323i
$89$	−3.38197			−0.358488			−0.179244	−	0.983805i	$-0.557365\pi$
$89$	−3.38197			−0.358488			−0.179244	+	0.983805i	$0.557365\pi$
$90$		0			0
$91$	−0.381966	−	1.17557i	−0.0400409	−	0.123233i
$92$	−6.13525	+	18.8824i	−0.639645	+	1.96862i
$93$		0			0
$94$	−8.09017	−	5.87785i	−0.834437	−	0.606254i
$95$	1.92705	−	5.93085i	0.197711	−	0.608493i
$96$		0			0
$97$	4.85410	−	3.52671i	0.492859	−	0.358083i	−0.313423	−	0.949613i	$-0.601476\pi$
$97$	4.85410	−	3.52671i	0.492859	−	0.358083i	0.806283	+	0.591530i	$0.201476\pi$
$98$	2.23607			0.225877
$99$		0			0
$100$	−7.14590			−0.714590
$101$	14.3992	−	10.4616i	1.43277	−	1.04097i	0.443281	−	0.896383i	$-0.353815\pi$
$101$	14.3992	−	10.4616i	1.43277	−	1.04097i	0.989492	−	0.144587i	$-0.0461855\pi$
$102$		0			0
$103$	−4.42705	+	13.6251i	−0.436210	+	1.34252i	0.455631	+	0.890169i	$0.349414\pi$
$103$	−4.42705	+	13.6251i	−0.436210	+	1.34252i	−0.891841	+	0.452348i	$0.850586\pi$
$104$	2.23607	+	1.62460i	0.219265	+	0.159305i
$105$		0			0
$106$	−7.76393	+	23.8949i	−0.754100	+	2.32088i
$107$	2.71885	+	8.36775i	0.262841	+	0.808941i	0.992183	+	0.124792i	$0.0398263\pi$
$107$	2.71885	+	8.36775i	0.262841	+	0.808941i	−0.729342	+	0.684149i	$0.760174\pi$
$108$		0			0
$109$	2.56231			0.245424			0.122712	−	0.992442i	$-0.460841\pi$
$109$	2.56231			0.245424			0.122712	+	0.992442i	$0.460841\pi$
$110$	2.92705	+	11.6372i	0.279083	+	1.10956i
$111$		0			0
$112$	0.809017	−	0.587785i	0.0764449	−	0.0555405i
$113$	0.236068	+	0.726543i	0.0222074	+	0.0683474i	0.961546	−	0.274644i	$-0.0885599\pi$
$113$	0.236068	+	0.726543i	0.0222074	+	0.0683474i	−0.939339	+	0.342991i	$0.888560\pi$
$114$		0			0
$115$	−8.66312	−	6.29412i	−0.807840	−	0.586930i
$116$	−14.5623	−	10.5801i	−1.35208	−	0.982341i
$117$		0			0
$118$	0.854102	+	2.62866i	0.0786265	+	0.241987i
$119$	−1.50000	+	1.08981i	−0.137505	+	0.0999031i
$120$		0			0
$121$	−9.69098	+	5.20431i	−0.880998	+	0.473119i
$122$		0			0
$123$		0			0
$124$	7.50000	+	23.0826i	0.673520	+	2.07288i
$125$	3.69098	−	11.3597i	0.330132	−	1.01604i
$126$		0			0
$127$	−11.0902	−	8.05748i	−0.984093	−	0.714986i	−0.0254737	−	0.999675i	$-0.508109\pi$
$127$	−11.0902	−	8.05748i	−0.984093	−	0.714986i	−0.958620	+	0.284690i	$0.908109\pi$
$128$	−4.83688	+	14.8864i	−0.427524	+	1.31578i
$129$		0			0
$130$	−3.61803	+	2.62866i	−0.317323	+	0.230548i
$131$	−14.6525			−1.28019			−0.640096	−	0.768295i	$-0.721106\pi$
$131$	−14.6525			−1.28019			−0.640096	+	0.768295i	$0.721106\pi$
$132$		0			0
$133$	−3.85410			−0.334193
$134$		0			0
$135$		0			0
$136$	1.28115	−	3.94298i	0.109858	−	0.338108i
$137$	−11.4721	−	8.33499i	−0.980131	−	0.712107i	−0.0223929	−	0.999749i	$-0.507128\pi$
$137$	−11.4721	−	8.33499i	−0.980131	−	0.712107i	−0.957738	+	0.287643i	$0.907128\pi$
$138$		0			0
$139$	6.13525	−	18.8824i	0.520386	−	1.60158i	−0.252879	−	0.967498i	$-0.581377\pi$
$139$	6.13525	−	18.8824i	0.520386	−	1.60158i	0.773264	−	0.634084i	$-0.218623\pi$
$140$	−1.50000	−	4.61653i	−0.126773	−	0.390168i
$141$		0			0
$142$	−28.9443			−2.42895
$143$	−3.14590	−	2.62866i	−0.263073	−	0.219819i
$144$		0			0
$145$	7.85410	−	5.70634i	0.652248	−	0.473886i
$146$	0.201626	+	0.620541i	0.0166867	+	0.0513564i
$147$		0			0
$148$	−5.78115	−	4.20025i	−0.475208	−	0.345259i
$149$	10.4721	+	7.60845i	0.857911	+	0.623309i	0.927316	−	0.374280i	$-0.122110\pi$
$149$	10.4721	+	7.60845i	0.857911	+	0.623309i	−0.0694050	+	0.997589i	$0.522110\pi$
$150$		0			0
$151$	−7.56231	−	23.2744i	−0.615412	−	1.89404i	−0.395223	−	0.918585i	$-0.629333\pi$
$151$	−7.56231	−	23.2744i	−0.615412	−	1.89404i	−0.220189	−	0.975457i	$-0.570667\pi$
$152$	6.97214	−	5.06555i	0.565515	−	0.410871i
$153$		0			0
$154$	6.28115	−	3.94298i	0.506150	−	0.317735i
$155$	−13.0902			−1.05143
$156$		0			0
$157$	5.29180	+	16.2865i	0.422331	+	1.29980i	0.905527	+	0.424290i	$0.139476\pi$
$157$	5.29180	+	16.2865i	0.422331	+	1.29980i	−0.483195	+	0.875513i	$0.660524\pi$
$158$	−6.90983	+	21.2663i	−0.549717	+	1.69185i
$159$		0			0
$160$	−8.78115	−	6.37988i	−0.694211	−	0.504374i
$161$	−2.04508	+	6.29412i	−0.161175	+	0.496046i
$162$		0			0
$163$	8.09017	−	5.87785i	0.633671	−	0.460389i	−0.223999	−	0.974589i	$-0.571911\pi$
$163$	8.09017	−	5.87785i	0.633671	−	0.460389i	0.857670	+	0.514200i	$0.171911\pi$
$164$	−28.8541			−2.25313
$165$		0			0
$166$	−16.8328			−1.30648
$167$	−13.5623	+	9.85359i	−1.04948	+	0.762494i	−0.972114	−	0.234509i	$-0.924652\pi$
$167$	−13.5623	+	9.85359i	−1.04948	+	0.762494i	−0.0773687	+	0.997003i	$0.524652\pi$
$168$		0			0
$169$	−3.54508	+	10.9106i	−0.272699	+	0.839281i
$170$	5.42705	+	3.94298i	0.416236	+	0.302413i
$171$		0			0
$172$	−3.43769	+	10.5801i	−0.262122	+	0.806728i
$173$	3.51722	+	10.8249i	0.267409	+	0.823001i	0.991129	+	0.132907i	$0.0424311\pi$
$173$	3.51722	+	10.8249i	0.267409	+	0.823001i	−0.723719	+	0.690095i	$0.757569\pi$
$174$		0			0
$175$	−2.38197			−0.180060
$176$	1.23607	−	3.07768i	0.0931721	−	0.231989i
$177$		0			0
$178$	6.11803	−	4.44501i	0.458566	−	0.333168i
$179$	−3.02786	−	9.31881i	−0.226313	−	0.696520i	−0.998156	−	0.0607066i	$-0.980665\pi$
$179$	−3.02786	−	9.31881i	−0.226313	−	0.696520i	0.771842	−	0.635814i	$-0.219335\pi$
$180$		0			0
$181$	−12.8541	−	9.33905i	−0.955438	−	0.694166i	−0.00335114	−	0.999994i	$-0.501067\pi$
$181$	−12.8541	−	9.33905i	−0.955438	−	0.694166i	−0.952087	+	0.305828i	$0.901067\pi$
$182$	2.23607	+	1.62460i	0.165748	+	0.120423i
$183$		0			0
$184$	−4.57295	−	14.0741i	−0.337122	−	1.03756i
$185$	3.11803	−	2.26538i	0.229242	−	0.166554i
$186$		0			0
$187$	−2.29180	+	5.70634i	−0.167593	+	0.417289i
$188$	13.4164			0.978492
$189$		0			0
$190$	4.30902	+	13.2618i	0.312609	+	0.962111i
$191$	−4.97214	+	15.3027i	−0.359771	+	1.10726i	0.593420	+	0.804893i	$0.297777\pi$
$191$	−4.97214	+	15.3027i	−0.359771	+	1.10726i	−0.953191	+	0.302369i	$0.902223\pi$
$192$		0			0
$193$	12.2533	+	8.90254i	0.882011	+	0.640819i	0.933783	−	0.357840i	$-0.116487\pi$
$193$	12.2533	+	8.90254i	0.882011	+	0.640819i	−0.0517717	+	0.998659i	$0.516487\pi$
$194$	−4.14590	+	12.7598i	−0.297658	+	0.916098i
$195$		0			0
$196$	−2.42705	+	1.76336i	−0.173361	+	0.125954i
$197$	−13.5279			−0.963820			−0.481910	−	0.876221i	$-0.660057\pi$
$197$	−13.5279			−0.963820			−0.481910	+	0.876221i	$0.660057\pi$
$198$		0			0
$199$	19.8541			1.40742			0.703710	−	0.710487i	$-0.251525\pi$
$199$	19.8541			1.40742			0.703710	+	0.710487i	$0.251525\pi$
$200$	4.30902	−	3.13068i	0.304694	−	0.221373i
$201$		0			0
$202$	−12.2984	+	37.8505i	−0.865311	+	2.66315i
$203$	−4.85410	−	3.52671i	−0.340691	−	0.247527i
$204$		0			0
$205$	4.80902	−	14.8006i	0.335876	−	1.03372i
$206$	−9.89919	−	30.4666i	−0.689709	−	2.12271i
$207$		0			0
$208$	1.23607			0.0857059
$209$	−10.8262	+	6.79615i	−0.748867	+	0.470100i
$210$		0			0
$211$	−21.3262	+	15.4944i	−1.46816	+	1.06668i	−0.487017	+	0.873393i	$0.661915\pi$
$211$	−21.3262	+	15.4944i	−1.46816	+	1.06668i	−0.981142	+	0.193287i	$0.938085\pi$
$212$	−10.4164	−	32.0584i	−0.715402	−	2.20178i
$213$		0			0
$214$	−15.9164	−	11.5639i	−1.08802	−	0.790495i
$215$	−4.85410	−	3.52671i	−0.331047	−	0.240520i
$216$		0			0
$217$	2.50000	+	7.69421i	0.169711	+	0.522317i
$218$	−4.63525	+	3.36771i	−0.313939	+	0.228090i
$219$		0			0
$220$	−12.3541	−	10.3229i	−0.832913	−	0.695967i
$221$	−2.29180			−0.154163
$222$		0			0
$223$	5.37132	+	16.5312i	0.359690	+	1.10701i	0.953240	+	0.302216i	$0.0977262\pi$
$223$	5.37132	+	16.5312i	0.359690	+	1.10701i	−0.593549	+	0.804798i	$0.702274\pi$
$224$	−2.07295	+	6.37988i	−0.138505	+	0.426274i
$225$		0			0
$226$	−1.38197	−	1.00406i	−0.0919270	−	0.0667889i
$227$	−1.09017	+	3.35520i	−0.0723571	+	0.222692i	−0.980695	−	0.195546i	$-0.937352\pi$
$227$	−1.09017	+	3.35520i	−0.0723571	+	0.222692i	0.908337	+	0.418238i	$0.137352\pi$
$228$		0			0
$229$	5.00000	−	3.63271i	0.330409	−	0.240056i	−0.410195	−	0.911998i	$-0.634539\pi$
$229$	5.00000	−	3.63271i	0.330409	−	0.240056i	0.740604	+	0.671941i	$0.234539\pi$
$230$	23.9443			1.57884
$231$		0			0
$232$	13.4164			0.880830
$233$	−1.85410	+	1.34708i	−0.121466	+	0.0882504i	−0.646860	−	0.762609i	$-0.723918\pi$
$233$	−1.85410	+	1.34708i	−0.121466	+	0.0882504i	0.525394	+	0.850859i	$0.323918\pi$
$234$		0			0
$235$	−2.23607	+	6.88191i	−0.145865	+	0.448926i
$236$	−3.00000	−	2.17963i	−0.195283	−	0.141882i
$237$		0			0
$238$	1.28115	−	3.94298i	0.0830448	−	0.255586i
$239$	−3.10081	−	9.54332i	−0.200575	−	0.617306i	−0.999866	−	0.0163622i	$-0.994792\pi$
$239$	−3.10081	−	9.54332i	−0.200575	−	0.617306i	0.799291	−	0.600944i	$-0.205208\pi$
$240$		0			0
$241$	12.0000			0.772988			0.386494	−	0.922292i	$-0.373686\pi$
$241$	12.0000			0.772988			0.386494	+	0.922292i	$0.373686\pi$
$242$	10.6910	−	22.1518i	0.687242	−	1.42397i
$243$		0			0
$244$		0			0
$245$	−0.500000	−	1.53884i	−0.0319438	−	0.0983130i
$246$		0			0
$247$	−3.85410	−	2.80017i	−0.245231	−	0.178170i
$248$	−14.6353	−	10.6331i	−0.929340	−	0.675205i
$249$		0			0
$250$	8.25329	+	25.4010i	0.521984	+	1.60650i
$251$	11.5623	−	8.40051i	0.729806	−	0.530235i	−0.159696	−	0.987166i	$-0.551051\pi$
$251$	11.5623	−	8.40051i	0.729806	−	0.530235i	0.889502	+	0.456931i	$0.151051\pi$
$252$		0			0
$253$	5.35410	+	21.2865i	0.336610	+	1.33827i
$254$	30.6525			1.92331
$255$		0			0
$256$	−2.78115	−	8.55951i	−0.173822	−	0.534969i
$257$	9.71885	−	29.9115i	0.606245	−	1.86583i	0.118250	−	0.992984i	$-0.462272\pi$
$257$	9.71885	−	29.9115i	0.606245	−	1.86583i	0.487995	−	0.872846i	$-0.337728\pi$
$258$		0			0
$259$	−1.92705	−	1.40008i	−0.119741	−	0.0869970i
$260$	1.85410	−	5.70634i	0.114987	−	0.353892i
$261$		0			0
$262$	26.5066	−	19.2582i	1.63758	−	1.18977i
$263$	−4.14590			−0.255647			−0.127824	−	0.991797i	$-0.540799\pi$
$263$	−4.14590			−0.255647			−0.127824	+	0.991797i	$0.540799\pi$
$264$		0			0
$265$	18.1803			1.11681
$266$	6.97214	−	5.06555i	0.427489	−	0.310589i
$267$		0			0
$268$		0			0
$269$	10.8541	+	7.88597i	0.661786	+	0.480816i	0.867266	−	0.497846i	$-0.165875\pi$
$269$	10.8541	+	7.88597i	0.661786	+	0.480816i	−0.205479	+	0.978661i	$0.565875\pi$
$270$		0			0
$271$	4.79180	−	14.7476i	0.291081	−	0.895855i	−0.693429	−	0.720525i	$-0.743901\pi$
$271$	4.79180	−	14.7476i	0.291081	−	0.895855i	0.984510	−	0.175330i	$-0.0560992\pi$
$272$	−0.572949	−	1.76336i	−0.0347401	−	0.106919i
$273$		0			0
$274$	31.7082			1.91556
$275$	−6.69098	+	4.20025i	−0.403481	+	0.253285i
$276$		0			0
$277$	−8.97214	+	6.51864i	−0.539083	+	0.391667i	−0.823744	−	0.566961i	$-0.808119\pi$
$277$	−8.97214	+	6.51864i	−0.539083	+	0.391667i	0.284661	+	0.958628i	$0.408119\pi$
$278$	13.7188	+	42.2223i	0.822802	+	2.53232i
$279$		0			0
$280$	2.92705	+	2.12663i	0.174925	+	0.127090i
$281$	−7.32624	−	5.32282i	−0.437047	−	0.317533i	0.347414	−	0.937712i	$-0.387060\pi$
$281$	−7.32624	−	5.32282i	−0.437047	−	0.317533i	−0.784460	+	0.620179i	$0.787060\pi$
$282$		0			0
$283$	5.02786	+	15.4742i	0.298875	+	0.919844i	0.981892	+	0.189441i	$0.0606677\pi$
$283$	5.02786	+	15.4742i	0.298875	+	0.919844i	−0.683017	+	0.730403i	$0.739332\pi$
$284$	31.4164	−	22.8254i	1.86422	−	1.35444i
$285$		0			0
$286$	9.14590	+	0.620541i	0.540808	+	0.0366934i
$287$	−9.61803			−0.567735
$288$		0			0
$289$	−4.19098	−	12.8985i	−0.246528	−	0.758736i
$290$	−6.70820	+	20.6457i	−0.393919	+	1.21236i
$291$		0			0
$292$	−0.708204	−	0.514540i	−0.0414445	−	0.0301112i
$293$	−10.2639	+	31.5891i	−0.599625	+	1.84546i	−0.0694203	+	0.997588i	$0.522115\pi$
$293$	−10.2639	+	31.5891i	−0.599625	+	1.84546i	−0.530205	+	0.847869i	$0.677885\pi$
$294$		0			0
$295$	1.61803	−	1.17557i	0.0942056	−	0.0684444i
$296$	5.32624			0.309581
$297$		0			0
$298$	−28.9443			−1.67670
$299$	−6.61803	+	4.80828i	−0.382731	+	0.278070i
$300$		0			0
$301$	−1.14590	+	3.52671i	−0.0660485	+	0.203276i
$302$	44.2705	+	32.1644i	2.54748	+	1.85085i
$303$		0			0
$304$	1.19098	−	3.66547i	0.0683076	−	0.210229i
$305$		0			0
$306$		0			0
$307$	2.56231			0.146239			0.0731193	−	0.997323i	$-0.476705\pi$
$307$	2.56231			0.146239			0.0731193	+	0.997323i	$0.476705\pi$
$308$	−3.70820	+	9.23305i	−0.211295	+	0.526102i
$309$		0			0
$310$	23.6803	−	17.2048i	1.34495	−	0.977166i
$311$	3.29180	+	10.1311i	0.186661	+	0.574482i	0.999973	−	0.00734490i	$-0.00233798\pi$
$311$	3.29180	+	10.1311i	0.186661	+	0.574482i	−0.813312	+	0.581827i	$0.802338\pi$
$312$		0			0
$313$	24.4164	+	17.7396i	1.38010	+	1.00270i	0.996871	+	0.0790445i	$0.0251869\pi$
$313$	24.4164	+	17.7396i	1.38010	+	1.00270i	0.383226	+	0.923655i	$0.374813\pi$
$314$	−30.9787	−	22.5074i	−1.74823	−	1.27016i
$315$		0			0
$316$	−9.27051	−	28.5317i	−0.521507	−	1.60503i
$317$	9.09017	−	6.60440i	0.510555	−	0.370940i	−0.302479	−	0.953156i	$-0.597814\pi$
$317$	9.09017	−	6.60440i	0.510555	−	0.370940i	0.813034	+	0.582216i	$0.197814\pi$
$318$		0			0
$319$	−19.8541	−	1.34708i	−1.11162	−	0.0754222i
$320$	21.0344			1.17586
$321$		0			0
$322$	−4.57295	−	14.0741i	−0.254840	−	0.784318i
$323$	−2.20820	+	6.79615i	−0.122868	+	0.378148i
$324$		0			0
$325$	−2.38197	−	1.73060i	−0.132128	−	0.0959964i
$326$	−6.90983	+	21.2663i	−0.382700	+	1.17783i
$327$		0			0
$328$	17.3992	−	12.6412i	0.960709	−	0.697996i
$329$	4.47214			0.246557
$330$		0			0
$331$	−9.41641			−0.517573			−0.258786	−	0.965935i	$-0.583323\pi$
$331$	−9.41641			−0.517573			−0.258786	+	0.965935i	$0.583323\pi$
$332$	18.2705	−	13.2743i	1.00272	−	0.728522i
$333$		0			0
$334$	11.5836	−	35.6506i	0.633826	−	1.95072i
$335$		0			0
$336$		0			0
$337$	4.91641	−	15.1311i	0.267814	−	0.824246i	−0.723218	−	0.690620i	$-0.757338\pi$
$337$	4.91641	−	15.1311i	0.267814	−	0.824246i	0.991032	−	0.133626i	$-0.0426622\pi$
$338$	−7.92705	−	24.3970i	−0.431175	−	1.32702i
$339$		0			0
$340$	−9.00000			−0.488094
$341$	20.5902	+	17.2048i	1.11502	+	0.931691i
$342$		0			0
$343$	−0.809017	+	0.587785i	−0.0436828	+	0.0317374i
$344$	−2.56231	−	7.88597i	−0.138150	−	0.425183i
$345$		0			0
$346$	−20.5902	−	14.9596i	−1.10693	−	0.804235i
$347$	19.0172	+	13.8168i	1.02090	+	0.741726i	0.966467	−	0.256792i	$-0.0826655\pi$
$347$	19.0172	+	13.8168i	1.02090	+	0.741726i	0.0544312	+	0.998518i	$0.482665\pi$
$348$		0			0
$349$	−2.56231	−	7.88597i	−0.137157	−	0.422126i	0.858762	−	0.512374i	$-0.171234\pi$
$349$	−2.56231	−	7.88597i	−0.137157	−	0.422126i	−0.995919	+	0.0902482i	$0.971234\pi$
$350$	4.30902	−	3.13068i	0.230327	−	0.167342i
$351$		0			0
$352$	5.42705	+	21.5765i	0.289263	+	1.15003i
$353$	18.0000			0.958043			0.479022	−	0.877803i	$-0.340992\pi$
$353$	18.0000			0.958043			0.479022	+	0.877803i	$0.340992\pi$
$354$		0			0
$355$	6.47214	+	19.9192i	0.343505	+	1.05720i
$356$	−3.13525	+	9.64932i	−0.166168	+	0.511413i
$357$		0			0
$358$	17.7254	+	12.8783i	0.936818	+	0.680638i
$359$	−8.20820	+	25.2623i	−0.433212	+	1.33329i	0.461695	+	0.887039i	$0.347241\pi$
$359$	−8.20820	+	25.2623i	−0.433212	+	1.33329i	−0.894907	+	0.446252i	$0.852759\pi$
$360$		0			0
$361$	3.35410	−	2.43690i	0.176532	−	0.128258i
$362$	35.5279			1.86730
$363$		0			0
$364$	−3.70820			−0.194363
$365$	0.381966	−	0.277515i	0.0199930	−	0.0145258i
$366$		0			0
$367$	11.2082	−	34.4953i	0.585063	−	1.80064i	−0.0139518	−	0.999903i	$-0.504441\pi$
$367$	11.2082	−	34.4953i	0.585063	−	1.80064i	0.599015	−	0.800738i	$-0.295559\pi$
$368$	−5.35410	−	3.88998i	−0.279102	−	0.202779i
$369$		0			0
$370$	−2.66312	+	8.19624i	−0.138449	+	0.426102i
$371$	−3.47214	−	10.6861i	−0.180264	−	0.554797i
$372$		0			0
$373$	0.673762			0.0348861			0.0174430	−	0.999848i	$-0.494447\pi$
$373$	0.673762			0.0348861			0.0174430	+	0.999848i	$0.494447\pi$
$374$	−3.35410	−	13.3350i	−0.173436	−	0.689538i
$375$		0			0
$376$	−8.09017	+	5.87785i	−0.417219	+	0.303127i
$377$	−2.29180	−	7.05342i	−0.118034	−	0.363270i
$378$		0			0
$379$	−24.6525	−	17.9111i	−1.26631	−	0.920030i	−0.267263	−	0.963624i	$-0.586119\pi$
$379$	−24.6525	−	17.9111i	−1.26631	−	0.920030i	−0.999049	+	0.0435936i	$0.986119\pi$
$380$	−15.1353	−	10.9964i	−0.776422	−	0.564104i
$381$		0			0
$382$	−11.1180	−	34.2178i	−0.568848	−	1.75073i
$383$	26.5623	−	19.2986i	1.35727	−	0.986115i	0.358657	−	0.933469i	$-0.383235\pi$
$383$	26.5623	−	19.2986i	1.35727	−	0.986115i	0.998613	−	0.0526453i	$-0.0167653\pi$
$384$		0			0
$385$	−4.11803	−	3.44095i	−0.209874	−	0.175367i
$386$	−33.8673			−1.72380
$387$		0			0
$388$	−5.56231	−	17.1190i	−0.282383	−	0.869086i
$389$	−3.32624	+	10.2371i	−0.168647	+	0.519042i	−0.999287	−	0.0377685i	$-0.987975\pi$
$389$	−3.32624	+	10.2371i	−0.168647	+	0.519042i	0.830640	+	0.556810i	$0.187975\pi$
$390$		0			0
$391$	9.92705	+	7.21242i	0.502033	+	0.364748i
$392$	0.690983	−	2.12663i	0.0348999	−	0.107411i
$393$		0			0
$394$	24.4721	−	17.7800i	1.23289	−	0.895746i
$395$	16.1803			0.814121
$396$		0			0
$397$	−36.5410			−1.83394			−0.916971	−	0.398955i	$-0.869373\pi$
$397$	−36.5410			−1.83394			−0.916971	+	0.398955i	$0.869373\pi$
$398$	−35.9164	+	26.0948i	−1.80033	+	1.30801i
$399$		0			0
$400$	0.736068	−	2.26538i	0.0368034	−	0.113269i
$401$	−15.7082	−	11.4127i	−0.784430	−	0.569922i	0.121875	−	0.992545i	$-0.461109\pi$
$401$	−15.7082	−	11.4127i	−0.784430	−	0.569922i	−0.906305	+	0.422623i	$0.861109\pi$
$402$		0			0
$403$	−3.09017	+	9.51057i	−0.153932	+	0.473755i
$404$	−16.5000	−	50.7818i	−0.820906	−	2.52649i
$405$		0			0
$406$	13.4164			0.665845
$407$	−7.88197	−	0.534785i	−0.390695	−	0.0265083i
$408$		0			0
$409$	−0.145898	+	0.106001i	−0.00721419	+	0.00524142i	−0.591387	−	0.806388i	$-0.701419\pi$
$409$	−0.145898	+	0.106001i	−0.00721419	+	0.00524142i	0.584172	+	0.811630i	$0.301419\pi$
$410$	10.7533	+	33.0952i	0.531067	+	1.63446i
$411$		0			0
$412$	34.7705	+	25.2623i	1.71302	+	1.24458i
$413$	−1.00000	−	0.726543i	−0.0492068	−	0.0357508i
$414$		0			0
$415$	3.76393	+	11.5842i	0.184764	+	0.568646i
$416$	−6.70820	+	4.87380i	−0.328897	+	0.238957i
$417$		0			0
$418$	10.6525	−	26.5236i	0.521030	−	1.29731i
$419$	−1.23607			−0.0603859			−0.0301929	−	0.999544i	$-0.509612\pi$
$419$	−1.23607			−0.0603859			−0.0301929	+	0.999544i	$0.509612\pi$
$420$		0			0
$421$	−4.57295	−	14.0741i	−0.222872	−	0.685929i	−0.998501	−	0.0547398i	$-0.982567\pi$
$421$	−4.57295	−	14.0741i	−0.222872	−	0.685929i	0.775629	−	0.631189i	$-0.217433\pi$
$422$	18.2148	−	56.0593i	0.886682	−	2.72893i
$423$		0			0
$424$	20.3262	+	14.7679i	0.987129	+	0.717191i
$425$	−1.36475	+	4.20025i	−0.0661999	+	0.203742i
$426$		0			0
$427$		0			0
$428$	26.3951			1.27586
$429$		0			0
$430$	13.4164			0.646997
$431$	3.16312	−	2.29814i	0.152362	−	0.110698i	−0.508992	−	0.860771i	$-0.669982\pi$
$431$	3.16312	−	2.29814i	0.152362	−	0.110698i	0.661355	+	0.750073i	$0.269982\pi$
$432$		0			0
$433$	−8.27051	+	25.4540i	−0.397455	+	1.22324i	0.529577	+	0.848262i	$0.322350\pi$
$433$	−8.27051	+	25.4540i	−0.397455	+	1.22324i	−0.927033	+	0.374980i	$0.877650\pi$
$434$	−14.6353	−	10.6331i	−0.702515	−	0.510407i
$435$		0			0
$436$	2.37539	−	7.31069i	0.113760	−	0.350119i
$437$	7.88197	+	24.2582i	0.377046	+	1.16043i
$438$		0			0
$439$	−4.85410			−0.231674			−0.115837	−	0.993268i	$-0.536955\pi$
$439$	−4.85410			−0.231674			−0.115837	+	0.993268i	$0.536955\pi$
$440$	11.9721	+	0.812299i	0.570749	+	0.0387248i
$441$		0			0
$442$	4.14590	−	3.01217i	0.197200	−	0.143274i
$443$	−6.98936	−	21.5110i	−0.332074	−	1.02202i	−0.968145	−	0.250389i	$-0.919441\pi$
$443$	−6.98936	−	21.5110i	−0.332074	−	1.02202i	0.636071	−	0.771631i	$-0.280559\pi$
$444$		0			0
$445$	−4.42705	−	3.21644i	−0.209862	−	0.152474i
$446$	−31.4443	−	22.8456i	−1.48893	−	1.08177i
$447$		0			0
$448$	−4.01722	−	12.3637i	−0.189796	−	0.584132i
$449$	−4.94427	+	3.59222i	−0.233335	+	0.169528i	−0.698309	−	0.715797i	$-0.746064\pi$
$449$	−4.94427	+	3.59222i	−0.233335	+	0.169528i	0.464974	+	0.885324i	$0.346064\pi$
$450$		0			0
$451$	−27.0172	+	16.9600i	−1.27219	+	0.798616i
$452$	2.29180			0.107797
$453$		0			0
$454$	−2.43769	−	7.50245i	−0.114407	−	0.352107i
$455$	0.618034	−	1.90211i	0.0289739	−	0.0891724i
$456$		0			0
$457$	4.38197	+	3.18368i	0.204980	+	0.148926i	0.685539	−	0.728036i	$-0.259566\pi$
$457$	4.38197	+	3.18368i	0.204980	+	0.148926i	−0.480560	+	0.876962i	$0.659566\pi$
$458$	−4.27051	+	13.1433i	−0.199548	+	0.614145i
$459$		0			0
$460$	−25.9894	+	18.8824i	−1.21176	+	0.880395i
$461$	6.00000			0.279448			0.139724	−	0.990190i	$-0.455378\pi$
$461$	6.00000			0.279448			0.139724	+	0.990190i	$0.455378\pi$
$462$		0			0
$463$	3.41641			0.158774			0.0793870	−	0.996844i	$-0.474704\pi$
$463$	3.41641			0.158774			0.0793870	+	0.996844i	$0.474704\pi$
$464$	4.85410	−	3.52671i	0.225346	−	0.163723i
$465$		0			0
$466$	1.58359	−	4.87380i	0.0733585	−	0.225774i
$467$	3.09017	+	2.24514i	0.142996	+	0.103893i	0.656983	−	0.753905i	$-0.271832\pi$
$467$	3.09017	+	2.24514i	0.142996	+	0.103893i	−0.513987	+	0.857798i	$0.671832\pi$
$468$		0			0
$469$		0			0
$470$	−5.00000	−	15.3884i	−0.230633	−	0.709815i
$471$		0			0
$472$	2.76393			0.127220
$473$	3.00000	+	11.9272i	0.137940	+	0.548414i
$474$		0			0
$475$	−7.42705	+	5.39607i	−0.340776	+	0.247589i
$476$	1.71885	+	5.29007i	0.0787832	+	0.242470i
$477$		0			0
$478$	18.1525	+	13.1885i	0.830275	+	0.603230i
$479$	13.7082	+	9.95959i	0.626344	+	0.455065i	0.855132	−	0.518411i	$-0.173476\pi$
$479$	13.7082	+	9.95959i	0.626344	+	0.455065i	−0.228788	+	0.973476i	$0.573476\pi$
$480$		0			0
$481$	−0.909830	−	2.80017i	−0.0414847	−	0.127677i
$482$	−21.7082	+	15.7719i	−0.988782	+	0.718392i
$483$		0			0
$484$	5.86475	+	32.4747i	0.266579	+	1.47612i
$485$	9.70820			0.440827
$486$		0			0
$487$	4.41641	+	13.5923i	0.200127	+	0.615926i	0.999878	+	0.0155954i	$0.00496438\pi$
$487$	4.41641	+	13.5923i	0.200127	+	0.615926i	−0.799752	+	0.600331i	$0.795036\pi$
$488$		0			0
$489$		0			0
$490$	2.92705	+	2.12663i	0.132231	+	0.0960712i
$491$	11.2812	−	34.7198i	0.509111	−	1.56688i	−0.284636	−	0.958636i	$-0.591873\pi$
$491$	11.2812	−	34.7198i	0.509111	−	1.56688i	0.793747	−	0.608248i	$-0.208127\pi$
$492$		0			0
$493$	−9.00000	+	6.53888i	−0.405340	+	0.294496i
$494$	10.6525			0.479278
$495$		0			0
$496$	−8.09017			−0.363259
$497$	10.4721	−	7.60845i	0.469739	−	0.341286i
$498$		0			0
$499$	−5.90983	+	18.1886i	−0.264560	+	0.814233i	0.727234	+	0.686390i	$0.240805\pi$
$499$	−5.90983	+	18.1886i	−0.264560	+	0.814233i	−0.991794	+	0.127843i	$0.959195\pi$
$500$	−28.9894	−	21.0620i	−1.29644	−	0.941921i
$501$		0			0
$502$	−9.87539	+	30.3933i	−0.440760	+	1.35652i
$503$	1.70820	+	5.25731i	0.0761650	+	0.234412i	0.981889	−	0.189455i	$-0.0606723\pi$
$503$	1.70820	+	5.25731i	0.0761650	+	0.234412i	−0.905724	+	0.423867i	$0.860672\pi$
$504$		0			0
$505$	28.7984			1.28151
$506$	−37.6631	−	31.4706i	−1.67433	−	1.39904i
$507$		0			0
$508$	−33.2705	+	24.1724i	−1.47614	+	1.07248i
$509$	4.91641	+	15.1311i	0.217916	+	0.670676i	0.998934	+	0.0461675i	$0.0147008\pi$
$509$	4.91641	+	15.1311i	0.217916	+	0.670676i	−0.781018	+	0.624509i	$0.785299\pi$
$510$		0			0
$511$	−0.236068	−	0.171513i	−0.0104430	−	0.00758731i
$512$	−9.04508	−	6.57164i	−0.399740	−	0.290428i
$513$		0			0
$514$	21.7320	+	66.8842i	0.958558	+	2.95014i
$515$	−18.7533	+	13.6251i	−0.826369	+	0.600392i
$516$		0			0
$517$	12.5623	−	7.88597i	0.552490	−	0.346824i
$518$	5.32624			0.234021
$519$		0			0
$520$	1.38197	+	4.25325i	0.0606032	+	0.186518i
$521$	−1.02786	+	3.16344i	−0.0450315	+	0.138593i	−0.971044	−	0.238899i	$-0.923213\pi$
$521$	−1.02786	+	3.16344i	−0.0450315	+	0.138593i	0.926013	+	0.377492i	$0.123213\pi$
$522$		0			0
$523$	−16.0623	−	11.6699i	−0.702356	−	0.510291i	0.178343	−	0.983968i	$-0.442926\pi$
$523$	−16.0623	−	11.6699i	−0.702356	−	0.510291i	−0.880699	+	0.473677i	$0.842926\pi$
$524$	−13.5836	+	41.8060i	−0.593402	+	1.82630i
$525$		0			0
$526$	7.50000	−	5.44907i	0.327016	−	0.237591i
$527$	15.0000			0.653410
$528$		0			0
$529$	20.7984			0.904277
$530$	−32.8885	+	23.8949i	−1.42859	+	1.03793i
$531$		0			0
$532$	−3.57295	+	10.9964i	−0.154907	+	0.476755i
$533$	−9.61803	−	6.98791i	−0.416603	−	0.302680i
$534$		0			0
$535$	−4.39919	+	13.5393i	−0.190193	+	0.585355i
$536$		0			0
$537$		0			0
$538$	−30.0000			−1.29339
$539$	−1.23607	+	3.07768i	−0.0532412	+	0.132565i
$540$		0			0
$541$	0.545085	−	0.396027i	0.0234350	−	0.0170265i	−0.576006	−	0.817445i	$-0.695390\pi$
$541$	0.545085	−	0.396027i	0.0234350	−	0.0170265i	0.599441	+	0.800419i	$0.295390\pi$
$542$	10.7148	+	32.9767i	0.460239	+	1.41647i
$543$		0			0
$544$	10.0623	+	7.31069i	0.431418	+	0.313443i
$545$	3.35410	+	2.43690i	0.143674	+	0.104385i
$546$		0			0
$547$	−8.50658	−	26.1806i	−0.363715	−	1.11940i	−0.950782	−	0.309861i	$-0.899717\pi$
$547$	−8.50658	−	26.1806i	−0.363715	−	1.11940i	0.587067	−	0.809538i	$-0.300283\pi$
$548$	−34.4164	+	25.0050i	−1.47020	+	1.06816i
$549$		0			0
$550$	6.58359	−	16.3925i	0.280725	−	0.698977i
$551$	−23.1246			−0.985142
$552$		0			0
$553$	−3.09017	−	9.51057i	−0.131407	−	0.404430i
$554$	7.66312	−	23.5847i	0.325575	−	1.00202i
$555$		0			0
$556$	−48.1869	−	35.0098i	−2.04358	−	1.48475i
$557$	6.90983	−	21.2663i	0.292779	−	0.901081i	−0.691180	−	0.722683i	$-0.742909\pi$
$557$	6.90983	−	21.2663i	0.292779	−	0.901081i	0.983958	−	0.178398i	$-0.0570914\pi$
$558$		0			0
$559$	−3.70820	+	2.69417i	−0.156840	+	0.113951i
$560$	1.61803			0.0683744
$561$		0			0
$562$	20.2492			0.854162
$563$	−14.9443	+	10.8576i	−0.629826	+	0.457595i	−0.856340	−	0.516413i	$-0.827267\pi$
$563$	−14.9443	+	10.8576i	−0.629826	+	0.457595i	0.226514	+	0.974008i	$0.427267\pi$
$564$		0			0
$565$	−0.381966	+	1.17557i	−0.0160694	+	0.0494566i
$566$	−29.4336	−	21.3848i	−1.23719	−	0.898869i
$567$		0			0
$568$	−8.94427	+	27.5276i	−0.375293	+	1.15503i
$569$	11.6180	+	35.7566i	0.487053	+	1.49900i	0.828985	+	0.559271i	$0.188919\pi$
$569$	11.6180	+	35.7566i	0.487053	+	1.49900i	−0.341931	+	0.939725i	$0.611081\pi$
$570$		0			0
$571$	46.6525			1.95235			0.976173	−	0.216995i	$-0.0696256\pi$
$571$	46.6525			1.95235			0.976173	+	0.216995i	$0.0696256\pi$
$572$	−10.4164	+	6.53888i	−0.435532	+	0.273404i
$573$		0			0
$574$	17.3992	−	12.6412i	0.726228	−	0.527636i
$575$	4.87132	+	14.9924i	0.203148	+	0.625226i
$576$		0			0
$577$	18.0344	+	13.1028i	0.750784	+	0.545476i	0.896070	−	0.443913i	$-0.146410\pi$
$577$	18.0344	+	13.1028i	0.750784	+	0.545476i	−0.145286	+	0.989390i	$0.546410\pi$
$578$	24.5344	+	17.8253i	1.02050	+	0.741435i
$579$		0			0
$580$	−9.00000	−	27.6992i	−0.373705	−	1.15014i
$581$	6.09017	−	4.42477i	0.252663	−	0.183570i
$582$		0			0
$583$	−28.5967	−	23.8949i	−1.18436	−	0.989627i
$584$	0.652476			0.0269996
$585$		0			0
$586$	−22.9508	−	70.6355i	−0.948091	−	2.91792i
$587$	−7.85410	+	24.1724i	−0.324173	+	0.997703i	0.647639	+	0.761947i	$0.275757\pi$
$587$	−7.85410	+	24.1724i	−0.324173	+	0.997703i	−0.971812	+	0.235756i	$0.924243\pi$
$588$		0			0
$589$	25.2254	+	18.3273i	1.03940	+	0.755165i
$590$	−1.38197	+	4.25325i	−0.0568946	+	0.175104i
$591$		0			0
$592$	1.92705	−	1.40008i	0.0792013	−	0.0575431i
$593$	15.5066			0.636779			0.318389	−	0.947960i	$-0.396858\pi$
$593$	15.5066			0.636779			0.318389	+	0.947960i	$0.396858\pi$
$594$		0			0
$595$	−3.00000			−0.122988
$596$	31.4164	−	22.8254i	1.28687	−	0.934963i
$597$		0			0
$598$	5.65248	−	17.3965i	0.231147	−	0.711397i
$599$	−17.2984	−	12.5680i	−0.706792	−	0.513515i	0.175345	−	0.984507i	$-0.443896\pi$
$599$	−17.2984	−	12.5680i	−0.706792	−	0.513515i	−0.882137	+	0.470992i	$0.843896\pi$
$600$		0			0
$601$	3.85410	−	11.8617i	0.157212	−	0.483849i	−0.841166	−	0.540777i	$-0.818130\pi$
$601$	3.85410	−	11.8617i	0.157212	−	0.483849i	0.998378	+	0.0569276i	$0.0181304\pi$
$602$	−2.56231	−	7.88597i	−0.104432	−	0.321408i
$603$		0			0
$604$	−73.4164			−2.98727
$605$	−17.6353	−	2.40414i	−0.716975	−	0.0977423i
$606$		0			0
$607$	−28.2984	+	20.5600i	−1.14860	+	0.834504i	−0.988294	−	0.152564i	$-0.951247\pi$
$607$	−28.2984	+	20.5600i	−1.14860	+	0.834504i	−0.160302	+	0.987068i	$0.551247\pi$
$608$	7.98936	+	24.5887i	0.324011	+	0.997204i
$609$		0			0
$610$		0			0
$611$	4.47214	+	3.24920i	0.180923	+	0.131448i
$612$		0			0
$613$	7.71885	+	23.7562i	0.311761	+	0.959503i	0.977067	+	0.212932i	$0.0683012\pi$
$613$	7.71885	+	23.7562i	0.311761	+	0.959503i	−0.665306	+	0.746571i	$0.731699\pi$
$614$	−4.63525	+	3.36771i	−0.187064	+	0.135910i
$615$		0			0
$616$	−1.80902	−	7.19218i	−0.0728874	−	0.289781i
$617$	−44.0689			−1.77415			−0.887073	−	0.461629i	$-0.847265\pi$
$617$	−44.0689			−1.77415			−0.887073	+	0.461629i	$0.847265\pi$
$618$		0			0
$619$	7.31966	+	22.5276i	0.294202	+	0.905461i	0.983488	+	0.180972i	$0.0579242\pi$
$619$	7.31966	+	22.5276i	0.294202	+	0.905461i	−0.689286	+	0.724489i	$0.742076\pi$
$620$	−12.1353	+	37.3485i	−0.487364	+	1.49995i
$621$		0			0
$622$	−19.2705	−	14.0008i	−0.772677	−	0.561383i
$623$	−1.04508	+	3.21644i	−0.0418704	+	0.128864i
$624$		0			0
$625$	6.00000	−	4.35926i	0.240000	−	0.174370i
$626$	−67.4853			−2.69725
$627$		0			0
$628$	51.3738			2.05004
$629$	−3.57295	+	2.59590i	−0.142463	+	0.103505i
$630$		0			0
$631$	5.34752	−	16.4580i	0.212882	−	0.655182i	−0.786416	−	0.617698i	$-0.788066\pi$
$631$	5.34752	−	16.4580i	0.212882	−	0.655182i	0.999297	−	0.0374844i	$-0.0119345\pi$
$632$	18.0902	+	13.1433i	0.719588	+	0.522812i
$633$		0			0
$634$	−7.76393	+	23.8949i	−0.308345	+	0.948989i
$635$	−6.85410	−	21.0948i	−0.271997	−	0.837120i
$636$		0			0
$637$	−1.23607			−0.0489748
$638$	37.6869	−	23.6579i	1.49204	−	0.936625i
$639$		0			0
$640$	−20.4894	+	14.8864i	−0.809913	+	0.588436i
$641$	−5.32624	−	16.3925i	−0.210374	−	0.647464i	−0.999450	−	0.0331683i	$-0.989440\pi$
$641$	−5.32624	−	16.3925i	−0.210374	−	0.647464i	0.789076	−	0.614296i	$-0.210560\pi$
$642$		0			0
$643$	18.8262	+	13.6781i	0.742434	+	0.539410i	0.893473	−	0.449118i	$-0.148262\pi$
$643$	18.8262	+	13.6781i	0.742434	+	0.539410i	−0.151038	+	0.988528i	$0.548262\pi$
$644$	16.0623	+	11.6699i	0.632944	+	0.459860i
$645$		0			0
$646$	−4.93769	−	15.1967i	−0.194271	−	0.597905i
$647$	22.2705	−	16.1805i	0.875544	−	0.636120i	−0.0565248	−	0.998401i	$-0.518002\pi$
$647$	22.2705	−	16.1805i	0.875544	−	0.636120i	0.932069	+	0.362281i	$0.118002\pi$
$648$		0			0
$649$	−4.09017	−	0.277515i	−0.160553	−	0.0108934i
$650$	6.58359			0.258230
$651$		0			0
$652$	−9.27051	−	28.5317i	−0.363061	−	1.11739i
$653$	8.76393	−	26.9726i	0.342959	−	1.05552i	−0.619708	−	0.784832i	$-0.712749\pi$
$653$	8.76393	−	26.9726i	0.342959	−	1.05552i	0.962667	−	0.270687i	$-0.0872510\pi$
$654$		0			0
$655$	−19.1803	−	13.9353i	−0.749438	−	0.544499i
$656$	2.97214	−	9.14729i	0.116042	−	0.357142i
$657$		0			0
$658$	−8.09017	+	5.87785i	−0.315388	+	0.229143i
$659$	19.1459			0.745818			0.372909	−	0.927868i	$-0.378360\pi$
$659$	19.1459			0.745818			0.372909	+	0.927868i	$0.378360\pi$
$660$		0			0
$661$	34.5410			1.34349			0.671745	−	0.740782i	$-0.265545\pi$
$661$	34.5410			1.34349			0.671745	+	0.740782i	$0.265545\pi$
$662$	17.0344	−	12.3762i	0.662062	−	0.481016i
$663$		0			0
$664$	−5.20163	+	16.0090i	−0.201862	+	0.621268i
$665$	−5.04508	−	3.66547i	−0.195640	−	0.142141i
$666$		0			0
$667$	−12.2705	+	37.7647i	−0.475116	+	1.46226i
$668$	15.5410	+	47.8303i	0.601300	+	1.85061i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−7.14590	+	5.19180i	−0.275454	+	0.200129i	−0.716932	−	0.697143i	$-0.754454\pi$
$673$	−7.14590	+	5.19180i	−0.275454	+	0.200129i	0.441478	+	0.897272i	$0.354454\pi$
$674$	10.9934	+	33.8343i	0.423451	+	1.30325i
$675$		0			0
$676$	27.8435	+	20.2295i	1.07090	+	0.778056i
$677$	−8.38197	−	6.08985i	−0.322145	−	0.234052i	0.414945	−	0.909846i	$-0.363801\pi$
$677$	−8.38197	−	6.08985i	−0.322145	−	0.234052i	−0.737090	+	0.675794i	$0.763801\pi$
$678$		0			0
$679$	−1.85410	−	5.70634i	−0.0711539	−	0.218989i
$680$	5.42705	−	3.94298i	0.208118	−	0.151207i
$681$		0			0
$682$	−59.8607	−	4.06150i	−2.29218	−	0.155523i
$683$	−2.20163			−0.0842429			−0.0421214	−	0.999112i	$-0.513412\pi$
$683$	−2.20163			−0.0842429			−0.0421214	+	0.999112i	$0.513412\pi$
$684$		0			0
$685$	−7.09017	−	21.8213i	−0.270901	−	0.833749i
$686$	0.690983	−	2.12663i	0.0263819	−	0.0811950i
$687$		0			0
$688$	−3.00000	−	2.17963i	−0.114374	−	0.0830975i
$689$	4.29180	−	13.2088i	0.163504	−	0.503215i
$690$		0			0
$691$	−5.06231	+	3.67798i	−0.192579	+	0.139917i	−0.679897	−	0.733308i	$-0.737975\pi$
$691$	−5.06231	+	3.67798i	−0.192579	+	0.139917i	0.487318	+	0.873225i	$0.337975\pi$
$692$	34.1459			1.29803
$693$		0			0
$694$	−52.5623			−1.99524
$695$	25.9894	−	18.8824i	0.985832	−	0.716249i
$696$		0			0
$697$	−5.51064	+	16.9600i	−0.208730	+	0.642406i
$698$	15.0000	+	10.8981i	0.567758	+	0.412501i
$699$		0			0
$700$	−2.20820	+	6.79615i	−0.0834623	+	0.256870i
$701$	2.96556	+	9.12705i	0.112008	+	0.344724i	0.991311	−	0.131538i	$-0.0419915\pi$
$701$	2.96556	+	9.12705i	0.112008	+	0.344724i	−0.879304	+	0.476262i	$0.841991\pi$
$702$		0			0
$703$	−9.18034			−0.346243
$704$	−33.0861	−	27.6462i	−1.24698	−	1.04195i
$705$		0			0
$706$	−32.5623	+	23.6579i	−1.22550	+	0.890377i
$707$	−5.50000	−	16.9273i	−0.206849	−	0.636615i
$708$		0			0
$709$	−17.0172	−	12.3637i	−0.639095	−	0.464330i	0.220444	−	0.975400i	$-0.429249\pi$
$709$	−17.0172	−	12.3637i	−0.639095	−	0.464330i	−0.859539	+	0.511070i	$0.829249\pi$
$710$	−37.8885	−	27.5276i	−1.42193	−	1.03309i
$711$		0			0
$712$	−2.33688	−	7.19218i	−0.0875783	−	0.269538i
$713$	43.3156	−	31.4706i	1.62218	−	1.17858i
$714$		0			0
$715$	−1.61803	−	6.43288i	−0.0605110	−	0.240576i
$716$	−29.3951			−1.09855
$717$		0			0
$718$	−18.3541	−	56.4881i	−0.684969	−	2.10812i
$719$	11.4377	−	35.2016i	0.426554	−	1.31280i	−0.474944	−	0.880016i	$-0.657532\pi$
$719$	11.4377	−	35.2016i	0.426554	−	1.31280i	0.901498	−	0.432782i	$-0.142468\pi$
$720$		0			0
$721$	11.5902	+	8.42075i	0.431640	+	0.313605i
$722$	−2.86475	+	8.81678i	−0.106615	+	0.328127i
$723$		0			0
$724$	−38.5623	+	28.0172i	−1.43316	+	1.04125i
$725$	−14.2918			−0.530784
$726$		0			0
$727$	−12.1459			−0.450466			−0.225233	−	0.974305i	$-0.572314\pi$
$727$	−12.1459			−0.450466			−0.225233	+	0.974305i	$0.572314\pi$
$728$	2.23607	−	1.62460i	0.0828742	−	0.0602116i
$729$		0			0
$730$	−0.326238	+	1.00406i	−0.0120746	+	0.0371618i
$731$	5.56231	+	4.04125i	0.205729	+	0.149471i
$732$		0			0
$733$	12.3820	−	38.1078i	0.457338	−	1.40754i	−0.411029	−	0.911622i	$-0.634831\pi$
$733$	12.3820	−	38.1078i	0.457338	−	1.40754i	0.868368	−	0.495921i	$-0.165169\pi$
$734$	25.0623	+	77.1338i	0.925067	+	2.84706i
$735$		0			0
$736$	44.3951			1.63643
$737$		0			0
$738$		0			0
$739$	−0.708204	+	0.514540i	−0.0260517	+	0.0189277i	−0.600735	−	0.799448i	$-0.705125\pi$
$739$	−0.708204	+	0.514540i	−0.0260517	+	0.0189277i	0.574683	+	0.818376i	$0.305125\pi$
$740$	−3.57295	−	10.9964i	−0.131344	−	0.404236i
$741$		0			0
$742$	20.3262	+	14.7679i	0.746200	+	0.542146i
$743$	−0.545085	−	0.396027i	−0.0199972	−	0.0145288i	0.577742	−	0.816220i	$-0.303934\pi$
$743$	−0.545085	−	0.396027i	−0.0199972	−	0.0145288i	−0.597739	+	0.801691i	$0.703934\pi$
$744$		0			0
$745$	6.47214	+	19.9192i	0.237121	+	0.729783i
$746$	−1.21885	+	0.885544i	−0.0446252	+	0.0324221i
$747$		0			0
$748$	14.1565	+	11.8290i	0.517614	+	0.432509i
$749$	8.79837			0.321486
$750$		0			0
$751$	7.41641	+	22.8254i	0.270629	+	0.832909i	0.990343	+	0.138639i	$0.0442727\pi$
$751$	7.41641	+	22.8254i	0.270629	+	0.832909i	−0.719714	+	0.694270i	$0.755727\pi$
$752$	−1.38197	+	4.25325i	−0.0503951	+	0.155100i
$753$		0			0
$754$	13.4164	+	9.74759i	0.488597	+	0.354986i
$755$	12.2361	−	37.6587i	0.445316	−	1.37054i
$756$		0			0
$757$	7.73607	−	5.62058i	0.281172	−	0.204284i	−0.438256	−	0.898850i	$-0.644404\pi$
$757$	7.73607	−	5.62058i	0.281172	−	0.204284i	0.719429	+	0.694566i	$0.244404\pi$
$758$	68.1378			2.47488
$759$		0			0
$760$	13.9443			0.505812
$761$	−20.5623	+	14.9394i	−0.745383	+	0.541552i	−0.894392	−	0.447283i	$-0.852392\pi$
$761$	−20.5623	+	14.9394i	−0.745383	+	0.541552i	0.149009	+	0.988836i	$0.452392\pi$
$762$		0			0
$763$	0.791796	−	2.43690i	0.0286649	−	0.0882216i
$764$	39.0517	+	28.3727i	1.41284	+	1.02649i
$765$		0			0
$766$	−22.6869	+	69.8232i	−0.819712	+	2.52281i
$767$	−0.472136	−	1.45309i	−0.0170478	−	0.0524679i
$768$		0			0
$769$	18.9443			0.683148			0.341574	−	0.939855i	$-0.389040\pi$
$769$	18.9443			0.683148			0.341574	+	0.939855i	$0.389040\pi$
$770$	11.9721	+	0.812299i	0.431446	+	0.0292732i
$771$		0			0
$772$	36.7599	−	26.7076i	1.32302	−	0.961228i
$773$	0.145898	+	0.449028i	0.00524759	+	0.0161504i	0.953646	−	0.300931i	$-0.0972973\pi$
$773$	0.145898	+	0.449028i	0.00524759	+	0.0161504i	−0.948398	+	0.317081i	$0.897297\pi$
$774$		0			0
$775$	15.5902	+	11.3269i	0.560015	+	0.406875i
$776$	10.8541	+	7.88597i	0.389640	+	0.283090i
$777$		0			0
$778$	−7.43769	−	22.8909i	−0.266654	−	0.820677i
$779$	−29.9894	+	21.7885i	−1.07448	+	0.780656i
$780$		0			0
$781$	16.0000	−	39.8384i	0.572525	−	1.42553i
$782$	−27.4377			−0.981170
$783$		0			0
$784$	−0.309017	−	0.951057i	−0.0110363	−	0.0339663i
$785$	−8.56231	+	26.3521i	−0.305602	+	0.940546i
$786$		0			0
$787$	15.4894	+	11.2537i	0.552136	+	0.401150i	0.828572	−	0.559882i	$-0.189154\pi$
$787$	15.4894	+	11.2537i	0.552136	+	0.401150i	−0.276436	+	0.961032i	$0.589154\pi$
$788$	−12.5410	+	38.5973i	−0.446755	+	1.37497i
$789$		0			0
$790$	−29.2705	+	21.2663i	−1.04140	+	0.756620i
$791$	0.763932			0.0271623
$792$		0			0
$793$		0			0
$794$	66.1033	−	48.0269i	2.34592	−	1.70441i
$795$		0			0
$796$	18.4058	−	56.6471i	0.652375	−	2.00780i
$797$	17.3435	+	12.6008i	0.614337	+	0.446342i	0.850939	−	0.525265i	$-0.176034\pi$
$797$	17.3435	+	12.6008i	0.614337	+	0.446342i	−0.236602	+	0.971607i	$0.576034\pi$
$798$		0			0
$799$	2.56231	−	7.88597i	0.0906479	−	0.278985i
$800$	4.93769	+	15.1967i	0.174574	+	0.537283i
$801$		0			0
$802$	43.4164			1.53309
$803$	−0.965558	−	0.0655123i	−0.0340738	−	0.00231188i
$804$		0			0
$805$	−8.66312	+	6.29412i	−0.305335	+	0.221839i
$806$	−6.90983	−	21.2663i	−0.243388	−	0.749072i
$807$		0			0
$808$	32.1976	+	23.3929i	1.13271	+	0.822959i
$809$	2.23607	+	1.62460i	0.0786160	+	0.0571178i	0.626399	−	0.779503i	$-0.284528\pi$
$809$	2.23607	+	1.62460i	0.0786160	+	0.0571178i	−0.547783	+	0.836620i	$0.684528\pi$
$810$		0			0
$811$	10.9443	+	33.6830i	0.384305	+	1.18277i	0.936983	+	0.349375i	$0.113606\pi$
$811$	10.9443	+	33.6830i	0.384305	+	1.18277i	−0.552678	+	0.833395i	$0.686394\pi$
$812$	−14.5623	+	10.5801i	−0.511037	+	0.371290i
$813$		0			0
$814$	14.9615	−	9.39205i	0.524400	−	0.329191i
$815$	16.1803			0.566773
$816$		0			0
$817$	4.41641	+	13.5923i	0.154511	+	0.475535i
$818$	0.124612	−	0.383516i	0.00435695	−	0.0134093i
$819$		0			0
$820$	−37.7705	−	27.4419i	−1.31900	−	0.958312i
$821$	−2.14590	+	6.60440i	−0.0748924	+	0.230495i	−0.981494	−	0.191492i	$-0.938667\pi$
$821$	−2.14590	+	6.60440i	−0.0748924	+	0.230495i	0.906602	+	0.421987i	$0.138667\pi$
$822$		0			0
$823$	39.5066	−	28.7032i	1.37711	−	1.00053i	0.379969	−	0.924999i	$-0.375935\pi$
$823$	39.5066	−	28.7032i	1.37711	−	1.00053i	0.997143	−	0.0755319i	$-0.0240655\pi$
$824$	−32.0344			−1.11597
$825$		0			0
$826$	2.76393			0.0961695
$827$	−42.7705	+	31.0746i	−1.48728	+	1.08057i	−0.512156	+	0.858892i	$0.671153\pi$
$827$	−42.7705	+	31.0746i	−1.48728	+	1.08057i	−0.975120	+	0.221677i	$0.928847\pi$
$828$		0			0
$829$	15.5279	−	47.7899i	0.539305	−	1.65981i	−0.194854	−	0.980832i	$-0.562423\pi$
$829$	15.5279	−	47.7899i	0.539305	−	1.65981i	0.734159	−	0.678978i	$-0.237577\pi$
$830$	−22.0344	−	16.0090i	−0.764827	−	0.555679i
$831$		0			0
$832$	4.96556	−	15.2824i	0.172150	−	0.529822i
$833$	0.572949	+	1.76336i	0.0198515	+	0.0610967i
$834$		0			0
$835$	−27.1246			−0.938686
$836$	9.35410	+	37.1895i	0.323518	+	1.28622i
$837$		0			0
$838$	2.23607	−	1.62460i	0.0772437	−	0.0561208i
$839$	−12.4377	−	38.2793i	−0.429397	−	1.32155i	−0.898721	−	0.438522i	$-0.855502\pi$
$839$	−12.4377	−	38.2793i	−0.429397	−	1.32155i	0.469324	−	0.883026i	$-0.344498\pi$
$840$		0			0
$841$	−5.66312	−	4.11450i	−0.195280	−	0.141879i
$842$	26.7705	+	19.4499i	0.922573	+	0.670288i
$843$		0			0
$844$	24.4377	+	75.2115i	0.841180	+	2.58889i
$845$	−15.0172	+	10.9106i	−0.516608	+	0.375338i
$846$		0			0
$847$	1.95492	+	10.8249i	0.0671717	+	0.371948i
$848$	11.2361			0.385848
$849$		0			0
$850$	−3.05166	−	9.39205i	−0.104671	−	0.322145i
$851$	−4.87132	+	14.9924i	−0.166987	+	0.513933i
$852$		0			0
$853$	22.8885	+	16.6295i	0.783689	+	0.569383i	0.906084	−	0.423098i	$-0.139057\pi$
$853$	22.8885	+	16.6295i	0.783689	+	0.569383i	−0.122395	+	0.992481i	$0.539057\pi$
$854$		0			0
$855$		0			0
$856$	−15.9164	+	11.5639i	−0.544012	+	0.395248i
$857$	−10.3607			−0.353914			−0.176957	−	0.984219i	$-0.556625\pi$
$857$	−10.3607			−0.353914			−0.176957	+	0.984219i	$0.556625\pi$
$858$		0			0
$859$	12.0000			0.409435			0.204717	−	0.978821i	$-0.434372\pi$
$859$	12.0000			0.409435			0.204717	+	0.978821i	$0.434372\pi$
$860$	−14.5623	+	10.5801i	−0.496571	+	0.360780i
$861$		0			0
$862$	−2.70163	+	8.31475i	−0.0920178	+	0.283202i
$863$	2.69098	+	1.95511i	0.0916021	+	0.0665528i	0.632644	−	0.774443i	$-0.281970\pi$
$863$	2.69098	+	1.95511i	0.0916021	+	0.0665528i	−0.541041	+	0.840996i	$0.681970\pi$
$864$		0			0
$865$	−5.69098	+	17.5150i	−0.193499	+	0.595529i
$866$	−18.4934	−	56.9169i	−0.628432	−	1.93412i
$867$		0			0
$868$	24.2705			0.823795
$869$	−25.4508	−	21.2663i	−0.863361	−	0.721409i
$870$		0			0
$871$		0			0
$872$	1.77051	+	5.44907i	0.0599570	+	0.184529i
$873$		0			0
$874$	−46.1418	−	33.5240i	−1.56077	−	1.13397i
$875$	−9.66312	−	7.02067i	−0.326673	−	0.237342i
$876$		0			0
$877$	1.09017	+	3.35520i	0.0368124	+	0.113297i	0.967774	−	0.251820i	$-0.0810290\pi$
$877$	1.09017	+	3.35520i	0.0368124	+	0.113297i	−0.930962	+	0.365117i	$0.881029\pi$
$878$	8.78115	−	6.37988i	0.296350	−	0.215311i
$879$		0			0
$880$	4.54508	−	2.85317i	0.153215	−	0.0961803i
$881$	4.32624			0.145755			0.0728773	−	0.997341i	$-0.476782\pi$
$881$	4.32624			0.145755			0.0728773	+	0.997341i	$0.476782\pi$
$882$		0			0
$883$	−9.14590	−	28.1482i	−0.307784	−	0.947262i	−0.978624	−	0.205659i	$-0.934066\pi$
$883$	−9.14590	−	28.1482i	−0.307784	−	0.947262i	0.670840	−	0.741602i	$-0.265934\pi$
$884$	−2.12461	+	6.53888i	−0.0714584	+	0.219926i
$885$		0			0
$886$	40.9164	+	29.7275i	1.37461	+	0.998715i
$887$	6.67376	−	20.5397i	0.224083	−	0.689657i	−0.774300	−	0.632818i	$-0.781898\pi$
$887$	6.67376	−	20.5397i	0.224083	−	0.689657i	0.998383	−	0.0568383i	$-0.0181020\pi$
$888$		0			0
$889$	−11.0902	+	8.05748i	−0.371952	+	0.270239i
$890$	12.2361			0.410154
$891$		0			0
$892$	52.1459			1.74597
$893$	13.9443	−	10.1311i	0.466627	−	0.339025i
$894$		0			0
$895$	4.89919	−	15.0781i	0.163762	−	0.504007i
$896$	12.6631	+	9.20029i	0.423045	+	0.307360i
$897$		0			0
$898$	4.22291	−	12.9968i	0.140920	−	0.433708i
$899$	15.0000	+	46.1653i	0.500278	+	1.53970i
$900$		0			0
$901$	−20.8328			−0.694042
$902$	26.5836	−	66.1904i	0.885137	−	2.20390i
$903$		0			0
$904$	−1.38197	+	1.00406i	−0.0459635	+	0.0333944i
$905$	−7.94427	−	24.4500i	−0.264077	−	0.812744i
$906$		0			0
$907$	−24.0344	−	17.4620i	−0.798051	−	0.579818i	0.112291	−	0.993675i	$-0.464181\pi$
$907$	−24.0344	−	17.4620i	−0.798051	−	0.579818i	−0.910342	+	0.413858i	$0.864181\pi$
$908$	8.56231	+	6.22088i	0.284150	+	0.206447i
$909$		0			0
$910$	1.38197	+	4.25325i	0.0458117	+	0.140994i
$911$	13.7082	−	9.95959i	0.454173	−	0.329976i	−0.337068	−	0.941480i	$-0.609435\pi$
$911$	13.7082	−	9.95959i	0.454173	−	0.329976i	0.791241	+	0.611504i	$0.209435\pi$
$912$		0			0
$913$	9.30495	−	23.1684i	0.307949	−	0.766762i
$914$	−12.1115			−0.400611
$915$		0			0
$916$	−5.72949	−	17.6336i	−0.189308	−	0.582629i
$917$	−4.52786	+	13.9353i	−0.149523	+	0.460185i
$918$		0			0
$919$	17.4164	+	12.6538i	0.574514	+	0.417409i	0.836742	−	0.547597i	$-0.184457\pi$
$919$	17.4164	+	12.6538i	0.574514	+	0.417409i	−0.262228	+	0.965006i	$0.584457\pi$
$920$	7.39919	−	22.7724i	0.243944	−	0.750782i
$921$		0			0
$922$	−10.8541	+	7.88597i	−0.357461	+	0.259710i
$923$	16.0000			0.526646
$924$		0			0
$925$	−5.67376			−0.186552
$926$	−6.18034	+	4.49028i	−0.203099	+	0.147560i
$927$		0			0
$928$	−12.4377	+	38.2793i	−0.408287	+	1.25658i
$929$	46.3328	+	33.6628i	1.52013	+	1.10444i	0.961423	+	0.275075i	$0.0887025\pi$
$929$	46.3328	+	33.6628i	1.52013	+	1.10444i	0.558707	+	0.829365i	$0.311297\pi$
$930$		0			0
$931$	−1.19098	+	3.66547i	−0.0390329	+	0.120131i
$932$	2.12461	+	6.53888i	0.0695940	+	0.214188i
$933$		0			0
$934$	−8.54102			−0.279471
$935$	−8.42705	+	5.29007i	−0.275594	+	0.173004i
$936$		0			0
$937$	19.4721	−	14.1473i	0.636127	−	0.462173i	−0.222390	−	0.974958i	$-0.571386\pi$
$937$	19.4721	−	14.1473i	0.636127	−	0.462173i	0.858517	+	0.512784i	$0.171386\pi$
$938$		0			0
$939$		0			0
$940$	17.5623	+	12.7598i	0.572819	+	0.416178i
$941$	−31.1525	−	22.6336i	−1.01554	−	0.737834i	−0.0501775	−	0.998740i	$-0.515979\pi$
$941$	−31.1525	−	22.6336i	−1.01554	−	0.737834i	−0.965364	+	0.260906i	$0.915979\pi$
$942$		0			0
$943$	19.6697	+	60.5371i	0.640533	+	1.97136i
$944$	1.00000	−	0.726543i	0.0325472	−	0.0236469i
$945$		0			0
$946$	−21.1033	−	17.6336i	−0.686128	−	0.573316i
$947$	−7.14590			−0.232210			−0.116105	−	0.993237i	$-0.537041\pi$
$947$	−7.14590			−0.232210			−0.116105	+	0.993237i	$0.537041\pi$
$948$		0			0
$949$	−0.111456	−	0.343027i	−0.00361802	−	0.0111351i
$950$	6.34346	−	19.5232i	0.205809	−	0.633415i
$951$		0			0
$952$	−3.35410	−	2.43690i	−0.108707	−	0.0789803i
$953$	7.38197	−	22.7194i	0.239125	−	0.735952i	−0.757422	−	0.652926i	$-0.773541\pi$
$953$	7.38197	−	22.7194i	0.239125	−	0.735952i	0.996547	−	0.0830265i	$-0.0264586\pi$
$954$		0			0
$955$	−21.0623	+	15.3027i	−0.681560	+	0.495182i
$956$	−30.1033			−0.973611
$957$		0			0
$958$	−37.8885			−1.22412
$959$	−11.4721	+	8.33499i	−0.370455	+	0.269151i
$960$		0			0
$961$	10.6459	−	32.7647i	0.343416	−	1.05693i
$962$	5.32624	+	3.86974i	0.171725	+	0.124765i
$963$		0			0
$964$	11.1246	−	34.2380i	0.358300	−	1.10273i
$965$	7.57295	+	23.3071i	0.243782	+	0.750283i
$966$		0			0
$967$	−48.3607			−1.55517			−0.777587	−	0.628775i	$-0.783557\pi$
$967$	−48.3607			−1.55517			−0.777587	+	0.628775i	$0.783557\pi$
$968$	−17.7639	−	17.0130i	−0.570954	−	0.546819i
$969$		0			0
$970$	−17.5623	+	12.7598i	−0.563892	+	0.409691i
$971$	3.87539	+	11.9272i	0.124367	+	0.382763i	0.993785	−	0.111314i	$-0.0355061\pi$
$971$	3.87539	+	11.9272i	0.124367	+	0.382763i	−0.869418	+	0.494077i	$0.835506\pi$
$972$		0			0
$973$	−16.0623	−	11.6699i	−0.514934	−	0.374121i
$974$	−25.8541	−	18.7841i	−0.828419	−	0.601882i
$975$		0			0
$976$		0			0
$977$	−47.2148	+	34.3035i	−1.51053	+	1.09747i	−0.544595	+	0.838699i	$0.683317\pi$
$977$	−47.2148	+	34.3035i	−1.51053	+	1.09747i	−0.965939	+	0.258769i	$0.916683\pi$
$978$		0			0
$979$	2.73607	+	10.8779i	0.0874451	+	0.347659i
$980$	−4.85410			−0.155059
$981$		0			0
$982$	25.2254	+	77.6359i	0.804976	+	2.47746i
$983$	−2.14590	+	6.60440i	−0.0684435	+	0.210647i	−0.979428	−	0.201792i	$-0.935323\pi$
$983$	−2.14590	+	6.60440i	−0.0684435	+	0.210647i	0.910985	+	0.412440i	$0.135323\pi$
$984$		0			0
$985$	−17.7082	−	12.8658i	−0.564230	−	0.409937i
$986$	7.68692	−	23.6579i	0.244801	−	0.753421i
$987$		0			0
$988$	−11.5623	+	8.40051i	−0.367846	+	0.267256i
$989$	24.5410			0.780359
$990$		0			0
$991$	−28.7639			−0.913716			−0.456858	−	0.889540i	$-0.651025\pi$
$991$	−28.7639			−0.913716			−0.456858	+	0.889540i	$0.651025\pi$
$992$	43.9058	−	31.8994i	1.39401	−	1.01281i
$993$		0			0
$994$	−8.94427	+	27.5276i	−0.283695	+	0.873124i
$995$	25.9894	+	18.8824i	0.823918	+	0.598611i
$996$		0			0
$997$	18.0557	−	55.5698i	0.571831	−	1.75991i	−0.0748954	−	0.997191i	$-0.523862\pi$
$997$	18.0557	−	55.5698i	0.571831	−	1.75991i	0.646726	−	0.762722i	$-0.276138\pi$
$998$	−13.2148	−	40.6709i	−0.418307	−	1.28742i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.m.a.190.1		4
3.2	odd	2		231.2.j.e.190.1	yes	4
11.2	odd	10		7623.2.a.bj.1.1		2
11.4	even	5	inner	693.2.m.a.631.1		4
11.9	even	5		7623.2.a.bk.1.2		2
33.2	even	10		2541.2.a.v.1.2		2
33.20	odd	10		2541.2.a.w.1.1		2
33.26	odd	10		231.2.j.e.169.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.j.e.169.1	✓	4	33.26	odd	10
231.2.j.e.190.1	yes	4	3.2	odd	2
693.2.m.a.190.1		4	1.1	even	1	trivial
693.2.m.a.631.1		4	11.4	even	5	inner
2541.2.a.v.1.2		2	33.2	even	10
2541.2.a.w.1.1		2	33.20	odd	10
7623.2.a.bj.1.1		2	11.2	odd	10
7623.2.a.bk.1.2		2	11.9	even	5

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:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.80902 + 1.31433i) q^{2} +(0.927051 - 2.85317i) q^{4} +(1.30902 + 0.951057i) q^{5} +(0.309017 - 0.951057i) q^{7} +(0.690983 + 2.12663i) q^{8} +O(q^{10})\)	\(q+(-1.80902 + 1.31433i) q^{2} +(0.927051 - 2.85317i) q^{4} +(1.30902 + 0.951057i) q^{5} +(0.309017 - 0.951057i) q^{7} +(0.690983 + 2.12663i) q^{8} -3.61803 q^{10} +(-0.809017 - 3.21644i) q^{11} +(1.00000 - 0.726543i) q^{13} +(0.690983 + 2.12663i) q^{14} +(0.809017 + 0.587785i) q^{16} +(-1.50000 - 1.08981i) q^{17} +(-1.19098 - 3.66547i) q^{19} +(3.92705 - 2.85317i) q^{20} +(5.69098 + 4.75528i) q^{22} -6.61803 q^{23} +(-0.736068 - 2.26538i) q^{25} +(-0.854102 + 2.62866i) q^{26} +(-2.42705 - 1.76336i) q^{28} +(1.85410 - 5.70634i) q^{29} +(-6.54508 + 4.75528i) q^{31} -6.70820 q^{32} +4.14590 q^{34} +(1.30902 - 0.951057i) q^{35} +(0.736068 - 2.26538i) q^{37} +(6.97214 + 5.06555i) q^{38} +(-1.11803 + 3.44095i) q^{40} +(-2.97214 - 9.14729i) q^{41} -3.70820 q^{43} +(-9.92705 - 0.673542i) q^{44} +(11.9721 - 8.69827i) q^{46} +(1.38197 + 4.25325i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(4.30902 + 3.13068i) q^{50} +(-1.14590 - 3.52671i) q^{52} +(9.09017 - 6.60440i) q^{53} +(2.00000 - 4.97980i) q^{55} +2.23607 q^{56} +(4.14590 + 12.7598i) q^{58} +(0.381966 - 1.17557i) q^{59} +(5.59017 - 17.2048i) q^{62} +(10.5172 - 7.64121i) q^{64} +2.00000 q^{65} +(-4.50000 + 3.26944i) q^{68} +(-1.11803 + 3.44095i) q^{70} +(10.4721 + 7.60845i) q^{71} +(0.0901699 - 0.277515i) q^{73} +(1.64590 + 5.06555i) q^{74} -11.5623 q^{76} +(-3.30902 - 0.224514i) q^{77} +(8.09017 - 5.87785i) q^{79} +(0.500000 + 1.53884i) q^{80} +(17.3992 + 12.6412i) q^{82} +(6.09017 + 4.42477i) q^{83} +(-0.927051 - 2.85317i) q^{85} +(6.70820 - 4.87380i) q^{86} +(6.28115 - 3.94298i) q^{88} -3.38197 q^{89} +(-0.381966 - 1.17557i) q^{91} +(-6.13525 + 18.8824i) q^{92} +(-8.09017 - 5.87785i) q^{94} +(1.92705 - 5.93085i) q^{95} +(4.85410 - 3.52671i) q^{97} +2.23607 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 5 q^{2} - 3 q^{4} + 3 q^{5} - q^{7} + 5 q^{8}+O(q^{10}) \) 4 * q - 5 * q^2 - 3 * q^4 + 3 * q^5 - q^7 + 5 * q^8	\( 4 q - 5 q^{2} - 3 q^{4} + 3 q^{5} - q^{7} + 5 q^{8} - 10 q^{10} - q^{11} + 4 q^{13} + 5 q^{14} + q^{16} - 6 q^{17} - 7 q^{19} + 9 q^{20} + 25 q^{22} - 22 q^{23} + 6 q^{25} + 10 q^{26} - 3 q^{28} - 6 q^{29} - 15 q^{31} + 30 q^{34} + 3 q^{35} - 6 q^{37} + 10 q^{38} + 6 q^{41} + 12 q^{43} - 33 q^{44} + 30 q^{46} + 10 q^{47} - q^{49} + 15 q^{50} - 18 q^{52} + 14 q^{53} + 8 q^{55} + 30 q^{58} + 6 q^{59} + 13 q^{64} + 8 q^{65} - 18 q^{68} + 24 q^{71} - 22 q^{73} + 20 q^{74} - 6 q^{76} - 11 q^{77} + 10 q^{79} + 2 q^{80} + 45 q^{82} + 2 q^{83} + 3 q^{85} + 5 q^{88} - 18 q^{89} - 6 q^{91} + 9 q^{92} - 10 q^{94} + q^{95} + 6 q^{97}+O(q^{100}) \) 4 * q - 5 * q^2 - 3 * q^4 + 3 * q^5 - q^7 + 5 * q^8 - 10 * q^10 - q^11 + 4 * q^13 + 5 * q^14 + q^16 - 6 * q^17 - 7 * q^19 + 9 * q^20 + 25 * q^22 - 22 * q^23 + 6 * q^25 + 10 * q^26 - 3 * q^28 - 6 * q^29 - 15 * q^31 + 30 * q^34 + 3 * q^35 - 6 * q^37 + 10 * q^38 + 6 * q^41 + 12 * q^43 - 33 * q^44 + 30 * q^46 + 10 * q^47 - q^49 + 15 * q^50 - 18 * q^52 + 14 * q^53 + 8 * q^55 + 30 * q^58 + 6 * q^59 + 13 * q^64 + 8 * q^65 - 18 * q^68 + 24 * q^71 - 22 * q^73 + 20 * q^74 - 6 * q^76 - 11 * q^77 + 10 * q^79 + 2 * q^80 + 45 * q^82 + 2 * q^83 + 3 * q^85 + 5 * q^88 - 18 * q^89 - 6 * q^91 + 9 * q^92 - 10 * q^94 + q^95 + 6 * q^97

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